Boxing's Grandmasters

Jul 13, 2013
199
5
I finally had a chance to finish a historical analysis of boxing's greatest fighters using the Elo rating system (the ranking system used by chess players).

ELO rating system

The Elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games. The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins.

If Player A has a rating of RA and Player B a rating of RB, the exact formula (using the logistic curve) for the expected score of Player A is

EA=1 / (1+10^((RB−RA)/400))

Similarly the expected score for Player B is EB=1 / (1+10^((RA−RB)/400))
This could also be expressed by

EA=QA/ (QA+QB) and EB=QB/(QA+QB) where QA=10^(RA/400) and QB=10^(RB/400)

A player whose rating is 100 points greater than their opponents is expected to win 64% of the time; if the difference is 200 points, then the expected probability of winning for the stronger player is 76%. This property of the Elo system allows us to compare fighters of different generations in fantasy match-ups.

Data
Boxrec is one source of historical boxing records, though incomplete, it is a good source for historical rankings, fighter biographical data, and match outcomes. Boxrec even has their own ranking system, which is described on their website. For this analysis, I used data from Boxrec to calculate the various rankings. Keep in mind Boxrec is incomplete and my sample is likely missing records and only goes until December 2014.

Rankings

Rank
Fighter Elo Max
1. Sugar Ray Robinson 2069.52
2. Harry Greb 2052.88
3. Benny Leonard 2019.76
4. Henry Armstrong 2010.28
5. Willie Pep 1978.91
6. Joe Louis 1975.84
7. Archie Moore 1975.61
8. Freddie Steele 1963.16
9. Ezzard Charles 1962.89
10. Barney Ross 1947.24
11. Ike Williams 1946.65
12. Kid Gavilan 1933.69
13. Freddie Miller 1933.29
14. Tony Canzoneri 1932.09
15. Mickey Walker 1924.69
16. Lou Ambers 1923.47
17. Carlos Monzon 1920.35
18. Tommy Loughran 1918.15
19. Young Corbett III 1916.57
20. Muhammad Ali 1909.32
21. Ceferino Garcia 1907.26
22. Jose Napoles 1900.59
23. Bobo Olson 1899.97
24. Duilio Loi 1898.70
25. Maxie Rosenbloom 1897.43


Rank
Fighter Elo Average
1. Sugar Ray Robinson 1855.00
2. Harry Greb 1817.61
3. Willie Pep 1806.41
4. Henry Armstrong 1759.86
5. Archie Moore 1756.91
6. Joe Louis 1739.19
7. Holman Williams 1732.01
8. Maxie Rosenbloom 1723.70
9. Luis Manuel Rodriguez 1721.78
10. Tony Canzoneri 1719.02
11. Freddie Miller 1716.27
12. Ezzard Charles 1715.72
13. Lew Tendler 1712.23
14. Kid Gavilan 1710.57
15. Kid Chocolate 1703.23
16. Young Stribling 1702.78
17. Ike Williams 1701.01
18. Benny Leonard 1699.89
19. Emile Griffith 1699.42
20. Lou Ambers 1689.37
21. Jackie Fields 1687.93
22. Tommy Gibbons 1687.08
23. Bobo Olson 1685.10
24. Wesley Ramey 1684.10
25. Muhammad Ali 1682.48


Highest Rated Bouts:


Fighter
Elo Record Opponent Elo Record Date
1. Jake LaMotta 1845.24 78-14-3 vs Sugar Ray Robinson (W,TKO) 2058.42 120-1-2 on 1951-02-14
2. Bobo Olson 1885.60 71-8-0 vs Sugar Ray Robinson (W,KO) 2014.54 137-4-2 on 1956-05-18
3. Sugar Ray Robinson (W,KO) 2003.29 136-4-2 vs Bobo Olson 1896.84 71-7-0 on 1955-12-09
4. Joe Louis 1966.90 58-1-0 vs Ezzard Charles (W,UD) 1918.10 66-5-1 on 1950-09-27
5. Henry Armstrong (D,PTS) 1987.04 106-12-6 vs Ceferino Garcia 1896.12 112-25-12 on 1940-03-01


Worst Mismatches of All-Time:


Fighter
Elo Record Opponent Elo Record
1. Al Benedict 985.94 10-26-0 vs Harry Greb (W,TKO) 1836.32 61-2-2
2. Willie Pep (W,PTS) 1898.36 161-4-1 vs Kenny Leach 1040.90 3-14-0
3. Willie Pep (W,PTS) 1872.37 185-6-1 vs Mario Eladio Colon 1043.31 15-47-8
4. Johnny Cockfield 10-84-9 867.80 vs Chalky Wright (W,TKO) 1774.65 153-34-18
5. Archie Moore (W,RTD) 1967.89 178-21-9 vs George Abinet 1073.68 6-14-1
 
Last edited:
Jun 7, 2013
927
147
Montreal, Canada
Really interesting, but I have some questions.

1-What does Elo max and average mean ?

2-You describe your formula to compare boxer A vs B, but where do the initial ratings come from ? Boxrec's career ratings or old rankings at a specific weight?

3-There's not a lot of boxers who boxed past the 70's on your lists, do you think your system is biased towards boxers who boxed more regularly ?
 
Jul 13, 2013
199
5
Really interesting, but I have some questions.

1-What does Elo max and average mean ?

2-You describe your formula to compare boxer A vs B, but where do the initial ratings come from ? Boxrec's career ratings or old rankings at a specific weight?

3-There's not a lot of boxers who boxed past the 70's on your lists, do you think your system is biased towards boxers who boxed more regularly ?
1. The Elo max is the highest Elo rating a boxer ever achieved. The average refers to the average Elo rating over the fighter's career. One measures the "peak" and the other measures "consistency".

2. Under the Elo system everyone starts usually starts out at 1200 ranking when your record is 0-0 and that's what I've done here as well.

3. Yes, that is entirely possible! Elo rating can undergo "deflation" or "inflation" if the overall number of boxers shrinks or grows significantly. I've been meaning to take a look at this, but this has been a side project and I never have enough time. I eventually want to try to develop a predictive system and see if the number crunching is actually worth anything.
 
Jul 19, 2013
152
5
Interesting!

However, I would be very much surprised if some sort of formular can ever be worked out, that is able to predict the outcome of fights any better than simply combining the eye-test with common sense.
 
Jul 13, 2013
199
5
Interesting!

However, I would be very much surprised if some sort of formular can ever be worked out, that is able to predict the outcome of fights any better than simply combining the eye-test with common sense.
I don't know of many applying statistics to boxing, though I'm sure there more people out there. Nearly all the successful professional gamblers are using computer models and statistics to handicap events.
 
Jul 19, 2013
152
5
Though I don't have the mathematical knowledge to really understand how these numbers are arrived at... I must admit, that I'm intrigued!

I have a couple of questions:

1
What is Mayweather's max score? And how far down the list is he? I find it strange, that he doesn't even make the top-25. Same thing with Ray Leonard. Is the reason, that they simply didn't have enough fights to gather points?

2
Bobo Olson is surprisingly high on the list (presumably because he had a lot of fights?)... so I wonder, what prediction this system would come up with regarding his chances (percentage-wise) in a fantasy match vs someone like Marvin Hagler?
 
Jul 13, 2013
199
5
Though I don't have the mathematical knowledge to really understand how these numbers are arrived at... I must admit, that I'm intrigued!

I have a couple of questions:

1
What is Mayweather's max score? And how far down the list is he? I find it strange, that he doesn't even make the top-25. Same thing with Ray Leonard. Is the reason, that they simply didn't have enough fights to gather points?

2
Bobo Olson is surprisingly high on the list (presumably because he had a lot of fights?)... so I wonder, what prediction this system would come up with regarding his chances (percentage-wise) in a fantasy match vs someone like Marvin Hagler?
Floyd is #30 on the list. His max Elo is 1883.31. Also this didn't include the Pacquiao (#50 all-time) fight, so he probably went up a few places. You're right that, in general, more wins will lead to higher ratings, but the level of competition also matters. Maybe I should modify the parameters to take into account the average number of fights per year each fighter had.

Marvin Hagler had a max Elo of 1847.43. Bobo's max rating was 1899.97. The difference is 1899.97 - 1847.43 = 52.54. So we get about 56% chance (according to the max Elo ratings) that Bobo Olson would win or draw.

https://www.reddit.com/r/chess/comments/2y6ezm/how_to_guide_converting_elo_differences_to/
 
Jul 19, 2013
152
5
Yeah, it's me again, with more questions!

You say, that we can use the Elo ratings to compare boxers from different eras... but wouldn't that only be true, if ability/skills were at a constant level over the years?

"Elo rating can undergo "deflation" or "inflation" if the overall number of boxers shrinks or grows significantly". What exactly does this mean? Does it mean, that a boxer who rises to the top today gets a higher rating than the best boxers in (for example) the 1890s... simply because the global talent pool is so much larger today?

As you say, BoxRec of course have their own system... and according to them, Pascual Perez is the highest scoring flyweight ever! I would be interested to know, where Perez ranks (amongst the flyweights) using your system? The reason I single out Perez, is because he has one of the "thinnest" records of any world champion... and it boggles my mind how a system can be devised, that makes him out to be the highest ranked flyweight of all time.Therefore it would be interesting to see, if your system ranks him differently.

Sorry about the many questions... but even though the math goes over my head, that can't stop me from finding stuff like this fascinating!
 
Jul 13, 2013
199
5
Yeah, it's me again, with more questions!

You say, that we can use the Elo ratings to compare boxers from different eras... but wouldn't that only be true, if ability/skills were at a constant level over the years?

"Elo rating can undergo "deflation" or "inflation" if the overall number of boxers shrinks or grows significantly". What exactly does this mean? Does it mean, that a boxer who rises to the top today gets a higher rating than the best boxers in (for example) the 1890s... simply because the global talent pool is so much larger today?

As you say, BoxRec of course have their own system... and according to them, Pascual Perez is the highest scoring flyweight ever! I would be interested to know, where Perez ranks (amongst the flyweights) using your system? The reason I single out Perez, is because he has one of the "thinnest" records of any world champion... and it boggles my mind how a system can be devised, that makes him out to be the highest ranked flyweight of all time.Therefore it would be interesting to see, if your system ranks him differently.

Sorry about the many questions... but even though the math goes over my head, that can't stop me from finding stuff like this fascinating!
Yes, you are right. Elo is a relative measure of skill, but it gives us a measure of how much better a fighter is than their peers. It could be that boxer's training and tactics have progressed so much that different eras are not comparable. This analysis is far from perfect, but it does give some objective measures.

You can think of the total amount of ratings points as somewhat fixed (there are parameters to overcome this), but essentially if a Sugar Ray Robinson retires he takes a lot of points with him. If there aren't enough replacement points for him, the total ratings points decrease. I haven't done enough analysis to determine whether this happens with the data I have.

Pascual Perez is definitely not the best flyweight under Elo. His max was 1617 and Pongsaklek Wonjongkam had a max of 1738, Roman Gonzalez had a max of 1626 (up to 2015). I don't currently have the fighter's categorized by weight class and would have to cross reference two separate databases. I can probably do this, but also I only have Boxrec's weight class which don't tell the whole story.