That is bizarre and disturbing. In means that British and American people reading the same text will have opposite views on what has been written. I will think it means "open to debate" and a yank will think it means "pointless to debate".

For another view on the accuracy of the Elo tables, see http://recherche.enac.fr/~alliot/el....

Your comment about Elo's assumption that the standard deviation of the distribution is the same for all players gave me pause for some thought. Clearly that was a necessary simplification for Elo but it would seem possible today to calculate a performance distribution for each rated player (or at least the top ones), and use each player's distribution in calculating their tailored t-distribution (perhaps another good use of the letter "t"!). I don't consider this concept absurd at all. For example, based on the current Candidates Tournament, I would assume that the SD in Giri's performance (all draws) distribution would be much different than Nakamura's or Anand's (5 decisive games each). Of course, I don't now if it would make a significant difference in the results.

While as a noun, the word is comparatively uncommonly used, as a verb that is not the case, though of course Over Here 'debate' is much more often employed.

The FIDE scoring tables (https://www.fide.com/fide/handbook...., Table 8.1b) indicate the probability of a win [ P(W/D) ] OR a loss [ P(L/D) ] for a player based on the rating difference between that player and his opponent. In certain situations it is desired to determine the probability of a win, a draw, or a loss [ P(W), P(D), P(L) ] for a player, again based on the rating difference between that player and his opponent.

This is surprisingly not easy to do, and additional information is needed. In his book, "The Rating of Chess players – Past & Present", he says "All data entering the rating system consist of total points scored in actually played game ... Discrimination as to how any point score is composed between wins, draws, and losses is beside the point." I think that the real reason that he ignored the effect of draws is that he developed his system when there weren't any cheap computers easily available to do calculations, and no on-line game databases containing the necessary information. And so he remarked that "Any consideration of draws in rating theory requires information on the probabilities of draws, as well as wins and losses, between individual players, information which is not readily available. Its accumulation would be inordinately laborious, and there has been little demand for it." Well, maybe not then.

Over a period of time I've been able to come up with only 3 articles describing methods for attempting to extract P(D) from P(W/D) and P(L/D), and in one of them the author threw up his hands when he realized that he needed additional information. These articles are:

1. "Individual Chess Game Probabilities based on Match Results". Written by Charles Roberson in 2012, the link no longer works. His method relates the P(W), P(D), and P(L) to the probabilities of a player winning or losing a match. I don't find it very convincing because he makes statements like "E(D) = Expected game draw percentage = Match play probability of losing" without substantiation, and when you plot P(W), P(D), and P(L) on the same chart you get a very sharp slope change in P(W) and P(L) that just doesn't look right.

2. "Bayesian Elo Rating" by Remi Coulom, written in 2004. (https://www.remi-coulom.fr/Bayesian...). His method calculates P(W), P(D), and P(L) using Bayes' Theorem by choosing a prior likelihood distribution over Elo ratings and computing a posterior distribution as a function of the observed results. Whatever that means.

Seriously, as Dr. Elo said, calculating P(W), P(D), P(L) from P(W/D), P(L/D) requires additional information, and the author estimates a Draw Likelihood by simulation. I think that this number represents the Expected Drawing Percentage [ E(D%) ] x standard deviation (SD) but I'm not sure. With E(D%) known then E(W%) and E(L%) can be calculated and from them P(W) and P(L). With P(W) and P(L) known then P(D) = 1 – P(W) – P(L) since all results are mutually exclusive.

3. "How to calculate probabilities of Win, draw and loss based on the ELO system" written in 2014 (https://math.stackexchange.com/ques...) with no user name given. The author attempts to calculate (PD) by looking at the expected score (EA, EB) in a game between 2 players (A and B) and, since FIDE considers a draw to be 1/2 White win and 1/2 Black win, the formulas:

EA = P(A wins) + 1/2*P(Draw) + 0*P(A loses) = P(A wins) + 1/2*P(Draw) EB = P(B wins) + 1/2*P(Draw) + 0*P(B loses) = P(B wins) + 1/2*P(Draw)

But then he realized that he needed additional information (which he would have known had he read Dr. Elo's book) and gave up, asking for suggestions. Which he didn't get.

Still, I used his method to calculate P(W) and P(L) using the P(D) calculated in articles 1 and 2 above. But no new information, the chart using P(D) from Article 1 looks just like the chart in Article 1 and the chart using the P(D) calculated using the P(D) from Article 2 looks just like the chart in Article 2.

I've created a spreadsheet describing the above in more detail as well as additional information such as:

1. The Percentage Expectancy Table (which is the same as FIDE's table 1b called the Scoring Probability) listed in Dr. Elo's book is wrong if a SD = 200 is used as Dr. Elo indicates he used. However, as user <Tiggler> pointed out, if a SD = 2000/7 is used instead, then the numbers match perfectly. I suppose another simplification made by Dr. Elo.

2. The FIDE Scoring Probability table (as well as Dr. Elo's Percentage Expectancy Table) only has 2 significant digits. As a result, each P(W/D) covers a range of rating differentials (RDiffs). It's easier to deal with probabilities if each rating differential has a unique probability associated with it, and this is listed in one of the spreadsheet tabs. Five significant digits are needed in order to uniquely associate each RDiff with a probability.

3. The probabilities calculated using the Match Results method are listed and plotted.

4. The probabilities calculated using the Bayes method are listed and plotted. This one is particularly interesting because you can see the effect of incorporating White's first move advantage into the probabilities. It also shows how to incorporate different White Advantage and Draw Likelihoods using data derived from the Opening Explorer database, the ChessTempo database, or any other database that provided a percentage of White wins, draws, and losses.

I was not satisfied with the results obtained by attempting to calculate P(W), P(D), and P(L) based on the articles I found. The Bayesian method seemed the most promising since it yielded the expected, or at least hoped-for, smooth curves. But, since neither the games database used nor the simulation was made available, the probabilities could not be modified to reflect the different P(W)s, P(D)s, and P(L)s at different player levels (both players rated 2200+, both players rated 2300+, etc.), since the EloDraw parameter was not known. And it was also not clear to me how the factor to incorporate White's opening advantage (EloAdvantage) was calculated. Besides, the resulting P(D) simply seemed too low, particularly at the higher player rating levels.

Then I had an epiphany. P(D) is the area under the P(D) curve, and the Draw percentage is based on the ratio of this area to the total area, i.e.

A[ P(D) ]% = A[ P(D) ]% / ( A[ P(W) ]% + A[ P(D) ]% + A[ P(L) ]% )

So I could iterate and find the value of EloDraw that resulted in A[ P(D) ]% being equal to the observed in the games database filtered to include only the player rating levels desired. And A[ P(D) ] was easy to calculate since we are effectively dealing with the discrete probability distribution of a random variable (i.e. the results of games), it was just the sum of all the P(D)s x 1601 (the spread of the distribution, + 800 + 1 in this case), since the width of each value of the sample is = 1. And the spread is not actually needed since we are calculating ratios, so the spread cancels out. Then, once the value of EloDraw is known, P(W) and P(L) can be calculated.

I've updated the spreadsheet to add the description of the Area method and a tab to calculate and plot P(W), P(D), and P(L) for the set of ChessTempo win, draw, and loss percentages corresponding to both players rated 2200+ and 2600+. You can download this updated spreadsheet from here: http://www.mediafire.com/file/syrgd....

To make the distinction clearer, I changed the names of the parameters EloAdvantage and EloDraw to WhiteAdvantage and DrawLikelihood respectively, since they no longer have anything to do with Elo distributions, including FIDE's P(W/D) and P(L/D).

Total number of games = 14,502 (an increase of about 180 games since 2-05-17)

White wins 4,167 games (28.7%)
Draws = 7,603 games (52.4%)
White loses 2,732 games (18.8%)
White's advantage = 9.9%

I filtered the data according to information in the Event column and I discarded games earlier than 1990 to be consistent with the KingBase data. This are the numbers for different types of games:

Classic 8,666 games (59.8%)
Blitz 3,205 games (22.1%)
Rapid 1,776 games (12.2%)
Blindfold 639 games (4.4%)
Exhibition 2 games (<0.1%)
Simultaneous 1 game (<0.1%)
Too Old 213 games (1.5%)

For Classic time control games only, here are the statistics:

White wins 2,141 games (24.7%)
Draws = 5,322 games (61.4%) (!)
White loses 1,203 games (13.9%)
White's advantage = 10.8%

So the incidence of draws for Classic time control games when both players are rated 2700+ is greater than when all games are considered. Which makes sense; I would think (I didn't calculate it) that the likelihood of errors is higher at faster time controls, never mind blindfold games.

As a check, here are the statistics for the recently completed Gashimov Memorial:

Total number of games = 45

White won 9 games (20.0%)
Draws = 29 games (64.4%)
White loses 7 games (15.6%)
White's advantage = 4.4%

Not too inconsistent, keeping in mind that this is a very small number of games so a substantial deviation from the means is expected.

‘I met the eponymous professor [Arpad E. Elo] during the chess olympics at Nice in 1974. He was besieged with requests by players wanting the rules bent to accommodate their own requests for international titles.

When the last of the supplicants had gone, Professor Elo said to me: “I think I have created a monster.” I think so too.’ (Bill Hartson NOW! magazine 1-7 August 1980, page 82.) C.N. 6742

<Moon Establishes His Innocence In Trial For Assault

Milwaukee, Wis. — (AP) — The moon and its phases Friday freed Paul Saunders from conviction on a charge carrying a maximum sentence of 30 years in the state prison.

Through the testimony of W.P. Stewart, federal meteorologist and Arpad E. Elo, astronomist at Marquette university, Saunders proved to the satisfaction of Municipal Judge George Shaughnessy that the darkness of the night made identification of the assailant of Mrs. Jessie Forbes impossible.

Mrs. Forbes complained that she was attacked by a pajama clad prowler in the bedroom of her home and identified Saunders, declaring she caught a glimpse of his face by moonlight. Saunders called upon Stewart and Elo to establish that on the night in question, the moon was in its last quarter and was so low in the sky that combined with the trees near the Forbes home shut off any light.

Saunders' wife testified he was home that night, and Judge Shaughnessy then ordered a verdict of “not guilty.”>

<Another problem with Elo ratings is that someone like, say, Alireza Firouzja can increasing his rating by playing aggressively against a slew of lower-rated players but playing solely for draws against higher-rated players. >

Firouzja doesn't do that, but anyway: if you can beat people rated 2600 and draw with people rated 2750, your rating ought to be 2750. If your rating is anything other than (roughly) 2750, the rating system is screwed up.

There are only two ways to get a high Elo rating: be really strong, or hide a copy of Stockfish in your shoe.

<I don’t know that a mathematical formula can account for such circumstances, but failing to account for such circumstances makes Elo ratings far from perfect.>

Method. At the beginning of a season (the lack of continuity of team membership makes it less useful over several years), each team has a rating of zero. After each round (Thursday to Monday in the NFL) a team gets 2 points for a win and -2 for a loss, 0 for a tie. To account for strength-of-schedule, each team is given a bonus of 1 for each win the teams the given team beat and -1 for each loss from each team it loses to. Each game played may affect every other team indirectly. I got about 70% from mid-season on. Nate Silver (I think) has an article on randomness in the NFL indicating that about 50% of a team's result is "random."

I have intended to do a study on the aging of results but just never took the time to do so. My idea was to date each game and have a decay of some amount (like 15/16 for the NFL) for each week. Thus games played several weeks earlier wouldn't count as much; the direct scores and strength terms could have different aging.

I think may work for chess tournaments. Maybe I can try this for the big tournaments from 1895 to 1905 or so. The results of similarly structured tournaments should carry over pretty well: Hastings 1895, St Petes 1896, Nuremberg 1896, etc.