Calculating Collusion

Continuing with the series on Soviet collusion in the 1950s and 1960s (see the previous post Solutions to Collusion), in 2006 Charles C. Moul and John V. Nye, both university professors in economics, published a study of the subject: Did the Soviets Collude? A Statistical Analysis of Championship Chess 1940-64.

Abstract: We expand the set of outcomes considered by the tournament literature to include draws and use games from post-war chess tournaments to see whether strategic behavior is important in such scenarios. In particular, we examine whether players from the former Soviet Union acted as a cartel in international tournaments - intentionally drawing against one another in order to focus effort on non-Soviet opponents - to maximize the chance of some Soviet winning. Using data from international qualifying tournaments as well as USSR national tournaments, we estimate models to test for collusion. Our results are consistent with Soviet draw-collusion and inconsistent with Soviet competition. Simulations of the period's five premier international competitions (the FIDE Candidates tournaments) suggest that the observed Soviet sweep was a 75%-probability event under collusion but only a 25%-probability event had the Soviet players not colluded.

Of the five Candidate Tournaments in the study -- Budapest 1950 through Curacao 1962 -- the Curacao event has always received the most attention, largely due to Fischer's public accusation of Soviet cheating. It was, however, the 1953 Zurich Candidates Tournament where collusion, if it occurred, caused the most damage to the chances of the non-Soviet players, Reshevsky in particular. Moul and Nye's findings for the event are summarized in the following table.

Focusing on the line for Reshevsky, the authors wrote, 'Our calculations indicate that he had a 27% chance of winning a fair tournament. With collusion, his chances fell to 8%.' As convincing as these numbers might be, the result is flawed, relying, as it did, on the Sonas Chessmetric historical ratings. On several occasions in the past I've taken issue with Sonas's results when they failed the test of common sense. This is another case.

The last column in the table ('No cartel: % win') is based on the 'Rating' column, as calculated by Sonas. The top three ratings are Reshevsky (2780.99), Smyslov (2764.92), and Najdorf (2753.04), which is the first red flag (the six digit accuracy is also suspicious, but I won't dwell on it). The authors infer from these ratings that 'Retroactive grading has shown that Reshevsky was the favorite going into the 1953 Candidates' tournament.' While he was certainly one of the favorites, I can't imagine that many chess historians, after examination of the games between the two players (Vasily Smyslov vs. Samuel Reshevsky, Chessgames.com), where the post-WWII results give a +4-0=9 advantage to Smyslov, would argue that Reshevsky was stronger than Smyslov in 1953.

The second red flag concerns four players bunched within a range of three rating points -- Bronstein (2723.87), Boleslavsky (2722.33), Stahlberg (2721.93), and Keres (2721.02) -- implying that Stahlberg was the equal of Bronstein, Boleslavsky, and Keres. A look at the historical record shows that Bronstein drew a title match with Botvinnik in 1951, that Boleslavsky drew a playoff match with Bronstein after the 1950 Candidates, losing only in tiebreak, and that Keres finished tied with Reshevsky in the 1948 title tournament. Stahlberg finished behind Bronstein and Boleslavsky in the 1948 Interzonal (Keres was exempt) and behind all three in the 1950 Candidates; had a lifetime negative score against each of the three; and finished 15th and dead last in the 1953 Candidates, 3.5 points behind second-to-last Euwe (Bronstein and Keres finished tied with Reshevsky for 2nd-4th). Stahlberg was an excellent player, one of the West's best at that time ('among the world's best ten for a few years around 1950', according to Hooper & Whyld), but he was not at the same level as the three Soviets.

Why are the Sonas calculations so misleading? My theory is that they fail to account for the Soviet era social barrier ('Iron Curtain', anyone?) between Soviet players and Western players. Soviet players rarely played in Western events and Western players were even rarer participants in Soviet events. The two groups played in different, almost separate chess universes. A comparison of their performances requires a calibration of the separate calculations, using the few events where they actually met. It is as though the Soviets were measured with a meterstick, the Westerners measured with a yardstick, and no one bothered to check that the meterstick and the yardstick were the same length. I also suspect that Sonas overlooked many Soviet events. Moul and Nye wrote,

[The Sonas] rating does require a minimum number of observed games to construct. Games without Sonas chess-ratings for both players are dropped from the sample. While this leads to the omission of a few Interzonal games, the vast majority of dropped games are from URS championships. These omissions will presumably drive up the average observed skill of Soviet players in URS championships, and thereby make our comparison to FIDE events even more compelling.

I have a problem with that last sentence. Because the 'dropped games' would be predominantly wins by the better players, and the kept games predominantly draws between players of equivalent ability, I would presume exactly the opposite. Near the start of their paper, the authors wrote,

For the purposes of econometric analysis, chess has numerous advantages which are not common in other sports. [...] Most important of all is that there exists a rating system which is a precise and accurate reflection of the performances of players and which is an excellent indicator of the relative strengths of players.

This prerequisite was not delivered by the Sonas system. There might have been collusion among the Soviet players, but it is not shown by this study.

More Zonal Clippings

I added a number of clippings for zonal tournaments. The first, for a Canadian championship, was sent to me via email. This sort of correspondence is always appreciated, thanks very much!

• 1966-69

The rest are screen captures from the Rusbase page on Soviet era Zonal Tournaments.

• 1975-78
  
• 1978-81
  
• 1981-84
  
• 1990-93
  
• 1993-96

My next step on the zonal project will be to create pages for clippings on cycles after 1993-96. I expect to find many of the crosstables already on the web.

Solutions to Collusion

The previous post, Collusion and Consequences, discussed pre-arranged games at the 1952 Saltsjobaden Interzonal. A few months after the tournament ended, an editorial in Chess Review (March 1953; 'edited and published by I.A. Horowitz'; p.65), presented a Western point of view on the Soviet collusion. I initially planned to give excerpts, but the document makes a number of points relevant to the early evolution of the World Championship, so I give it in entirety.

Syndicate Chess
Russian chess is an instrument of Russian national policy. The government supports an elaborate program of chess activities. Clubs and leagues are organized: competition is subsidized. Chess is taught in the grade schools, with various phases, such as mating with King, Bishop, and Knight, a required subject in each grade. Players are encouraged and, if successful, they are suitably rewarded. In return for this paternal interest, Russian masters must produce. They must win every trophy, title, match, and tournament in sight. They have to show the world that, although the game of chess is one of the two or three things which they have not invented, the Russians, nonetheless, are its most capable exponents.

By and large, this activity has been of benefit to chess. For example, a large number of great players have been developed. The Kremlin cannot supply an individual with talent. But, once they see he has it, they make it possible for him to realize his chess potentialities.

The government, however, is not selfless in its policies. What it wants is for its players to bring it an unbroken string of international successes. The game of chess itself is only a Pawn. The best interests of chess will be sacrificed any time that the bureaucrats in charge of it see the slightest gain in doing so.

The Russian players are good. Very good. They are sometimes not in form. But, when they meet Western players, they are always at their best.

They are soldiers in a war; they are the standard-bearers of Soviet culture. Any time a Russian master is permitted to show his face in the international arena, he must be at concert pitch. He is bound to be in the pink, physically and mentally. He is certain to be armed with all the latest weapons, both offensive and defensive, of opening analysis.

Since they are modern soldiers, they have lots of service troops. In the World Championship tournament, the Russian representatives -- Botvinnik, Keres, Smyslov -- arrived at The Hague attended by a large contingent of auxiliaries. It included, among others, a doctor, a cook, and a most impressive panel of eminent analysts. Such kibitzers as Kotov, Flohr, Bondarevsky, Alatortsev, Lilienthal, Tolush, and Ragozin worked on the adjourned positions. Or, if Euwe or Reshevsky, the non-Russian competitors, found an innovation in an opening, they would devote themselves to finding its refutation.

The Soviet grandmasters also have an additional advantage. Russia controls the meetings of the FIDE -- the Federation Internationale des Echecs. It has the titleholder, plus a disproportionate number of the world's leading players. Thus, it needs the other countries less than it itself is needed. It has a strong position, and no false scruples stop it from making the most of it. Then, in the second place, most Western chess federations are chronically short of funds. Consequently, there are times when they may neglect to send representatives to meetings. Moscow, on the other hand, fills its entire quota of delegates. So do its assorted satellites. What is more, the Western nations (such of them as do attend) cast their ballots as individuals. The communist states always vote as a bloc. They are therefore able to dictate the time and place, conditions and even the composition of any tournaments which have a bearing on the World Championship.

In themselves, none of the above actions are culpable. In fact, some are even meritorious. It is clearly good for chess to have strong, brilliant players and to have them playing profound, exciting and beautiful games. Insofar as Russian policy produces such players and such games, all of us who love chess are their very grateful debtors.

Alas -- let us face it. We expect a successful football coach or big-league baseball manager to make use of every angle, edge, percentage, or advantage. One or two are even known to occasionally push their weight around. We are not used to anyone treating chess as if it were of a similar importance. If the Russians choose to do so, they are strictly within their rights. We have no right to begrudge them their successes.

Still -- we can't help feeling worried.

Some time later in the year, a large tournament will be held [1953 Zurich Candidates]: its winner will then play Botvinnik for the title. A small number of Westerners and nine -- nine -- Russians will be the competitors.

We are worried by this tournament.

We want it to be won by the best player in it. Or, at any rate, the one who is playing best at the time. We hope that this will be Reshevsky. It it happens otherwise -- if another player wins it -- we will not feel too tragic. We are ready to salute him -- no matter who he is, no matter what his nation -- provide that he wins it fairly.

The Russians have a different attitude. They do not care who wins -- or even how he wins -- just so long as he's a Russian!

But each Russian player is an agent of his state. He is thus allied in a common purpose with the others. This is supposed to be a tournament of individuals. Each player in a tournament is supposed to play his best against each of the others. Then, and only then, is it possible to tell which one is the best among them. But the nine Russians in it form a unit of their own (and the Hungarian, Szabo, may be counted on this, too). They play as a team: a syndicate.

Just how this works was shown in the recent Interzonal tournament at Saltsjobaden [1952]. In it were five Russian competitors. Their own Soviet periodicals have always heaped scorn on so-called "grandmaster draws". In their own all-Russian tournaments, they go in for an aggressive, battle-royal type of chess. At Saltsjobaden, however, such games did not suit their purpose. The members of the Russian syndicate, when they came to play each other, calmly called each game a draw, after 16 to 22 moves!

In this coming tournament, the Russian group will constitute more than three-fifths of the entries. Each of them will play about three-fifths of his games against his team mates. The way in which he plays these games will be determined by what suits Soviet interests. If after several rounds, it seems that no Western player has a chance to win the tournament, we may get an honest contest. If, on the other hand, it should turn into a duel between Sammy Reshevsky, and, say, Vasily Smyslov, we are sure that no Russian will venture to beat Smyslov and thus make him lose the prize.

In this observation, we have mentioned but one hazard. There are others. For example, in a gruelling tournament, a day of rest is an incalculable asset. And, in such a duel as we have suggested, we can be sure that Reshevsky would have to work to the utmost against every opponent, Westerner or Soviet. Whereas, if Smyslov should have rigged games or even routine draws, he would be freed of the strain of tournament tension and resting through the majority of his games. As freshness and alertness count so heavily in chess, this factor cannot be disregarded.

We are casting no aspersions. In the Soviet ideology, the state is paramount. If the Kremlin, for some reason, wants to win a prize at chess, it is then the player's duty to help it get it. If this requires winning, he has to try to win. If it requires losing, he must do his best to lose. According to Soviet lights, he is doing nothing bad. In fact, if he did not do so -- he would then be anti-social. When we hint that Russian players may throw games to one another, we are saying nothing slanderous. Rather we are paying them a compliment. We are saying that Soviet chess players are very good Soviet citizens.

Our sense of ethics is different. A tournament which is rigged fills the Western chess lover with nausea.

Our game has always cut across national boundaries. It should continue to do so. If the Russian chess players play as chess players, then it's proper to have nine, or even more, in a tournament. If they play as Russians, it is a dangerous thing to have even two of them.

We think that the sensible thing is to have two tournaments: one for Western players and another for the Soviets. Let the winners play each other -- and the winner meet Botvinnik.

We are sure the Russians won't agree. We will have to reconcile ourselves to playing the tournament on their terms.

In that case, all we can hope is that unpleasantness can be avoided. That a Russian will get such an early that his allies will feel it safe to play fair and scrupulous chess. Or -- even better -- that some Western player, some Samson like Reshevsky, gets into an inspired streak and wins, in spite of all the machinations of the Soviet Philistines.

Despite a dubious premise or two (I'm not sure that chess was taught systematically in Soviet elementary schools) and an unsubstantiated charge of game throwing ('if it requires losing, he must do his best to lose'), I think it makes a good case that the chess board was not a level playing field for Reshevsky. By introducing matches instead of round robin tournaments, the imbalance was solved satisfactorily for the Candidates. It was solved less satisfactorily for the Interzonals by limiting the number of Soviet players advancing to the Candidates. This led to unforeseen consequences for the Soviets.

Collusion and Consequences

One of the small tasks in last week's post about Catching up on Maintenance was to review the earliest Interzonals. This led me to an interesting report from the November 1952 issue of Chess Review (p.323) concerning the 1952 Saltsjobaden Interzonal Tournament, which was the qualifier for the 1953 Zurich Candidates Tournament:

Soviet entrants made a clean sweep of the top five places, which qualified them to take part in the World Championship Candidates Tournament of 1953 to determine the next challenger for the world title. Seeded in this coming event are Samuel Reshevsky of the USA, Dr. Max Euwe of Holland, and the first five players in the Candidates' tournament of 1950 -- D.Bronstein, I.Boleslavsky, V.Smyslov, and P.Keres, all of Russia, and M.Najdorf of Argentina.

A noteworthy circumstance in the Saltsjobaden affair was the pacific attitude of the Russian players toward one another. All games among them were drawn! Kotov, for example, who fell with fury upon most of his non-Russian rivals, was content to play the shortest possible "grandmaster draws" with his compatriots: vs. Averbach, 20 moves; vs. Geller, 15 moves; vs. Petrosian, 15 moves; vs. Taimanov, 17 moves. Since Kotov proved to be the class of the tournament, a sterner attitude on his part toward the other Russians might well have enabled an "outsider" to squeeze into the charmed circle of qualifiers.

The two-tiered Soviet dominance is highlighted in the following portion of the 1952 Saltsjobaden page that I just referenced.

Of the ten games played between Soviet opponents, only Taimanov - Averbakh was longer than 22 moves. This apparent collusion had a number of consequences. The Chess Review report continued with the following news item.

Our Stockholm correspondent, Z. Nilsson, reports that a FIDE committee meeting in February [1953] may add to the World Championship Candidates Tournament qualifiers from the Saltsjobaden event. Four contenders tied for the fifth and last qualifying place and though Averbach qualified on S.B. points, the tiebreak was extremely minute [numbers are shown on my page]. The fact, moreover, that Averbach's place completed an all-Russian qualification and puts nine Russians to three non-Russians in the Candidates Tournament, very likely was considered.

I'm not sure why Reshevsky and Euwe were seeded into the 1953 Candidates Tournament, although it makes sense that it was because of their participation in the 1948 FIDE Title Tournament, won by Botvinnik. Chess Review added an item about Reshevsky.

Hermann Helms reports in the Brooklyn Daily Eagle that Samuel Reshevsky, declaring the 9-3 setup in favor of Russians is inequitable, is unwilling to play in the 1953 World Championship Candidates Tournament for which he is seeded. He is willing to meet any of the leading Russians in straight match play, as he has done with Najdorf and Gligoric, but his challenge to Paul Keres, the Soviet Champion, has brought no reply so far. It hardly seems possible that the addition of three Candidates (one from Communist Hungary) will alter Reshevsky's stand.

I suspect that the 1952 Interzonal and 1953 Candidates Tournament were the origin of later FIDE rules that limited the number of Soviet players advancing from an Interzonal to a Candidates event. With the goal of documenting the findings on my various pages specific to the results of these events, this is worth further investigation and I'll spend a few future posts on the subject.