Those who saw the Timberwolves finish off the Suns in the first round of the playoffs and witnessed Ant-man’s 40 point explosion and this moment in particular:
We all had the same question pop into their minds: Where was Michael Jordan, nine months before Anthony Edwards was born? I have yet to confirm Jordan’s presence in Atlanta in December of 2000, but if the Internet is to believed, it will be confirmed soon.
While I can’t yet demonstrate the DNA link between the two players, I can confirm that Ant’s playing style is the most similar I’ve seen to MJ since Kobe. Is there a way to see this in the statistics? Where does Ant-Man 2023 rank on the “MJ Similarity” metric (the combined absolute value of the difference between last year’s stats and MJ’s career averages)?
Surprisingly, Ant is Only the Third Most Jordan-Like Player, Statistically
Looking more closely at Ant-Man vs. Jordan’s statistical DNA, you may notice that at least in terms of the big three stats (points, rebounds, and assists), Anthony is very similar to Michael. He’s 90% Jordan. Next year, if he improves by 11% across the board and gets 29 ppg, 6 rebounds, and 6 assists, the stat line will be very Jordan-like indeed. However, it’s in the defensive stats where he is the least GOAT-like. In terms of steals and blocks, he’s only 58% Jordan. Dad’s still got a few things to teach him about defense, but on offense, Ant-Man is indeed a superstar.
While we’re on the subject of defensive stats, let’s look at the league leaders from last season:
2023-2024 Season Top Players Ranked by Blocks + Steals
Looking at only two stats is an overly simplified way of looking at Defensive Player of the Year, but I’ll bet they’re a good indication that the DPOY will indeed be our favorite Alien. Wemby dominated defensively this season, but how good were his stats from a historical perspective? If you look at the best Blocks + Steals seasons over the last 50 years, it turns out he’s still got some room to improve before he’s at the Olajuwon / Robinson level. He’s only tied for the 25th best season with some defensive slacker named Michael Jordan. However, he did notch the best numbers on this list in almost 20 years!
Top Blocks + Steals Seasons in the last 50 Years
Because of his combination of offensive and defensive statistics, I’ll still argue that Wemby is the future of the NBA over Ant-Man. Once again, here are the top 20 most productive players (MPPs) last season:
Most Productive NBA Players (2023-2024 Season)
Notice that Ant Edwards and Wemby are in a virtual tie as the 11th and 12th most productive players this season.
However, as Wemby played six fewer games, Ant-Man drops further down the list when you compare their per-game productivity:
Most Productive NBA Players per Game (2023-2024 Season)
The biggest difference between the two is when you look at the per-minute productivity. Wemby skyrockets to 5th most productive in the league and Ant Edwards falls out of the top 20 with his 1.09 FPPM stat.
Most Productive NBA Players per Minute (2023-2024 Season)
Time will tell which player improves more in the next few years, but it’s safe to say that at 20 and 23 years old, Wemby and Ant-Man have years ahead of them to reach their full potential. It’s a great time to be an NBA fan.
Victor Wembanyama, affectionately dubbed “Wemby,” entered the NBA last October amid sky-high expectations, even higher than his towering 7’4″ frame. Before even stepping onto the court, predictions about his career varied widely — from potential future GOAT, evoking comparisons to the likes of Kareem Abdul-Jabbar, to the cautionary tales of Shawn Bradley and Ralph Sampson, whose careers, despite their impressive heights and skills, were cut short by injuries and ended with unmet expectations. Wemby’s unique blend of size, agility, and skill along with his rail-thin build set the stage for heated debates. LeBron James can be given credit for creating an otherworldly nickname when he spoke about Wemby’s abilities at a press conference: “Everybody’s been a unicorn over the last few years, but he’s more like an alien.”
Wemby was drafted #1 by the Spurs, which meant he would play for legendary coach Gregg Popovich who has more wins under his belt than any other coach in NBA history. The fact that the two prior #1 picks in Spurs history were David Robinson and Tim Duncan only added to the pressure. If Wemby performed at any level below hall-of-famer, fans would be disappointed. So how did he do?
When analyzing basketball data, I like to keep it simple: in a nod to fantasy sports, I just add up the stats of all the major categories. A player’s production on a per-minute basis (FPPM or “fantasy points per minute”) and on a per-game basis (FPPG) are informative statistics, as well as the total for the season (FPPG x # of games = “total production”). If you recall my blog entry last year, I defended “total production” as a solid way to rank players because it was simple and objective and correlated well with popular lists of all-time greats such as the one produced by ESPN.
So, how did Wemby’s year stack up against the most productive rookie seasons in the last 50 years?
Most Productive Rookie Seasons (Last 50 Years)
By this metric, Alien had a great rookie season, ranking #18 and above some clowns named Julius Erving, Magic Johnson, and LeBron James. However, since he only played in 69 out of the 82 games, it gets even better when you look at his per game productivity.
Most Productive Rookie Seasons Per Game (Last 50 Years)
On a per-game basis, he ranks 5th behind David Robinson, Michael Jordan, Shaq, and George McGinnis(?). Hold on, who’s this guy again? I looked him up. It turns out that the reason he’s a “rookie” in my data at the age of 25 is because he came from the ABA fresh after winning the ABA MVP award. Okay, so technically, he was an NBA rookie, but this was not his first year playing professionally. So, to reiterate: Wemby’s productivity on a per-game basis in his first year was higher than anyone in the last 50 years other than the ABA MVP in his first NBA season, Shaq, the GOAT, and David Robinson, who came into the league as a 24 year old. Did I mention that Wemby is only 20 years old?
But wait, there’s more! Wemby played much of the season on “minutes restriction” to protect his ankle, after stepping on a ballboy’s foot. Notice that he’s the only player on any of these lists having played less than 30 minutes per game. He was so frustrated by his lack of minutes, he even checked himself into a game without the coach’s consent once. (Coach Pop just took him back out again.) So you know this one’s going to be good: what are the most productive rookie seasons per minute? (Minimum 10 games and 10 minutes per game)
Most Productive Rookie Seasons per Minute (Last 50 Years)
You’re reading that right. On a per-minute basis, Wemby was the most productive rookie over the last 50 years. Let this sink in: his overall total productivity was higher than LeBron James’s rookie year despite playing 10 fewer games and an average of 10 minutes less per game. Bottom line: Wemby is more on the Kareem path than the Bradley one.
Speaking of Kareem, you may recall from last year’s blog that his 1975 season was the most productive single season in my dataset (last 50 years):
Most Productive Seasons (Last 50 Years)
Notice that his productivity per minute (FPPM of 1.33) was actually lower than Wemby’s this year (1.38)! It’s probably too much to imagine that Wemby could keep up his frenetic productivity for 41 minutes per game and 81 games in a season like Kareem did. Or is it? Considering the fact that the 20-year-old Alien may be the worst version of Alien that we will ever see, he actually has decent a shot at topping this list someday, especially if he can avoiding stepping on any more ballboys.
So it appears that Wemby will indeed be the future of the NBA, but who is the present? Well, there’s a new entry on the “Most Productive Seasons (per Game)” list:
Most Productive Seasons (per Game, Last 50 Years)
And it’s a new #1! On a per game basis, Luka Doncic just had the most productive season in the last 50 years. Joel Embiid is the new #4, having gone statistically wild during his injury-shortened season. And Giannis barely gets a mention for putting in the 13th most productive season in the last 50 years.
On a per minute basis, Embiid almost took the top spot in modern NBA history, where he played Wemby-like minutes and still put up 30 points and 14 rebounds per game.
Most Productive Seasons (per Minute, Last 50 Years)
I extended that list to the top 25 seasons, for no particular reason.
Anyway, back to the question of who’s the player of the present of the NBA. My winner of the MPP (“Most Productive Player”) for 2023 is…
MPP (Most Productive Player) Award Winners
Luka Doncic for the second year in a row! The guy is a beast and at 25 years old, is at the peak of his game. He’ll undoubtedly be considered among the all-time greats when he’s done.
Speaking of which, here’s the current list of the players with the highest average career productivity in the modern NBA…
Highest Average Productivity (Last 50 Years)
Luka just passed up LeBron James! Of course, we’re not comparing apples to apples here, because eventually, even Luka will get older (and slower?) and drop down the list by the time he retires. But who knows, if he continues at his current rate for a few years, he could even spend some time above MJ! At that point, maybe he should consider retiring young and claim statistical GOAThood. Jokic is also no joke, sneaking into the #5 spot. I also see some 20-year-old who’s new to the list at #10 somehow, despite not playing that much. The potential for that guy is off the charts.
For completeness, here’s how I rank the top 20 MPP candidates this year:
Jokic and the Greek Freak performed similarly to Luka Magic, but his incredible productivity per game put him out of reach. Also take note: LeBron is still in the top 10 at 39 years of age! His durability and consistency is truly incredible. I understand the “LeBron is GOAT” arguments. I don’t agree, but I understand. It’s becoming more clear that old LeBron > old Jordan. We’ll know for sure next year when we see if LeBron can top 40-year-old Jordan’s 82 game season with 20 PPG, 6.1 RPG, 3.8 APG, and 1.5 SPG.
When comparing MJ against LeBron, There’s definitely a pre-baseball Jordan and a post-baseball Jordan to consider…
Michael Jordan statistics by age compared to LeBron at same age
Before taking time off to play baseball, Jordan’s total productivity, per-game productivity, and per-minute productivity topped LeBron’s every single year (except when MJ had a broken foot in 1985). These are the types of statistics that Jordan supporters (like me) point to. Young Jordan > young LeBron, even if you ignore important considerations like Championships, MVPs, and his Defensive Player of the Year title.
However, look at the years after baseball. Suddenly LeBron is more productive per minute and per game and is only sometimes less productive overall because he’s not in the habit of playing 82 games per season.
What’s interesting is that Jordan came back out of retirement again at age 39 and gave us a couple more seasons to compare against LeBron. The comparison doesn’t look too good for the 39-year-old version of MJ. LeBron, the oldest player in the NBA, is still killing it. He’ll outperform “old Jordan” again next year if he can stay healthy and average over 20 points per game at age 40. There’s something to be said about LeBron’s unnatural ability to play at an extremely high level for such a long time.
But there isn’t a human alive who could dominate offensively and defensively like pre-baseball Jordan. But an Alien? Time will tell…
Despite the fact that LeBron James has now scored more total points than anyone in the history of the NBA, it appears that a consensus has been reached that his longevity and consistent greatness has never quite reached the Michael Jordan level. Recently, Jordan’s rookie card has skyrocketed in value, the MVP trophy has been redesigned in his likeness, and the majority of players asked have given him the nod, usually mentioning his playoff dominance (including two three-peats as champion and six Finals MVPs) or the intimidation factor his opponents experienced, playing against someone who was simultaneously the league’s best offensive player as well as the best defensive player.
However, as a data scientist, I can’t help but wonder how you’d rank players in a completely objective way. What if you just measured players based on their average performance during the regular season over their careers? They say there’s no “I” in team, but certainly the best player have collected all of the points, assists, rebounds, steals, and blocks that they could. Maybe calling it a ranking of the “best” players is too much, but you could certainly argue that it would be an interesting list of the most “productive” players. Would ranking players this way create a list similar to ESPN’s recent ranking of the 74 best players of all time or would it be completely different?
Unfortunately, I could only find complete data back to 1973 (NBA.com only had data back to 1996(?!)), so I missed Kareem Abdul-Jabbar’s first four seasons. However, I do have all of the stats necessary to compare LeBron and MJ and rank them among all of the players who had careers in the last 50 years. I know they say you can’t compare players across eras, but we’re going to do it anyway…
And yes, I know that more players averaged over 30 points per game this season than any season since the 1960s. When measuring productivity, it seems that with the modern higher-paced game, statistics would be easier to come by. I considered controlling for that, but I’m not so sure that it’s fair. What if modern-day players are generally just better than players were 20 years ago? My approach is: when in doubt, just keep it simple. It’s always okay to add asterisks later if something looks weird.
One last thing: in addition to adding up all of the points, assists, rebounds, blocks, and steals for every season played (“Total Production”), I also divided that by the number of games played in each season (for lack of a better name for the stat, let’s call it “Fantasy Points per Game”) and also by the number of minutes played (“Fantasy Points per Minute”). This will give us a few different ways to compare players. Total Production would favor durable players, FPPG would take durability out of it and measure what players do when they’re healthy, while FPPM would benefit players who may not play a lot, but definitely filled the stats sheets while they were on the floor.
Before we get to the “most productive players” list, there were quite a few interesting Top 10 lists that you may have never seen…
First thing to note is that Kareem of 1975 was a beast: 28 points, 17 rebounds, 5 assists, and 4 blocks per game, and played 81 out of the 82 possible games. And #2 all-time goes to Russell Westbrook’s massive triple double season in 2016. Then there’s a lot of Michael Jordan. Notice that he’s the only player who played all 82 games on this list and he did it three times. Except for his broken foot season, the guy just wouldn’t take a day off (except for baseball, sigh).
Hey, while we’re here, let’s take a little trip through history and see who was the most productive player (MPP) each season for the last 50 years…
In the last 50 years, these would be the top recipients of the MPP trophy:
Michael Jordan: 6
Kareem Abdul-Jabbar: 6
LeBron James: 5
James Harden(!): 4
Kobe Bryant: 3
Shaquille O’Neal: 3
Kevin Durant: 3
Larry Bird: 3
David Robinson: 3
Not a bad list. It’s interesting to see that Jordan’s statistical reign of terror was when he 24-29 (at which point the big men took over the productivity title) and when he was 28, his championship reign of terror began and he won the NBA Finals in his next six complete seasons (stretching over 8 years because of the baseball hiatus). This might be the strongest argument for his GOAT status: For a stretch of a dozen straight years, MJ was either the statistically most productive NBA player or the leader of the championship team (or off playing baseball, sigh).
Another interesting “most productive of all-time” list is to compare by age, from the most productive 18-year-old (Kobe) to the most productive 44-year-old (Kevin Willis, who played 5 games and averaged a whopping 2.4 points per game, this game is not kind to “old” players!)…
Look at that TotalProduction column. It ramps up to a peak at 28-29 years old and then it’s “over the hill” in terms of nba productivity! No 30 year old in history has surpassed 4000 total stats (although LeBron fought father time and got close at age 33). Also surprising is to see Karl Malone own the ages 36-39, where I would think LeBron would take over the list. The key is the Games column: Karl pretty much played ALL the games and was just as durable and age-resistant as LBJ.
The top seasons of the last 50 years in terms of FPPG…
Bob McAdoo, there’s a name from the past! He only played half the season, but I wonder how he feels being sandwiched between Michael Jordan and Michael Jordan? The guy was a badass: scored 34 points and collected 14 rebounds per game that season! Also, we see a couple more recent seasons in the list, which might help explain how so many players can be averaging 30 points per game these days: “Load Management”. If it’s true that teams are resting their stars more than they used to (and it appears that way), then it looks like the idea of ranking players based on total production during a season instead of per game statistics won’t give the modern player the boost we’d expect based on the higher scoring averages.
For completeness, here are the TOP FPPM seasons in the last 50 years…
So THIS is what the game has evolved towards. No seasons are on this list before 2016. It looks like the modern approach is: play 85% of the games and play 70% of the minutes so you can just go full throttle. Each of the Greek Freak’s last 5 seasons is on the list of the 10 most productive seasons per minute since 1973. We should probably just rename the stat “GF” in his honor.
And I’m assuming this would be the “MJ” stat…Pretty much.
Wow, if it weren’t for the fact that it’s based on one season, that’s a pretty good looking GOAT list right there. These are the players with the highest output per minute, who also played every single game in a season. I suppose if you want an exclusive MJ list, you could just do this…
Anyway, without further ado, here’s the list of the top 50 players, ranked by their career average productivity per season. Note: there are some partial careers here (like Kareem) and players currently active (like LeBron and Luka) who can rise or fall in this list in the future.
The Top Average Productivity Ranking (Last 50 Years)
Rank
Player Name
Avg Season
1
Michael Jordan
3,201
2
Karl Malone
3,179
3
LeBron James
3,149
4
L. Doncic
3,013
5
Kareem Abdul-Jabbar*
2,968
6
N. Jokic
2,929
7
Russell Westbrook
2,915
8
Larry Bird
2,856
9
Giannis Antetokounmpo
2,829
10
James Harden
2,816
11
Trae Young
2,793
12
Magic Johnson
2,776
13
Hakeem Olajuwon
2,762
14
David Robinson
2,719
15
Charles Barkley
2,694
16
Kevin Durant
2,685
17
Tim Duncan
2,625
18
Damian Lillard
2,616
19
Dominique Wilkins
2,568
20
Allen Iverson
2,538
21
Shaquille O’Neal
2,536
22
Isiah Thomas
2,534
23
Clyde Drexler
2,529
24
J. Tatum
2,527
25
K. Towns
2,525
26
D. Issel
2,519
27
Patrick Ewing
2,511
28
J. Embiid
2,500
29
Kobe Bryant
2,478
30
Julius Erving**
2,445
31
J. Randle
2,440
32
Alex English
2,439
33
A. Edwards
2,429
34
Anthony Davis
2,426
35
Donovan Mitchell
2,399
36
Kevin Garnett
2,386
37
Stephen Curry
2,373
38
Dirk Nowitzki
2,344
39
Rick Barry
2,331
40
B. Daugherty
2,308
41
Chris Paul
2,304
42
P. Banchero
2,297
43
Gary Payton
2,283
44
John Stockton
2,273
45
Antoine Walker
2,271
46
Dwyane Wade
2,269
47
D. DeRozan
2,264
48
D. Booker
2,239
49
J. Morant
2,228
50
N. Vucevic
2,198
*Kareem’s first four years were better than his average years, so his true productivity average based on known statistics would be a little over 3075. However, steals and blocks weren’t tracked over 50 years ago, so you could argue that he missed #1 here based on a technicality!
**I also just peeked at Dr. J’s lifetime statistics and his average total productivity, including his ABA years, actually puts him above Michael Jordan! However, there’s big asterisk: in three of his four ABA years, he played 84 games, which isn’t possible in the NBA. If you prorate his stats down for those years to 82 games, he drops into the #2 slot below Michael. Then again, they didn’t count steals and blocks in 1971… it never ends!
I looked at this list a month ago and LeBron was #2, so his injury-shortened season this year dropped him down a slot. If he can stay healthy, I expect him to regain that #2 slot next year. And look at Luka Magic and Jokic! Jokic is closing in on that “over the hill” age and can be expected to start drifting down the list in a few years, but Luka is only 24 years old! Considering the season he just had, he may be starting his own reign of terror in the league right now.
If we were looking at the complete set of historical NBA stats, Wilt Chamberlain would almost certainly be the regular season productivity GOAT. I have a friend who’s constantly pushing the “Wilt is GOAT” narrative online. Rather than argue with him about championships and stuff, I usually respond with “I have eyes”. If you’ll open your mind to subjective arguments for a second, pretend you’re an NBA scout and that Wilt’s highlight reel actually came from a college prospect you were thinking about drafting:
Be honest. How skilled does he look and how skilled do his opponents look?
The game has clearly changed, and modern players are much more skilled than the average player 50+ years ago. Evidently the “economics of pro basketball exploded” in the 1970’s, so it’s hardly surprising that the quality and skill of the average athlete would explode as well. You can argue Wilt was the most “dominant” player of all time. But not GOAT.
Anyway, I digress.
For the “LeBron is GOAT” people out there, here’s the list you want to see: top players by TOTAL productivity.
The Iron Men of the NBA (last 50 years)…
Rank
PlayerName
Lifetime Productivity
1
LeBron James
62,974
2
Karl Malone
60,408
3
Kevin Garnett
50,114
4
Tim Duncan
49,871
5
Hakeem Olajuwon
49,719
6
Kobe Bryant
49,566
7
Dirk Nowitzki
49,216
8
Shaquille O’Neal
48,186
9
Michael Jordan
48,012
10
Kareem Abdul-Jabbar*
47,491
11
Russell Westbrook
43,730
12
John Stockton
43,184
13
Charles Barkley
43,101
14
Patrick Ewing
42,679
15
Jason Kidd
41,503
16
Chris Paul
41,478
17
Carmelo Anthony
41,411
18
Paul Pierce
41,143
19
Kevin Durant
40,281
20
Robert Parish
39,863
21
Vince Carter
39,445
22
James Harden
39,426
23
D. Howard
39,089
24
Gary Payton
38,805
25
Pau Gasol
38,690
26
Dominique Wilkins
38,526
27
David Robinson
38,063
28
Clyde Drexler
37,937
29
Moses Malone
37,392
30
Larry Bird
37,126
31
Alex English
36,590
32
Dwyane Wade
36,306
33
Magic Johnson
36,089
34
Scottie Pippen
35,841
35
Ray Allen
35,824
36
Allen Iverson
35,535
37
Reggie Miller
35,391
38
L. Aldridge
33,315
39
Buck Williams
33,107
40
S. Marion
32,978
41
Isiah Thomas
32,939
42
Steve Nash
32,393
43
Kevin Willis
32,190
44
O. Thorpe
32,069
45
Z. Randolph
31,966
46
T. Cummings
31,905
47
Joe Johnson
31,807
48
Clifford Robinson
31,778
49
D. DeRozan
31,690
50
A. Jamison
31,391
*Actually, when adding Kareem’s missing first four years, even his known statistics would put him at the top here with 65,854. So LeBron needs another year or two before he can safely say that there is no asterisk and that he’s definitely the all-time total productivity leader of the NBA.
Maybe this is the way you rank the players, but I don’t think people generally agree with that. Actually, we can quantify how close these lists approximate what people think of as the GOAT by looking at the correlation between these lists and the ESPN list (the gaps in the ESPN list below are players who didn’t play in the last 50 years).
(1) The Average Productivity list correlates better with the ESPN list (0.56 correlation > 0.43 correlation), which makes sense. People usually think of basketball as a sprint, not a marathon.
(2) Karl Malone is #2 on both my lists and #17 on the ESPN list. Is he underrated? Statistically, I suppose so, but I also know why ESPN has him lower than you’d expect. I remember the experience of watching him play. Let’s just say that the hardest all-time record LeBron to break may be Malone’s free throw record. Basically, he found a stats-hack and rode that puppy for years. Not entertaining, but effective, I’ll give him that. It’s also possible that ESPN penalized him for his trademark hand behind the head dunk.
(3) My ranking is not kind to players who have a lot of injury-shortened seasons. I’m actually a little surprised Jordan comes out on top in spite of two very short seasons: broken foot and returning from baseball. Those two seasons brought his average down a lot and don’t forget that he even played for the Wizards at age 40! Other players with a handful of injury seasons like Moses Malone get thrown far down the list.
(4) Kawhi Leonard! ESPN has him at #25 and I’ve got him at #167. What’s going on there? This is clearly a case where winning rings is highly respected in the sports community, but they’re not reflected in the regular season statistics my number-crunching is focused on. In the case of Steve Nash, MVP trophies carry a lot of weight in the ESPN rankings as well.
(5) As I look down the list for underrated players, it’s mostly players who are currently playing and may regress towards the ends of their careers. However, there are a few exceptions worth noting: Dominique Wilkins (my rank = 19, ESPN rank = 46), Clyde Drexler (my rank = 23, ESPN rank = 57), and Alex English (my rank = 32, ESPN rank = 67). These guys seem to have filled up the stat sheet much more than ESPN recognizes. Here’s a comparison between Dominique Wilkins (ESPN rank 46) and Kawhi Leonard (ESPN rank 25)…
It’ll probably take a second to make sense of what I did here. I joined Dominique’s career stats with Kawhi’s career stats by age. For example, how did 23-year-old ‘Nique compare with Kawhi at 23? If you look at the PlayersAge column and find 23, you’ll see that Dominique had 17.5 ppg, 5.8 rpg, 1.6 apg, while Kawhi had 12.8 ppg, 6.2 rpg, and 2 apg. In terms of my summary statistics, they were dead even in terms of stats per minute. However, Dominique played 4 minutes more per game on average, so his stats per game was higher. And he played 16 more games (the full 82), so his total productivity is much higher (+622).
It turns out that this same pattern pretty much holds for every year in common between the two players. The only year in which Kawhi had higher total productivity was when they were both 32, Dominique played only 42 games and put 168 fewer points on the stat sheet than Kawhi. Over their careers on average, the players are even per minute, but Dominque is +912 in total annual productivity. Basically, Dominque = Kawhi + minutes + games. My list doesn’t consider championships, so it’s like “where’s the love for ‘Nique and Drexler?”
Let’s be honest though, you’re not reading this blog to see the comparison of Dominque vs. Kawhi. It’s this one…
In terms of overall averages, there’s actually not a lot of statistical daylight between these two! However, LeBron made up huge chunks of his productivity deficit in two years: (1) when they were 23, MJ broke his foot and played limited minutes in 18 games and (2) when they were 32, MJ came back for the last 17 games of the season in “baseball shape.”
However, it’s fair to say that in terms of total productivity, Jordan gets the clear nod. In the 13 ages they played in common, MJ was more productive in 9 of them. The only other season LeBron was more productive than MJ was the year after the baseball return. So you could say that MJ went 10-3 against LeBron in a head-to-head productivity competition.
However, there is something for LeBron fans here. Notice the FPPM and FPPG statistics. There is a significant difference between BB (“before baseball”) and AB (“after baseball”). MJ beat LeBron in both of these stats in every single season BB (except for the broken foot season when there was a cap on MJ’s minutes, much to his frustration). However, LeBron has been beating MJ in both of these stats every single season AB. The only reason Jordan comes out ahead in overall productivity after baseball is because he played 82 games per season. After baseball, Michael transitioned a bit from Air Jordan to Chill Jordan, but still came to play every game. That said, kudos to LeBron for coming to work every single season.
It’ll be interesting to see if LeBron can keep it up and outperform MJ’s Washington Wizard years. In particular, Jordan’s final year at 40 years old was pretty remarkable: 82 games played with 20 ppg, 6.1 rpg, and 3.8 apg. In fact, it puts him on top of this list, which you’ve probably never seen:
These guys left the game with their heads held high. As a kid I remember being pretty upset about Dr. J retiring, thinking “this guy is still great, why is he leaving?” It’s rare for a star to be able to swallow their pride like Vince Carter did and try to push their rickety 40-year-old bodies to keep up with the young guns.
For symmetry, here are the most productive rookie seasons of the last 50 years…
David Robinson spoiled Jordan’s potential “best first year and best last year” flex. He came into the league as a 24-year-old after his active duty in the Navy was complete, ready to dominate. He even surpassed his idol Ralph Sampson’s first year stats (Sampson is the reason Robinson wore the #50). Also of note, Dr. J’s “first year” here is his NBA rookie year. He was in the ABA from 1971-1976.
I’ve probably worn you guys out with the endless stats here, but I’ve got a couple last good ones for you. I like the idea above of head-to-head comparisons “by age”, so a question came to mind. What if I compare ESPN’s top players to each other in a round-robin tournament in which all of them matched up against every other one and I calculated their “productive season win %” (recall that MJ had a 10/13 = 77% win rate against LeBron – it’s in the list below).
Match-up results…
PlayerName1
PlayerName2
Win Percentage
Kareem Abdul-Jabbar
Kobe Bryant
72.73
Kareem Abdul-Jabbar
Larry Bird
77.78
Kareem Abdul-Jabbar
LeBron James
66.67
Kareem Abdul-Jabbar
Magic Johnson
83.33
Kareem Abdul-Jabbar
Michael Jordan
50.00
Kareem Abdul-Jabbar
Shaquille O’Neal
84.62
Kareem Abdul-Jabbar
Tim Duncan
92.86
Kobe Bryant
Kareem Abdul-Jabbar
27.27
Kobe Bryant
Larry Bird
38.46
Kobe Bryant
LeBron James
31.58
Kobe Bryant
Magic Johnson
46.15
Kobe Bryant
Michael Jordan
15.38
Kobe Bryant
Shaquille O’Neal
41.18
Kobe Bryant
Tim Duncan
50.00
Larry Bird
Kareem Abdul-Jabbar
22.22
Larry Bird
Kobe Bryant
61.54
Larry Bird
LeBron James
38.46
Larry Bird
Magic Johnson
77.78
Larry Bird
Michael Jordan
25.00
Larry Bird
Shaquille O’Neal
76.92
Larry Bird
Tim Duncan
46.15
LeBron James
Kareem Abdul-Jabbar
33.33
LeBron James
Kobe Bryant
68.42
LeBron James
Larry Bird
61.54
LeBron James
Magic Johnson
69.23
LeBron James
Michael Jordan
23.08
LeBron James
Shaquille O’Neal
72.22
LeBron James
Tim Duncan
76.47
Magic Johnson
Kareem Abdul-Jabbar
16.67
Magic Johnson
Kobe Bryant
53.85
Magic Johnson
Larry Bird
22.22
Magic Johnson
LeBron James
30.77
Magic Johnson
Michael Jordan
11.11
Magic Johnson
Shaquille O’Neal
50.00
Magic Johnson
Tim Duncan
45.45
Michael Jordan
Kareem Abdul-Jabbar
50.00
Michael Jordan
Kobe Bryant
84.62
Michael Jordan
Larry Bird
75.00
Michael Jordan
LeBron James
76.92
Michael Jordan
Magic Johnson
88.89
Michael Jordan
Shaquille O’Neal
71.43
Michael Jordan
Tim Duncan
80.00
Shaquille O’Neal
Kareem Abdul-Jabbar
15.38
Shaquille O’Neal
Kobe Bryant
58.82
Shaquille O’Neal
Larry Bird
23.08
Shaquille O’Neal
LeBron James
27.78
Shaquille O’Neal
Magic Johnson
50.00
Shaquille O’Neal
Michael Jordan
28.57
Shaquille O’Neal
Tim Duncan
38.89
Tim Duncan
Kareem Abdul-Jabbar
7.14
Tim Duncan
Kobe Bryant
50.00
Tim Duncan
Larry Bird
53.85
Tim Duncan
LeBron James
23.53
Tim Duncan
Magic Johnson
54.55
Tim Duncan
Michael Jordan
20.00
Tim Duncan
Shaquille O’Neal
61.11
Which can be summarized neatly like this…
Player Name
Avg Win %
Kareem Abdul-Jabbar
75.43
Michael Jordan
75.27
LeBron James
57.76
Larry Bird
49.73
Tim Duncan
38.60
Kobe Bryant
35.72
Shaquille O’Neal
34.65
Magic Johnson
32.87
Kareem and Michael are in a virtual tie for first place in this “tournament.” Keep in mind that each of these players is matching up against other players only for the ages they both played, so this is a complicated statistic to calculate. In fact, for the SQL geeks out there, enjoy the gory details behind this query at the bottom of this article.
One last thing. For those of you curious what such a “round-robin tournament” list would look like right now with some of today’s stars, you’re welcome…
Player Name
Avg Win %
LeBron James
81.80
Giannis Antetokounmpo
59.85
Kevin Durant
59.47
K. Towns
56.81
N. Jokic
55.79
L. Doncic
52.14
James Harden
51.99
Russell Westbrook
51.69
L. Ball
50.00
Damian Lillard
47.50
Trae Young
47.22
J. Morant
44.79
Anthony Davis
42.80
Stephen Curry
41.24
J. Embiid
36.62
K. Irving
23.05
Okay, enough already with the stats overload. Go take a nap! (And let me know what I overlooked and need to include in my next blog).
– J
“The SQL Query”…
–TotalProduction Summarized!…………………………………
WITH Players AS (
SELECT * FROM nba WHERE PlayerName IN (‘Kareem Abdul-Jabbar’, ‘Larry Bird’, ‘Kobe Bryant’, ‘Magic Johnson’, ‘Michael Jordan’, ‘Shaquille O’Neal’, ‘Tim Duncan’, ‘LeBron James’)
),
PlayerCombinations AS (
SELECT
P1.PlayerName AS PlayerName1,
P2.PlayerName AS PlayerName2,
P1.Age AS Age1,
P2.Age AS Age2,
P1.TotalProduction – P2.TotalProduction AS TotalProductionDiff
FROM
Players P1
CROSS JOIN Players P2
WHERE
P1.PlayerName <> P2.PlayerName
AND ROUND(P1.Age, 0) = ROUND(P2.Age, 0)
),
WinCount AS (
SELECT PlayerName1, PlayerName2, COUNT(*) AS Wins
FROM PlayerCombinations
WHERE TotalProductionDiff > 0
GROUP BY PlayerName1, PlayerName2
),
LossCount AS (
SELECT PlayerName1, PlayerName2, COUNT(*) AS Losses
FROM PlayerCombinations
WHERE TotalProductionDiff < 0
GROUP BY PlayerName1, PlayerName2
),
TotalCount AS (
SELECT
W.PlayerName1,
W.PlayerName2,
W.Wins,
L.Losses,
W.Wins + L.Losses AS Total
FROM
WinCount W
INNER JOIN LossCount L ON W.PlayerName1 = L.PlayerName1 AND W.PlayerName2 = L.PlayerName2
By now you’ve probably seen the viral video of Steph Curry draining 105 3-pointers in a row during practice. You’re probably thinking “that guy can shoot well!”, but it’s a lot more than that. Historically, he’s shot an amazing 65% during the NBA 3-point shootout competition, but let’s be generous and say that his 3-point shooting percentage during practice is 80%. To put that in perspective, there are only a few hundred NBA players in history who have a career free throw percentage that high. So, what are the chances, you ask, that someone who shoots with an accuracy of 80% would make 105 in a row? About 1 in 15 billion. Yeah, it was a lucky streak.
Now, there is another explanation which traditionally hasn’t been taken seriously by people in the data wonk profession: the Hot Hand. It’s even been called the Hot Hand Fallacy. There have been several studies concluding that there is no evidence that those of us who feel like we’re on a “hot streak” aren’t deluding ourselves and being fooled by randomness. They have a point that randomness is much streakier than we expect, but I’ve always thought that if we had a controlled environment, the evidence for the Hot Hand would become clear (and not just because I somehow made 32 free throws in a row once). After examining the NBA Three-Point Shootout data, Gary Smith and I showed in our latest book that, given the relatively few contests in history, the mere existence of Craig Hodges 1991 streak of 19 consecutive baskets provides strong evidence in favor of the hot hand hypothesis.
Now, cherry-picking extreme examples is normally not a good way to gather statistical evidence. However, it can be considered compelling if you appropriately take into account how large the number of events there were from which you were cherry-picking. In the Hodges case, this means looking at how many participants there have been in the history of the NBA Three-Point Shootout. There simply haven’t been enough shooters in the contest’s history to expect a shooting streak like that if there’s no such thing as a Hot Hand!
Some other NBA news today indirectly provided another reason to believe in the Hot Hand. Curry just broke the Warriors franchise record for most consecutive free throws made in a row: 61. The NBA all-time record is 97 straight. That’s an amazing number, but how can the all-time streak of consecutive makes from 15 feet be smaller than the number of consecutive makes on Curry’s highlight reel of 3-pointers, more than seven feet further away from the basket?
Once again, I argue that the Hot Hand is the answer. In the NBA, free throws are usually shot in pairs, so players don’t have a chance to settle in and establish a hot streak. Shooting free throws is more in line with the statisticians assumption that each shot is an independent event; whether or not you made your last free throw 10 minutes ago doesn’t affect the likelihood that you’ll make the free throw you’re shooting now.
In order to decide whether or not Curry’s videotaped shooting streak is evidence that the Hot Hand is real, we need to account for the universe of attempts from which his 3-point shooting streak was cherry-picked. Let’s say there are 500 trillion basketball players in the world and that they all shoot 50% from behind the 3-point line (the NBA average is 35%). Now, let’s assume that they’ve each made a videotaped attempt at Curry’s feat once per day for the 13.8 billion year history of the universe (never mind that 3-pointers were invented only 40 years ago). How many times would you expect to see Curry’s feat replicated? About 0.00006 times. Of course, that’s if you assume the Hot Hand is a fallacy.
A couple days ago, college basketball player J. J. Culver made the news by scoring an astounding 100 points in a game. Since it was against Southwestern Adventist University and not the New York Knicks, it’s not as impressive as Wilt Chamberlain’s 100-point game in the NBA. However, players at every level have progressed a lot since 1962. Or have they?
It’s incredibly difficult to compare players across different eras, since the defense evolves along with the offense. It certainly appears in video footage that NBA players in the 1960s are light-years behind modern players. Even the championship teams of that era subjectively look like Division I college teams at best. However there are two statistics that can be compared across decades: free throw percentage and the NBA Three-Point Contest shooting percentage. If players have gotten better over the years, there’s no reason to think that they only improved in some ways and not others, so their improvement should be statistically apparent across the board, including these two.
Well, it turns out that I’ve compiled a nice dataset with all of the scores in history from the NBA 3-Point Contest from various sources (including watching videos) and historical NBA free throw stats are readily available. Unfortunately, there are various numbers of 2-point “money balls” in the shooting contest, so I don’t have the exact shooting percentage, just the percentage of possible points scored. However, it’s reasonable to use this as a very good approximation of shooting percentage, since it’s hard to imagine why a player would shoot significantly better or worse when he knows the ball is worth two points. So let’s do this!
Starting with the less interesting stats, there is a significant improvement in league-wide free throw percentage over the years…
It’s not a big difference, but it’s there. The trendline shows a historical 0.06% improvement per year with a p-value of less than 0.0001, which means that it’s extremely unlikely that there would be a trend like this if the year the stats were collected were unrelated to shooting percentage. However, it looks like there were a few really bad years at the beginning that could be making all the difference. So let’s look at it since 1950.
The slope has definitely decreased (it’s now at 0.04% per year), but it’s still statistically significant at the p=0.0001 level). Of course, it would’ve been easier to simply average the shooting percentage of the last five years in the dataset and compare it to the average for the first five years and show that it’s improved by 6.9% since then. However, doing a linear regression like this provides a more accurate estimate of the actual improvement (73*0.0006 = 4.4% improvement since the beginning) since it considers all of the data. It also tells you whether or not the relationship is statistically significant. So you can see why linear regressions are a statistician’s best friend; it’s easily interpretable and fun! (BTW, the R-Squared metric is a “goodness of fit” measure that ranges from 0 to 1 (perfect fit) and this is saying that the year explains 30% of the variance in free throw scores. The other 70% probably being the presence of Wilt Chamberlain or Shaquille O’Neal dragging the percentage down. Joking!)
Okay, now for the fun one: Are NBA 3-point shooters getting better as well? During the first years of the NBA 3-Point Shootout first took place, there were some incredible performances from shooters like Craig Hodges (made 19 straight shots in one round) and Larry Bird (won the first three contests). Maybe the “splash brothers” from Golden State are outliers and that the long-distance shooting accuracy has generally remained stable since the 1980s.
It doesn’t look like it! Due to the small number of shots in the contest each year, the data is much noisier than the free throw percentage, but the trend is still clear: recent players are better shooters. The slope is steeper than the free throw trend, with an improvement of 0.26% per year, but because of the volatility in the data, the p-value isn’t as small (p=0.0013). Another way to think of the level of statistical significance is to say that we have provided strong evidence against the hypothesis that shooters are equally skilled across the decades. In science, you can’t really prove a hypothesis is true, you can only provide evidence that’s consistent with it or falsify it.
We can’t talk about the history of the NBA three-point contest without addressing the question: who is the best shooter in the contest’s history? If you simply sort by shooting percentage, this is what you get:
So, the highest shooting percentage in the contest history is Joe Harris, with an astonishing 75% accuracy. However, this isn’t the whole story. Here is the same list, with important piece of additional data: the total number of shots taken:
There is a statistical tendency for the tops (and bottoms) of ranked lists to be monopolized by the smallest sets of data. This is because it’s easier to achieve extreme results with only a few tries. Intuitively, this makes sense. If someone says “I’m the best shooter in basketball; I’m shooting 100% this year”, you already know that they’ve only made a couple baskets at most. In this case, the effect is not as extreme as it normally is, because if a shooter was on fire in one shooting round, they probably advanced to another round (it’s truly remarkable that Danny Green didn’t make it to the finals in 2019 after shooting 68%!). However, you do see a lot of players at the top of the list who only shot a couple rounds. So, how do we adjust for this “small sample size effect” and compare shooters with varying numbers of shots?
I don’t think we can. How can you say who’s a better shooter, between Joe Harris, who made 75% of his 50 shots, or Steph Curry, who made 65% of 250 shots? The only thing I think we can do is to control for the number of shots and compare players who shot the same number of rounds. Starting with the most shots and working backwards, the winner of the “475 shots” category is…
Craig Hodges! Of course, it’s hard to call him the best shooter since there’s nobody with that many shots to compare him with, and his 56% shooting isn’t particularly noteworthy (the overall average was 52%). However, he did leave us with this unforgettable performance, so he deserves recognition for that.
Similarly, Dale Ellis, and Dirk Nowitzki were the only shooters with their number of shots and only shot about 50%. However, when we get down to players with 250 shots, it gets interesting…
These shooters are no clowns. Who could have imagined that Reggie Miller would rank last on any 3-Point Shooting ranking? So, we have our first candidate for best shooter in the Three-Point Contest history. Steph Curry, with 65% accuracy, ranks best in the first contested category.
Next up is the 200-shot category.
With a 60% shooting accuracy, Kyrie Irving edges out Curry’s coach Steve Kerr. Now, I realized that I lied earlier. We can compare across these categories, if the shooter with more shots also has a higher percentage! We can unquestionably state that Curry’s 65% with 250 shots is more impressive than Irving’s 60% performance with 200 shots. So, Curry can still be considered the top shooter.
Next up: 175 Shots.
Klay Thompson takes this title with 63% shooting. Now, it’s unclear whether his higher percentage would hold up if she shot another 25 times, so we can’t clearly rank him above Kyrie Irving. However, we can say that Curry’s higher percentage is still objectively the best.
150 Shots…
We finally have a true contender for Curry. Tim Legler has technically shot a higher percentage than Curry (66% to 65%), however if he took another 100 shots, it’s fairly likely that he would regress toward the mean a bit and fail to keep up his accuracy. Since we don’t truly know what his mean is, I don’t think there’s an objective way to judge who’s more impressive unless we got Tim out there to shoot a few more rounds.
125 shots…
In the 125-shot category, Devin Booker takes it with 62% shooting. Both Curry and Legler outperformed this with more shots, so this means we can leave Booker out of the overall “most impressive shooter” contention.
100 shots…
Marco Belinelli takes this category, with a Steph-matching 65% accuracy. However, it’s more impressive to shoot 65% over 250 shots than to do it with 100 shots, so Steph and Legler’s performances are still the best.
75 shots…
Jim Les wins this one with 56% shooting, but again falls behind Steph and Legler.
Next up is the highly-contested 50-shot category. These are all the remaining players who won at least one shootout round.
Joe Harris shot a remarkable 75%, so even though the sample size is so small, we can’t rule out that his performance gives him the title for most impressive 3-Point Contest shooter in history.
So we’ve boiled it down to three contenders. Who do you consider most impressive? Your guess is as good as mine…
Steph Curry: 65% of 250 shots
Tim Legler: 66% of 150 shots
Joe Harris: 75% of 50 shots
UPDATE: Since publishing this blog article, my co-author Gary Smith (he knows a lot of things) pointed out that there is a statistical way to compare Joe Harris to Steph Curry here. He said “there is a difference-in-proportions test for the null hypothesis that two probabilities are equal” which is another way of saying that you can attempt to falsify the hypothesis that Curry’s and Harris’s shooting percentages are the same. Here’s what I get when I plug in Curry’s and Harris’s shooting percentages…
So, this is saying that the shot data we have is not sufficient to argue that Harris’s shooting performance was significantly better than Curry’s. However, it is suggestive that he may be better; in fact, if he had made two more shots out of the 50, this test would have supported the idea that Harris’s performance was significantly better than Curry’s. Time will tell!
(Below is the data I used… enjoy! Oh yeah, and buy my book, thanks!)
You may have heard that, contrary to conventional wisdom, most research discredits the idea that NBA players can get “hot”(see here and here). Researchers say that sequences of made baskets occur just as often as you’d expect if they each shot was completely independent. I have always been skeptical of this conclusion, but other than nit-picking the way the studies analyzed the data (for example, not accounting for varying levels of defense or time elapsed between shots), I couldn’t think of a way to statistically demonstrate it. I felt that best way to measure hot streaks would probably be to analyze the 3-point-shooting contest, which takes most of the other variables out of the equation, but how could there possibly be a large enough sample size to demonstrate that a player’s shooting percentage is a less accurate predictor of a shot’s success rate than the result of the prior few shots?
Then, I read Economist Gary Smith‘s upcoming book, Lucky – The Surprising Role of Luck in Our Everyday Lives (keep an eye open for it this year – it’s great), and saw an argument that considered the length of the longest streaks of made baskets in relation to the total shots taken. In my mind, this was the missing tool I’d been waiting for. We have a record of all NBA participants in the 3 point contest (on sites like this) and we have a list of the longest streaks of made shots (see this one on Wikipedia). So we’re set!
Before we get to the data crunching, here’s a little background: once a year, the best 3-point shooters in the NBA are invited to compete against each other for the title of 3-point contest champion. The way the contest works is that the players take turns trying to make as many shots as they can out of 25 (from 5 different spots behind the 3-point line) in one minute. There have been slight variations in the rules over the years regarding “money balls” that are worth 2 points each, but for the purpose of this analysis, we’ll consider only the makes vs. the misses.
The first thing we need to know is the general shooting percentage for the competitors. Historical data shows that the competitors average about 51% of the best possible score, so that’s what I’m considering the baseline percentage. Since there’s not a huge discrepancy between the shooting percentages of the top players, I simplified the problem by treating them all as if they are the same player, with a shooting percentage that’s indistinguishable from a coin-flip.
Here’s how we can determine whether or not hot streaks exist: suppose they don’t exist. This means that the series of makes and misses from these contests should be indistinguishable from a series of people flipping coins against each other. That’s because coin flips are known to be independent events and have streaks that are only due to luck, and not a “hot hand.” If it turns out that I can tell you how to look at a string of 1s and 0s and determine whether it represents baskets or coin flips, then the baskets must not be independent events.
Well, there have been almost 350 competitors over the years, so the first question I had was: if 350 people were flipping sets of 25 coins, how often would we see a streak of heads like this. Yes, that happened; Craig Hodges drained 19 in a row in 1991. The math gets a little hairy with the principal of inclusion / exclusion considerations, so I was more comfortable writing a small computer program to simulate 10,000,000 sets of coin flips (Monte Carlo method) and keep track of the longest streaks. Here’s what I got…
Streaks of at least 19 heads occurred 68 times out of 10 million. So that means that my friend Mr. Carlo would put the probability that we’d only see a Craig Hodges of coin-flippers 0.00068% of the time, even if we had 350 cracks at it. This was pretty strong evidence for the existence of a hot streak (at least for one man), but I wasn’t totally comfortable with the conclusion yet. The second longest streak was only 13 makes in a row (Stephen Curry this year), and based on the simulation, a streak of that length wouldn’t be an outlandish result after all these years, happening almost a third of the time.
Here were the average number of occurrences of each streak length per 350 sets (25 flips for each set)…
19 heads – 0.00
18 heads – 0.00
17 heads – 0.01
16 heads – 0.02
15 heads – 0.03
14 heads – 0.08
13 heads – 0.16
12 heads – 0.33
11 heads – 0.75
10 heads – 1.53
It didn’t sit well with me that the evidence for hot streaks seemingly rested on one supernatural accomplishment, so I looked for another way to spot the “hot hand” in the data. Instead of just looking at the longest streak, what if we considered the total number of very long streaks? Based on the data above, we’d expect 2.91 players on average to have streaks of at least 10 by now. Well, it turns out that we have seven…
This seems pretty strong; we’ve seen more than twice as many streaks of 10 or more than we’d expect from flipping coins. But how unlikely is it?
I had my friend Mr. Carlo run 100 alternate histories of 350 sets in which NBA players flipped coins instead of shooting baskets and here’s what I got…
Well, I think this is enough to call it. If hot streaks are imaginary, seeing 7 players out of 350 hit at least 10 in a row would only occur about once in 100 times. So, the next time you hear someone complaining about how stupid people are to think that streaks exist, like this guy, ask him the last time he saw someone flip 19 heads in a row. Or 77 in a row.
I would not describe myself as a “gambler.” Although I enjoy thinking about casino games, I almost never play them. One exception was the time my wife and I went with friends to a casino in Barona. While we were there, we saw a promotion: if we join their card club and play slots for 2 hours, they would refund our losses or double our wins, up to $200. After confirming that we could ensure ourselves no worse than a break-even gambling session, my friend and I hit the video poker machines. We played for $1 a hand until there were 15 minutes left. I still had $150 of my $200 left, so I bumped up the bets to $5 each. Then, I hit a royal flush. I waited at the machine until someone came and counted out $4000 in cash. After he handed over the stack of money and left, I realized that any losses occurring now were actual losses, so I stopped playing and waited out the remainder of the time before collecting my additional $200 matching prize and leaving the casino. I haven’t played video poker there or anywhere else since then. Casinos must hate guys like me.
When I started playing online poker (against people, not casinos), I only invested $50 and slowly built my bankroll up to $100. At that point, I was so paranoid that other players would cheat me or beat me out of all of my money, I took out my initial $50 back out. From then on, I was on “house money” and never looked back.
After my father-in-law found out that I was playing online poker and saw my chart above, he took my wife aside and advised her to secretly stash away some money so she could take care of our daughter when I inevitably blew through all of our savings. She just busted up, because he obviously didn’t know me very well.
The first guy that I met with an actual gambling problem was someone I worked with when I was a software developer consulting for HdL Software. He would not only sneak out of his house at night to go to the casino (leaving his young kid alone), his game of choice was the one with arguably the worst odds in the house: Keno. It wasn’t enough that he played with a horrible return on investment; he would have the computer to continually auto-pick his numbers for him without even requiring him to push a button. And as if that weren’t enough, he’d have two machines running at a time and burning through his money while he would stand there enjoying a drink.
Of course, occasionally he’d show up at work with a wad of cash talking about his big win. However, even he had no illusions about the direction of his cash flow. He estimated that his hourly loss was around $100 for each hour he spent in the casino. He wanted to quit, but just couldn’t. I was curious why, if he was going to gamble, he wouldn’t at least play games with much better odds, like blackjack. Eventually, I figured out that it was because blackjack doesn’t have the potential for a “big win”. You typically can only win twice the amount that you bet. So I came up with an idea for him.
I asked him what he considered a “big win” and he said $20,000. I looked it up, and for you to win $20k with a $1 bet, you need to pick and hit 8 numbers. The chances of this occurring are 0.00043%. So here’s what I told him to do: learn and play basic strategy at blackjack, but when he wins a hand, let it ride and bet his winnings on the next hand. For example, if he were at a $1 table, if he doubled up 15 times in a row, it would be worth $32,768! His response was that the chances of winning 15 hands in a row was too incredibly low. I showed him how, at about 49.5% chance of winning, the odds of 15 wins in a row is 0.00262%, or about 6 times as good as the Keno big win, and it paid over 50% more! When the logic sank in, rather than switch to blackjack, he actually stopped gambling for the first time since I’d known him. Until that moment, he had never truly realized how badly the odds were stacked against him. Of course, he started gambling again a few months later, but I had almost cured him.
The second guy with a gambling problem I met was someone who got so tired of losing his money at online poker, he had told the bank to stop allowing him to send money to online casinos. When he found out I had developed a simple all-in or fold poker strategy that was exploiting the fact that some poker sites allowed you to buy-in as a short-stack, he desperately wanted me to teach it to him. I was pretty sure that “the System” would probably work for him, as it had for others who knew much less about poker, but had a feeling it wouldn’t end well. However, the question nagged at me: if someone with a gambling addiction actually had a strategy that made money, would he still have a gambling problem? Or would he just be a profitable work-a-holic?
I eventually shared the System with him and at first, he was a poker monster. He made $12,000 in the first month. Once, when he took my wife and me out to dinner to celebrate his success, I asked him to show me his bankroll chart and it didn’t quite look like mine. His had occasional huge losses in it. I asked what that was about and he said that other players would heckle him through the chat box and challenge him to heads-up matches, which he would eventually accept and get crushed. He turned to my wife and said “I’m sick Cathy.” (she’s a psychotherapist) “It’s horrible when you know it about yourself.” I told him to turn off the chat window!
He seemed to be under control and profitable until he told me about his plans to play at the $50 big blind level. Even buying in as a short-stack meant he’d be betting $500 on each hand. I had never played at or evaluated the system above the $20 big blind level, so I didn’t recommend it. The System was exploitive, not optimal. That means that it could be beaten by knowledgeable players, and generally, the higher the stakes, the more knowledgeable the player. Even though my friend was making a lot of money, he had gotten bored. His first trip to the $50 big blind level didn’t go well; he lost $4500 in one evening. He didn’t keep me up-to-date on his results anymore, but when I ran into him much later, he admitted that he had given the entire $12,000 back to the poker economy. The experiment had run its course and his gambling addiction had emptied his wallet again, even when the game should have had a positive expected return.
Other friends had their own stories with the System. One friend said he was willing to invest $1000 and was full of confidence. I told him to start out at the $2 big blind level, betting $20 per hand, and trained him for about an hour at my house. He had learned the strategy well and was ready to go home and try it on his own. An hour later, he called us up…
“I’m taking you guys to steak dinner, I’m up $1000!”
“That’s not possible at the limits you’re playing at.”
“I’m looking at my balance right now and it says up a grand.”
“Go back to the table you were playing at.”
“Hmm, it’s not letting me buy back in for less than $940.”
“The maximum buy-in for those tables is $200!”
Then, I realized what had happened. He had accidentally played at 10x the stakes he intended to. He had been betting $200 per hand instead of $20 and just happened to get lucky. His ADD sometimes caused him to let little details like that slip by. However, on the bright side, it also gave him the super-power to play 10-12 tables at a time, which would have given me a stroke due to the stress of trying to keep up. He eventually made well over $10k and unlike the gambler, he kept his winnings.
My favorite success story came from a friend who couldn’t be more different from the problem gamblers. He promised to stick to the System and told me “as an upstanding actuary, I have absolutely no creativity.” He told me he didn’t play poker and didn’t like gambling and I told him “you’re perfect.” His statistical mind and distaste for gambling gave him endless patience to play at low stakes. He never went down more than $2.50 and was continually playing at micro-stakes to ensure it stayed that way. I started to harass him into playing higher stakes and eventually his wife joined in, saying “I don’t want my husband playing a video game all day for $4 an hour.” He finally relented to the pressure and bumped up the bet-sizes. It paid off as he soon pocketed a few thousand dollars. At one point he wrote me this email:
“I had a rough night tonight and then a roller coaster ride at the end. Could not win anything. Even my best hands ended up split pot, until my final table.
$4 bb…I get an AK so of course I go all in. I get 1 caller and I get 2 more K’s on the draw to beat his pocket 10’s. Whew. I now have $120 in my stack. Then on my last hand, I get an AK suited. I almost did not want to go all in given my bad luck all night, but I follow the rules and go for it. One guy folds and says ‘it is tiring folding after the stupid ass betting in front of me.’ Then, the next guy calls me, the same one from the last hand.
The cards come out as 7,6,A,A,A. Sweet!
He had pocket queens but my 4 aces beat his full house for a big win! I then left the table to a comment of ‘now he leaves’. I ended down on the night with -$80. So those last few hands saved my ass.
Such drama! I love it.”
A couple of things impressed me about this email: First, he didn’t get superstitious like most people and allow his previous bad luck to make him risk-averse or risk-seeking. He knew that risk is not to be avoided or sought out, it is only to be weighed. He trusted that the System worked and went all-in for that reason and that reason only. The other thing that struck me is that he was happy to end the session down $80. Poker is actually just one long session, but most people have a hard time calling it a day when they’re down. They’re tempted to keep playing even after they’re tired, and maybe even increase the stakes in an effort to get even again. The outcome shouldn’t really matter to you, just the quality of your decisions.
So is poker gambling? It can be, but doesn’t have to be. Played profitably, it’s more like an investment that can be relied on to eventually provide a positive return. Is it a game of skill? Most definitely.
In the game of Texas Hold ‘Em, each player’s hand at showdown is composed of the best five cards out of seven: their initial two cards plus five community cards (cards shared by all of the other players). You probably already know that AA (“pocket Aces”) is the best hand to start with, but what is the worst? Many people say 7-2 offsuit, since it’s the lowest hand that, unlike 3-2 offsuit, has no potential to make a straight. However, if you were offered a choice between the two hands in a heads-up situation, you’d pick 2-7, since it’s ahead (has the highest card) before any additional cards are dealt. Poker calculators, like this one, show that 7-2 has a 55.87% chance of beating 3-2 if all five community cards are dealt out (with an 18.15% chance of a tie). These probabilities are calculated by dealing out all possible future sets of 5-cards and tracking the results.
Now suppose I offered you this challenge: We can play heads-up poker (no-limit Texas Hold ‘Em), each selecting our own hand from one of three possible starting hands, and you get to pick your cards first. I’ll even tell you my strategy ahead of time: it will be to go all-in, as soon as possible, every hand. The three hands to choose from are:
(1) A pair of 2s, (2) Jack-Ten suited, or (3) Ace-King offsuit
Which hand would you pick?
At first, AK looks good, since it’s considered one of the top starting hands in general. However, even a pair as low as 22 wins 52.75% of the time vs AK, since it’s already a pair and the chances that an ace or a king shows up when the next five cards are dealt out is less than 50/50. So, do you pick 22 as your starting hand? If so, I would select Jack-Ten suited, which, thanks to possible flushes and straights, actually DOES have a better than 50/50 chance of improving to the winning hand (53.28% chance of winning vs. 22). So, Jack-Ten suited must be the best hand? Not so fast: AK has a 58.61% chance of beating Jack-Ten suited. This is a non-transitive game! Simply by choosing first, you will be at a disadvantage.
Here’s another surprising poker scenario that actually occurred during a tournament I played on a cruise. I was very short on chips and was in the big blind (a forced bet, like an ante), which required me to put a third of my chips into the pot before even looking at my cards. Everyone folded around to the guy next to me, who went all-in. I looked down at my hand and it was one of the absolute worst: 8-2 offsuit. Easy fold right?
Believe it or not, I should call and here’s why: I had 1200 in chips before the hand and 400 of them went into the pot because of the blind bet. That means that I had to decide whether or not to call 800 for a chance to double-up to 2400 (when an opponent goes all-in for more chips than you have in your stack, it’s the same as if he only bet the amount you have left). When you look at it that way, it becomes clear than any chances of winning over 33% will make me a profit in the long run. Suppose someone were offering $1 lottery tickets that win 40% of the time and had a prize of $3? You’d buy as many tickets as you could get your hands on, even though the odds are against winning. It’s the expected profit of $0.20 per ticket ($3 prize * 40% chance = $1.20 on average) that compels you to “gamble” in this case.
It turns out that if you assume my opponent was going all-in with a random hand here, I actually have about a 34% chance of winning. When I called, he kicked himself for not realized that I was so short-stacked that he didn’t have any fold equity (value in bluffing). I caught him with a measly 4-3, but he ended up winning and busting me out anyway.
This is an example of being “pot committed”, which means that it was profitable to call even though I was almost certain to have the worst hand. There are times when this concept can be used to your advantage. Suppose you have $90 at a table where the blinds are $5/$10. Someone raises to $30 and the action gets to you and you decide to go all-in with AK. If everyone else folds and the action gets back to the original raiser, he has to decide whether to call $60 for a chance at a $195 pot (small blind of $5 + big blind of $10 + his original raise of $30 + your all-in of $90 + another $60 if he decides to call). He only needs a $60 / $195 = 30.8% of winning in order to break-even. Suppose he had a 2-3 offsuit and you showed him your AK. He’d still have over a 34% chance of winning and should therefore call! Congratulations, you just got someone to call your all-in with a worse hand than yours, which is good for you.
The very fact that you were low on chips gave you an exploitable opportunity. Since anyone who raises should go through the same mathematical reasoning as above and come to the conclusion that they have to call you, all you need to do is figure out when you have a better hand and collect your money. It may be impossible to know that for any particular hand, but you can ensure that your all-in is expected to be profitable. Online poker allows you to download the “hand history” from the games you play in. If there’s any data wonk living within you, you would realize that digging through those files would give you a good sample of the range of hands that people normally raise with. All you need after that is the handy poker calculator above and the patience to identify which potential hands would beat that range on average. This is precisely the kind of analysis I did to come up with a very profitable “short-stack” strategy for online poker.
It turns out that in the situation above, AQ, AK, and all pairs 7 or higher are profitable for your all-in move. Surprisingly, the range of profitable all-in hands increases to include a pair of sixes at the $10/$20 big blind level, since the original raisers get more creative and have a wider range of hands that they would get stuck calling with. The moral to the story is that while many players focus on “tells” and “feel”, math geeks can and do find profitable situations by simply crunching the numbers. Bad luck will always occasionally strike, but, as a Swedish proverb states, “luck doesn’t give, it only lends.”
By the way, for those interested in how my man vs. machine match against PokerSnowie turned out, see the end of my man vs. machine blog entry here.
As a game freak and a data wonk, there are few things more interesting to me than the ongoing battle between man and machine, with popular games serving as the battlefield. For each game, there’s only one time in human history when machines take us down and never look back, and for almost all games, that moment in time is in the recent past. These stories of seemingly unbeatable champions finally meeting their match and conceding defeat give us a glimpse into the unlimited potential for future problem-solving techniques. Welcome to my short history of Man vs. Machine.
Backgammon (1979) – BKG 9.8
When world champion Luigi Villa lost a backgammon match 7-1 to a program by Hans Berliner in 1979, it was the first time that a bot had beaten a world champion in any game. Later analysis of the games showed that the human was actually the stronger player and only lost due to bad luck, but Pandora’s box had been opened. In the 90’s, when neural networks revolutionized the bots, machines had truly reached the level of top humans. TD-Gammon was developed in 1991 and was followed in 1992 by Jellyfish and Snowie. There were no databases of moves and no expert advice given to the machines. They were only taught to track certain features on the board (like the number of consecutive blocking points) and to decide for themselves whether they were meaningful. They played themselves millions of times, following a simple racing strategy at first, but soon learned what maximized wins and began to appropriately value and seek better positions. It’s truly like AI; the bots had taught themselves how to play backgammon!
I asked my friend Art Benjamin (who was the all-time point leader in the American Backgammon Tour at the time) when it became clear that bots were truly superior and he said…
I guess I would say it happened in the mid to late 90s with Jellyfish and then Snowie. Can’t offer an exact date and I can’t think of a specific event. There was a backgammon server called FIBS (First Internet Backgammon Server) that was big in the 90s and the top rated player was Jellyfish. Only later was it revealed that it was a Bot. I think that gave it instant recognition as a force to be reckoned with.
At one of the backgammon tournaments, Art introduced me to Jeremy Bagai, who did something that I think is awesome. He wrote a book that used Snowie to locate and analyze mistakes in the classic strategy guides. He basically took the bibles of backgammon and fixed them, according to what the bots had discovered. How great would it be to have books like that in every field, showing specific cases where objective progress has been made? I think the toughest program out there these days is eXtreme Gammon, so maybe it’s time for another edition of that book that corrects Snowie’s mistakes?
Checkers (1994) – Chinook
In 1989, a team led by Jonathan Schaeffer from the University of Alberta created a computer program that could play checkers called Chinook. In 1990, Chinook was already ready to take its first crack at the world title, but fell short against Marion Tinsley. Tinsley, who is considered the best checkers player of all-time, won 4 games to Chinook’s 2, with 33 draws. In the rematch in 1994, it seemed that Chinook might actually have a chance against the seemingly unbeatable human champion (to give an idea of his dominance, Tinsley won his 1989 world title with a score of 23 draws, 9 wins, and 0 losses!) However, after 6 draws, the match came to an unfortunate and premature end: Tinsley had to concede due to abdominal pains, later diagnosed as cancerous lumps on his pancreas.
Using strategies such as minimax heuristic, depth-first search, and alpha-beta pruning, in combination with an opening database and a set of solved end-games, Chinook held onto its title with a 20-game draw against the #2 player, Don Lafferty, but hadn’t yet truly become unbeatable. During the match, Lafferty broke Chinook’s 149-game unbeaten streak, which I believe earned him the title of “last human to beat a top computer program at checkers.”
After the next match, in 1995, it was official: machine had surpassed man. Don Lafferty fell by a score of 1-0 with 35 draws. A couple years later, Chinook retired after being unbeaten for 3 years. If there were any doubts about whether or not Tinsley would still be able to beat Chinook, those questions were put to rest in 2007 when it was announced that checkers was solved. Schaeffer’s team had done it: they proved that checkers is a draw if both sides play perfectly.
Chess (1997) – Deep Blue
Deep Blue became the first computer program to win a chess game vs. a current world champion when it took a point off of Kasparov on its way to a 4-2 loss in 1996. However, what most people remember is the rematch in 1997, which “Deeper Blue” actually won, 3.5 to 2.5. At one point during the match, the program ran into a bug and played a random move, which unnerved Kasparov, since he was familiar enough with computer strategies to know that no machine would have selected the move. Under huge psychological pressure and suspicion that the other team was cheating, Kasparov blundered away the match against the IBM behemoth, which was capable of evaluating 200 million positions per second.
Several matches followed between human champions and top computer programs that resulted in draws, so computer superiority in chess wasn’t actually clearly established until 2005, when Hydra was unleashed on the world. It dispatched 7th-ranked Michael Adams by a brutal score of 5.5 to 0.5. 2005 may also be the year that goes down in history as the last time a human beat a top machine in tournament play (Ruslan Ponomariov). As of 2008, it was still true that humans playing alongside computers (“centaurs”) were superior to bots playing by themselves, but these days, it looks like even that is no longer the case. The top commercial chess programs available today include Komodo, Houdini, and Rybka and they are continuing to improve, leaving humans far behind.
Chess may never be solved like checkers was, but impressive progress has been made on the endgame, which has now been solved for 7 pieces or less on the board. Similar to the insights in Jeremy Bagai’s backgammon book, there are endgames that were presumed to be draws for many years that turn out to be wins if played perfectly, in one case only if over 500 perfect moves are played (good luck learning that one!) I love this quote from Tim Krabbe about his experience with these solved endgames:
The moves are beyond comprehension. A grandmaster wouldn’t be better at these endgames than someone who had learned chess yesterday. It’s a sort of chess that has nothing to do with chess, a chess that we could never have imagined without computers. The Stiller moves are awesome, almost scary, because you know they are the truth, God’s Algorithm – it’s like being revealed the Meaning of Life, but you don’t understand a word.
Othello (1997) – Logistello
This story is short and sweet. Computer scientist Michael Buro started developing an Othello-playing bot called Logistello in 1991 and retired it seven years later, after it dispatched the world champion Takeshi Murakami by a score of 6-0. Othello is so popular in Japan, 9 television stations covered the event. Afterwards, Murakami said “I don’t think I made any mistakes in the last game. I believed I could win until the end.”
Scrabble (2006) – Quackle
The next human champion to fall to a computer in his respective game was David Boys. Boys, the 1995 world champion, had qualified for the honor to face the machine by beating out around 100 humans in an 18-round match. He looked like he would send the machine back for another development cycle after winning the first 2 rounds, but Quackle didn’t crack under the pressure and won the remaining games to take the match 3-2. As usual, beating the world champion wasn’t enough for the game freaks of the world; Mark Richards and Eyal Amir took things to the next level by building a bot that takes into account the opponent’s plays to predict what tiles are in his rack. It then selects moves that block high-scoring opportunities the opponent might have, proving that AI truly is ultimately evil.
Jeopardy (2011) – Watson
In 2011, IBM was back in the business of high-profile man vs. machine matches when it created Watson and took down two of the best all-time Jeopardy champions. In the end, it had a higher score than both humans put together and, as with Deep Blue, the machine itself was a beast: 2,880 parallel processors, each cranking out 33 billion operations per second, and had 16 terabytes of RAM. Despite some humorous mistakes, such as the time it considered milk to be a non-dairy powdered creamer, Watson’s victory strikes me as the most impressive in this list. The difficulty in developing a system able to interpret natural language and deal with puns and riddles and come up with correct answers in seconds (searching the equivalent of a million books per second) is off the charts. We’re in the world of Sci-Fi, folks.
Poker (2015?) – PokerSnowie?
I’m going out on a limb here and predicting that poker is the next game to fall to the bots and that the moment is just about here. Being a game of imperfect information, poker has been particularly resistant to the approaches that were so successful for games such as backgammon, in which the machine taught itself how to play. An optimal poker strategy generated this way tends to include betting patterns that an experienced player can recognize and exploit.
By the turn of the century, pokerbots had gotten pretty good at Limit Hold ‘Em (eventually winning a high-profile heads-up game against professionals), but the more popular variation, No Limit Hold ‘Em remained elusive. The University of Alberta made the first significant step in changing that when they planned to hold the first-ever No Limit category in their Poker Bot competition at the 2007 Association for the Advancement of Artificial Intelligence (AAAI) conference. Coincidentally, shortly after this was announced, a friend of a friend named Teppo Salonen, who had won 2nd place the prior year in the limit competition, came up to my house for a game. I joined others in pestering him to enter the no-limit category, since the competition would never be softer (if it’s possible to consider competition offered by universities such as Carnegie Mellon and the University of Alberta to be “soft”). I knew a thing or two about beating bots at poker, since I had downloaded and beat up on the best bots that were available at the time, so Teppo invited me to serve as his strategic advisor and sparring partner. Months later, after many iterations, (and after Teppo overcame a last-minute technical scare) BluffBot was ready to go and entered the competition. And WON. What we had done didn’t really sink in until I read the response from one of the researchers who were blind-sided by Bluffbot:
They are going up against top-notch universities that are doing cutting-edge research in this area, so it was very impressive that they were not only competitive, but they won… A lot of universities are wondering, “What did they do, and how can we learn from it?”
The following year, the world once again made sense again as the University of Alberta team took the title. Things were pretty quiet for a few years until mid 2013, when PokerSnowie hit the market. As a former backgammon player, seeing the name “Snowie” in the title got my attention, so I was one of the first to buy it and enter the “Challenge PokerSnowie” to establish its playing strength. PokerSnowie categorizes its opponents based on their error rates and was handily beating every class of opponent with the sole exception of “World Class” players Heads Up. I was one of the few who managed to eek out a victory over it (minimum of 5,000 hands played), but could tell that it was significantly stronger than any other bots I’d played against. It was recently announced that the AI has been upgraded, and I suspect that it may be enough to push the bot out of my reach and possibly anyone else’s.
It appears that it’s time for a 5,000 hand rematch against the new AI to find out if it has passed me up as I suspect it has. I’ll periodically post my results and let you know if, at least for a little longer, the poker machines can still be held at bay. See results below!
http://xkcd.com/1002/
Round 1 of 10: after 500 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$580.50 (+$1.16 per hand)
Error Rate: 7.15 (“world class”)
Blunders: 13
Notes: I’m on a huge card rush, prepare for regression to the mean.
Round 2 of 10: after 1000 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$609.00 (+$0.61 per hand)
Error Rate: 7.51 (“world class”)
Blunders: 25
Notes: I extended my lead a bit, but not surprisingly, my winrate did regress towards zero. My error rate also crept higher (despite one fewer “blunder”) and pushed me closer to the threshold for “expert”, which is 8. I’m including the error rates so that if Snowie makes a sudden comeback, it should be clear whether or not it was due to the quality of my play suddenly taking a turn for the worse or Snowie finally getting some cards.
Round 3 of 10: after 1500 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$322.00 (+$0.21 per hand)
Error Rate: 7.19 (“world class”)
Blunders: 31
Notes: PokerSnowie took a big bite out of my lead in round 3 despite a drop in my error rate as well as my blunder rate (only 6 in the last 500 hands). As the Swedish proverb says: “luck doesn’t give, it only lends.”
Round 4 of 10: after 2000 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$362.50 (+$0.18 per hand)
Error Rate: 7.49 (“world class”)
Blunders: 42
Notes: Despite making a slight profit in the last 500 hands, my error rate increased and my average winnings per hand has continued to drop. The match is still a statistical dead heat.
Round 5 of 10: after 2500 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$497.50 (+$0.20 per hand)
Error Rate: 7.51 (“world class”)
Blunders: 49
Notes: My error rate crept slightly higher, but I was able to raise my winnings per hand for the first time. Snowie’s going to have to catch some cards in the last half of the match to get that $500 back.
Round 6 of 10: after 3000 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$40 (+$0.01 per hand)
Error Rate: 7.55 (“world class”)
Blunders: 62
Notes: Wow, what a difference a round of 500 hands can make! Practically my entire lead was wiped out, despite only a slight uptick in my error rate. Just as I was starting to write Snowie off as too passive, it handed me a nice beating. With four rounds left, the match is truly up for grabs.
Round 7 of 10: after 3500 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
PokerSnowie +$29.50 (+$0.01 per hand)
Error Rate: 7.88 (“world class”)
Blunders: 72
Notes: Snowie took the lead for the first time in the match, but I’m glad not to be losing by much more. I was down $400 until about 100 hands ago, but after betting a few big draws that hit, I almost pulled back to even. More concerning is the fact that my error rate increased by a big amount this round, almost demoting me to “expert” status. It turns out my biggest blunder led to one of my biggest pots: Snowie says I made a huge mistake betting my small flush on the turn instead of checking. The outcome was great, however, since Snowie happened to hit a set (pocket pair that matched a card on the board) and check-raised me all-in. I called and my flush held up. The last card was a scary fourth heart, so I doubt I would have gotten as much from the hand if I had checked. I’m not sure why PokerSnowie was so sure betting my flush was a mistake (maybe to control the size of the pot in case my flush was already behind or got counterfeited on the river?) Could be a sign PokerSnowie knows something I don’t.
Round 8 of 10: after 4000 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$583 (+$0.15 per hand)
Error Rate: 7.99 (“world class”)
Blunders: 82
Notes: I hit back with a rush of cards and had my best round so far (in terms of results). Unfortunately, my error rate crept higher again, putting me at the border between “world class” and “expert” in PokerSnowie’s eyes. I would hate for the program to lose respect for me, so I’m going to have to start making better decisions. Of course, PokerSnowie could just be punishing me, since one of my biggest “errors” was calling its pot-sized all-in on the river with one measly pair. It turned out that I caught PokerSnowie bluffing and won $234 on the hand.
Round 9 of 10: after 4500 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$869.50 (+$0.19 per hand)
Error Rate: 7.85 (“world class”)
Blunders: 85
Notes: Only 3 blunders this time and I extended my lead. It’s looking bad for PokerSnowie, as it will need an epic rush in the last 500 hands to pull out the match.
Round 10 of 10: after 5000 hands (0.5/1.0 blinds, 100 BB buy-in cash game, with auto-rebuy at 70%)…
Jay +$1749 (+$0.35 per hand)
Error Rate: 8.03 (“expert”)
Blunders: 100
Notes: When I posted an “epic rush” would be necessary for PokerSnowie to win, I didn’t actually believe it was possible for $870 to change hands between us in the last 500 hands with $0.50/$1 blinds. Incredibly, it happened, although in my favor. I hit practically every draw and if I didn’t know any better, I’d say the machine went on tilt, as it repeatedly bluffed off its chips like it was a fire sale. The program did get some revenge, however, by demoting my rating into the “expert” range by crediting me with 15 blunders during this round. Let’s look at a few of the big ones:
1. I raised to $3 with QJ on the button and Snowie re-raised to $9. I called and my QJ became the best possible hand when the flop came 89T rainbow (no two cards matching suits). Snowie bet $9 and I only called, reasoning that I didn’t have to worry about any flush draws (and also couldn’t represent them). I also didn’t want to end the fire sale if Snowie was going to keep bluffing at pots. My decision was tagged by Snowie as a huge error. Then, on the turn, a completely harmless offsuit 2 came. Snowie bet again, this time $18, and again I only called for the same reasons. This was also flagged as a major blunder. The river brought another 2, and Snowie continued with a bet of $72. I conservatively called, thinking that an all-in for its last $77.50 here might only get called by a full house (Snowie finally liked my decision, although it said to mix in an all-in 4% of the time). It turns out that Snowie had AA (was evidently value-betting and assuming that I would continue calling with only a pair?) and lost the $216 pot.
2. Snowie raised to $3 pre-flop and I called with K8. The flop came 83T, all diamonds, which was great, since I had 2nd pair and my King was a diamond. I checked, hoping Snowie would continuation bet, but Snowie checked as well. The turn card was a 9 of hearts and I bet $3, which Snowie called. The river card was a 9 of diamonds, giving me the flush, but also pairing the board. I bet $6 and Snowie raised with a huge overbet of $54. It was certainly possible that it was trying to get value for its full house or ace-high flush, but it just didn’t smell right. If it had the ace of diamonds, why hadn’t it bet on the flop or raised on the turn to build a pot? And with a paired board, what would it do if I re-raised its huge overbet on the river? On the other hand, if it had flopped a set (which turned into a full house on the river to justify the huge bet), would it really have checked on the flop and only called on the turn and not made me pay to see a fourth diamond appear? Anyways, I called its bet and won the $120 pot when it flipped over J9 for three of a kind, which it had decided to turn into a massive bluff-raise. Fire sale! Snowie labeled my call as a huge blunder (ranking the king-high flush’s showdown strength as only a 0.59 out of 2.00).
3. In this hand, I had AK on the button and raised to $3. Snowie re-raised to $9, which I re-re-raised to $18. Snowie re-re-re-raised to $54 and I called. Snowie flagged my call as a huge mistake, saying I should have raised yet again. The flop came 658 with two clubs we both checked. The turn brought a third club and Snowie bet $54 and I folded. Evidently, it had a wider range than I imagined with all of that pre-flop raising, as it turned out to only have a KQ (with the king of clubs) which it had turned into a semi-bluff on the turn to take the pot. I can’t say I’ve seen many people 5-bet before the flop with King-high, so I’m still not sure about the “6-bet with AK” idea.
I’m happy to have defended humanity’s honor once again, but my confidence that PokerSnowie will take over the world was shaken a bit by its performance. If the “fire sale” strategy is a big part of its gameplan, it may still be a few years and AI upgrades before it can take down a top human.
Some guy named Michael Jordan had 4 of the top 10 seasons of all time.
The first 20 seasons in my dataset
And the last 30. Congrats Luka on your first MPP this year!
A couple recent seasons sneak into the list
Just kidding! The statistical pitfall of small sample size in all of its glory – Mr. Mitrou-Long played 30 seconds and got three points. Best season ever! 
Greek Freak! And all recent seasons (half of the list is in the last two seasons)!
Pretty much.
But this is data-mining (don’t tell Gary Smith on me)
Side-by-Side Comparison with ESPN’s list (in ESPN order)
Too small to read, click here!
Who’s more productive, MJ or LeBron?
This could be called the “why did they retire again?” list
A lot of familiar names here
