I've been involved in some speculation as to the nature of Elo ratings and in particular the meaning of what may or may not be inflation. I'd just love to be good enough at the right things to take this up, it's a fascinating opportunity for somebody.

Just advertised in the ACF Bulletin.

Ratings doctorate.

Project summary, Rating and ranking sports players and teams using Minimum Message Length

Rating systems go back at least as far as Harkness (1949) and the better-known Elo (1961) system for rating chess players. More recent attempts have been made to refine these systems in a variety of ways. We refine the systems further using the Bayesian information-theoretic Minimum Message Length (MML) principle from statistics, machine learning, econometrics, inductive inference and ``data mining'' (Wallace and Boulton, Computer J, 1968) (Dowe, Handbook of Philos of Statistics, 2011). This includes dealing with the challenging Neyman-Scott-like situation where, for some players and teams, there are few games per player or few games between different groups of players. Our enhanced modelling will be for a range of games and sports - including advantages such as, e.g., first move (as in chess), home ground and location, surface (as in tennis), etc. We will apply this to rating and ranking individuals and teams. We also refine how quickly ratings can change depending upon the strength of the player.

Pay: 3-year PhD scholarship, Aus$26,667p.a. scholarship top-up

The successful candidate will have an undergraduate degree and will be at least semi-literate in at least one of mathematics and information theory, or at least interested in both areas. Some experience in computer programming in at least one programming language is highly desirable.

Some background: Chris Wallace published the first paper on Minimum Message Length (MML) in Wallace & Boulton (1968). Wallace & Dowe (1999a) was once the Computer J (OUP)'s most downloaded article - and currently remains as Chris Wallace's most cited co-authored work by a researcher still active in the area. David Dowe co-authored the first papers on MML Bayesian nets which combine both discrete (multi-valued) and continuous-valued attributes. Dowe has a forthcoming (2011) piece on MML to appear in the forthcoming Handbook of Philosophy of Statistics, Elsevier.

It is a requirement of Monash University (in coastal Melbourne, Australia) that students have at least a minimum proficiency in the English language in at least one of IELTS and/or TOEFL.

See www.MRGS.monash.edu.au for more information.

Prospective students should direct their enquiries to David Dowe.

Assoc. Prof. David Dowe, Ph.D.; School of Comp. Sci & Softw. Eng.;

Clayton School of I.T.; Monash Univ.; Clayton; Vic 3168; Australia

Tel: 61 3 9905-5776 www.csse.monash.edu.au/~dld

I've been involved in some speculation as to the nature of Elo ratings and in particular the meaning of what may or may not be inflation. I'd just love to be good enough at the right things to take this up, it's a fascinating opportunity for somebody.

Just advertised in the ACF Bulletin.

Ratings doctorate.

Project summary, Rating and ranking sports players and teams using Minimum Message Length

Rating systems go back at least as far as Harkness (1949) and the better-known Elo (1961) system for rating chess players. More recent attempts have been made to refine these systems in a variety of ways. We refine the systems further using the Bayesian information-theoretic Minimum Message Length (MML) principle from statistics, machine learning, econometrics, inductive inference and ``data mining'' (Wallace and Boulton, Computer J, 1968) (Dowe, Handbook of Philos of Statistics, 2011). This includes dealing with the challenging Neyman-Scott-like situation where, for some players and teams, there are few games per player or few games between different groups of players. Our enhanced modelling will be for a range of games and sports - including advantages such as, e.g., first move (as in chess), home ground and location, surface (as in tennis), etc. We will apply this to rating and ranking individuals and teams. We also refine how quickly ratings can change depending upon the strength of the player.

Pay: 3-year PhD scholarship, Aus$26,667p.a. scholarship top-up

The successful candidate will have an undergraduate degree and will be at least semi-literate in at least one of mathematics and information theory, or at least interested in both areas. Some experience in computer programming in at least one programming language is highly desirable.

Some background: Chris Wallace published the first paper on Minimum Message Length (MML) in Wallace & Boulton (1968). Wallace & Dowe (1999a) was once the Computer J (OUP)'s most downloaded article - and currently remains as Chris Wallace's most cited co-authored work by a researcher still active in the area. David Dowe co-authored the first papers on MML Bayesian nets which combine both discrete (multi-valued) and continuous-valued attributes. Dowe has a forthcoming (2011) piece on MML to appear in the forthcoming Handbook of Philosophy of Statistics, Elsevier.

It is a requirement of Monash University (in coastal Melbourne, Australia) that students have at least a minimum proficiency in the English language in at least one of IELTS and/or TOEFL.

See www.MRGS.monash.edu.au for more information.

Prospective students should direct their enquiries to David Dowe.

Assoc. Prof. David Dowe, Ph.D.; School of Comp. Sci & Softw. Eng.;

Clayton School of I.T.; Monash Univ.; Clayton; Vic 3168; Australia

Tel: 61 3 9905-5776 www.csse.monash.edu.au/~dld

I've been involved in some speculation as to the nature of Elo ratings and in particular the meaning of what may or may not be inflation. I'd just love to be good enough at the right things to take this up, it's a fascinating opportunity for somebody.

Just advertised in the ACF Bulletin.

Ratings doctorate.

Project summary, Rating and ranking sports players and teams using Minimum Message Length

Rating systems go back at least as far as Harkness (1949) and the better-known Elo (1961) system for rating chess players. More recent attempts have been made to refine these systems in a variety of ways. We refine the systems further using the Bayesian information-theoretic Minimum Message Length (MML) principle from statistics, machine learning, econometrics, inductive inference and ``data mining'' (Wallace and Boulton, Computer J, 1968) (Dowe, Handbook of Philos of Statistics, 2011). This includes dealing with the challenging Neyman-Scott-like situation where, for some players and teams, there are few games per player or few games between different groups of players. Our enhanced modelling will be for a range of games and sports - including advantages such as, e.g., first move (as in chess), home ground and location, surface (as in tennis), etc. We will apply this to rating and ranking individuals and teams. We also refine how quickly ratings can change depending upon the strength of the player.

Pay: 3-year PhD scholarship, Aus$26,667p.a. scholarship top-up

The successful candidate will have an undergraduate degree and will be at least semi-literate in at least one of mathematics and information theory, or at least interested in both areas. Some experience in computer programming in at least one programming language is highly desirable.

Some background: Chris Wallace published the first paper on Minimum Message Length (MML) in Wallace & Boulton (1968). Wallace & Dowe (1999a) was once the Computer J (OUP)'s most downloaded article - and currently remains as Chris Wallace's most cited co-authored work by a researcher still active in the area. David Dowe co-authored the first papers on MML Bayesian nets which combine both discrete (multi-valued) and continuous-valued attributes. Dowe has a forthcoming (2011) piece on MML to appear in the forthcoming Handbook of Philosophy of Statistics, Elsevier.

It is a requirement of Monash University (in coastal Melbourne, Australia) that students have at least a minimum proficiency in the English language in at least one of IELTS and/or TOEFL.

See www.MRGS.monash.edu.au for more information.

Prospective students should direct their enquiries to David Dowe.

Assoc. Prof. David Dowe, Ph.D.; School of Comp. Sci & Softw. Eng.;

Clayton School of I.T.; Monash Univ.; Clayton; Vic 3168; Australia

Tel: 61 3 9905-5776 www.csse.monash.edu.au/~dld

This review is easier to read in worldcat format:
worldcat.org/profiles/Tom2718/reviews/3053806?reviewaction=fetchfull
than on goodreads:
goodreads.com/review/show/1893592289

The late Professor Apad E. Elo designed the chess rating system that shows players not only which of them is the best, but by how much.

Elo’s book is a well-written explanation of various ways of evaluating competitors, of the history of chess ratings, and of his rating system. A nice bonus is Elo’s assessment of the relative ratings of past masters, including many whose careers long predated the advent of Elo’s numerical system.

THE ELO RATING SYSTEM:
The Elo rating system is based on a simple presumption: If player A beats player B, say, 3 games to 1, and player B beats player C, say, 3 games to 1, then player A should beat player C, 3/1 times 3/1, 9 games to 1. Then take the logarithms of the win-loss ratios: these are the rating differences. Here, if we use base-3 logs, player A is 1 point above player B, player B is 1 point above player C, player A is 2 points above player C. And the predicted win-loss ratio of any two players is the base of the log scale to the power of the rating difference.

(For chess, a draw counts as half a win, and half a loss.)

Simple and elegant. If the presumption is true, so is the predictive value of the relative ratings. There is neither theory nor observation to justify the presumption. There’s nothing contest-specific in the arithmetic. It’s easy to imagine contests where a different presumption holds. BUT—even if the underlying idea isn’t accurate, STILL it MAY give useful and reasonable ratings under certain conditions.

For example, suppose at golf Al always scores in the 70s, Charlie always scores in the 80s, and Beth scores in the 70s half the time, and in the 80s half the time. Suppose when Beth scores in the 70s, she’s equally likely to win or lose a match with Al; when she scores in the 80s, she’s equally likely to win or lose a match with Charlie. Here A beats B 3 to 1; B beats C 3 to 1; A beats C every match (infinity to 1). And, consider a lumberjack race across a pond, running on floating logs strung end-to-end. The winner is first across, or, last to fall in, whichever happens first. Here suppose Al runs fast, but, 1 time in 4, he falls in near the start. Suppose Beth runs at medium speed, but, 1 time in 4, she falls in near the finish. Suppose Charlie runs slowly, but never falls in. Here Al beats Beth 3 times to 1; Beth beats Charlie 3 times to 1; Al beats Charlie 3 times to 1. So Elo’s presumption of A over B 3 to 1, B over C 3 to 1 gives A over C 9 to 1 doesn’t hold in these contests: A over C could be 3 to 1 or infinity to 1 or anything in between. And that’s without considering “rock-paper-scissors” results, where A beats B, B beats C, and C beats A—an element of which is at least possible where there’s more than one dimension to the contest. Still, if ratings are based primarily on tournament results (1 game each against many opponents) rather than match results (many games with one opponent), and all players play a fair mix of opponents, above, near, and below their ratings, then everyone’s rating will include some results that overestimate their rating, and other results that underestimate their rating, by the Elo scale. Likewise, as everyone plays white half the time and black half the time, it doesn’t matter that white is a slight advantage: results average out for everyone.

My sense is, chess is more nearly like the golf example above, in that the substantially-stronger player is virtually guaranteed to win, but there is an element of the lumberjack example with chess too, in that, if the stronger player does lose, it’s likely due to a self-inflicted wound, which an opponent of even low skill could capitalize on. For example, once, our one master came to the club exhausted after a long day at work. He left his queen en prise in a rated game, which even the lowly 1600-rated opponent was able to convert to a win.

The U.S. Chess Federation designates “rating classes”:
rating class
2400+ senior master
2200-2399 master
2000-2199 expert
1800-1999 class A
1600-1799 class B
1400-1599 class C
1200-1399 class D
100-1199 class E
(Although there’s no reason ratings can’t be negative, USCF’s minimum is 100. Most tournament players are rated at least 1000. For estimating winning chances, only rating difference matters.)

First the Elo arithmetic, then how it’s used to arrive at ratings:

For Elo’s chess ratings, he chose 400 times the base-10 log of the win-loss ratio to define the rating difference:

Where:
L is your losses,
W is your wins,
Delta R is your opponent’s rating minus your rating:

L/W Delta R = 400*log(L/W)/log(10)
1/1 0
4/3 50
3/2 70
2/1 120
3/1 190
4/1 240

Notes:

If you replace the L/W ratios with their reciprocals, the rating differences become negative.

It’s tempting to say, “10/1 is 400 points: then 100/1 is 800 points, 1000/1 is 1200 points, . . .” But such exactitude is an illusion. What’s accurate is that for any substantial rating difference, the lower-rated player expects a negligible chance of winning. Likewise, “3/2 is 70 points, 4/3 Is 50 points, so 70 - 50 = 20 points is (3/2) / (4/3) = 9/8.” Again, such exactitude is an illusion. Even in a 100-game contest where each competitor has an exactly 50/50 chance of winning a game, it’s likely that the result will be anywhere between about 45/55 and about 55/45, that is, about -35 rating points to +35 rating points. Also, you may do better against Boris than most players of your rating, or worse against Bobby than most players of your rating, due to differences of playing style.

The magnitude of the advantage of playing white can be approximated by looking at, for example, the 48-game Karpov-Kasparov match: 40 draws, 5 wins by white, 3 wins by black: In this match, white outplayed black by 400*log(25/23)/log(10) = 15 Elo points.

If one player wins or loses all games, the rating difference is infinite. (In practice, U.S. Chess Federation avoids infinities by starting each player with a “performance rating,” 400 points below the rating of each opponent the new player loses to, 400 points above the rating of each opponent the new player beats, averaged over the first 25 games.)

Only rating differences are meaningful. There’s no reason ratings can’t be negative.

This scale gives presumed W/L probabilities for any given rating difference between two players. What Elo does with this information is, for each event, calculates, based on the players’ relative ratings, what score (total number of games won, each draw counting as half a win) each player expected. Then, if the player actually scored more than expected, points are added to the player’s rating. Conversely for a player who scores lower than expected for the player’s rating relative to his opponents, the player’s rating is reduced. In this way ratings change, tournament by tournament, until they reflect the player’s actual strength relative to his opponents.

Numerically, from the above presumed logarithmic relation,
L/W = 10^(Delta R / 400)
presumed win probability, wins / games = W / (W + L)
= 1 / ( 1 + 10^(Delta R / 400) )

One of the most interesting things Elo does with this process in his book is to establish relative ratings of chess masters over more than a century, from Paul Morphy in the mid-1800s, up to the date of publication. This was possible because these masters played others of previous and later generations, and none of them won or lost all their matches. So using the masters’ match results, Elo by iteration found the relative ratings for each master that predicted their actual results. That is, he started by assuming the same rating for each master, he then added points to the assumed ratings of those whose actual results were better than predicted, and conversely. Repeating until actual results matched predicted ones, he got an internally self-consistent set of relative ratings.

Notice that only relative ratings can be inferred from competition. The method tells only how players fare relative to each other—not whether as a group they are strong or weak players.

The chess federations do not use the above iterative method over the players’ whole careers to establish ratings. Instead they add points to players’ ratings after each event who outperformed their ratings’ predictions, and conversely.

NATURAL RATING DEFLATION
One of Elo’s most significant contributions to the practice of rating chessplayers is his recognition of the natural process by which ratings decrease with time—and his elegant solution, bonus points.

A new, inexperienced player joins the league and establishes a rating. During his playing career he gains skill and his rating increases. He retires from competition with greater skill, and a higher rating, than he started at. The problem is that, although his increase in skill is real, his increase in rating points all comes at the expense of his opponents’ ratings. As our new player gains rating points for exceeding his number of wins expected, his opponents lose the same number of rating points, for falling short of their expected wins. This process removes rating points from the pool.

To put them back, Elo awards bonus points to players who gain more rating points in a single tournament than random chance would suggest is likely. This adds rating points to the total, to compensate for the natural loss.

For those of us interested in such things, Elo’s book is a delight.

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