03 March 2010

Cumulative Scores

In Chigorin Stumbles at Hastings 1895, I developed a new database query that generated a table showing the round-by-round progress of the leaders at Hastings 1895. It's a useful tool to identify the critical games in a round-robin (all-play-all) event.

I liked the concept so much that I used it to generate a similar table -- I call it a 'Cumulative Score' -- for each of the following World Championship events...

...i.e. the first FIDE World Championship and the five candidate events covered by the study that I criticized in Calculating Collusion.

The cumulative score for the 1948 FIDE title event, where play was divided between The Hague and Moscow, is shown on the left. The three character codes at the top of the table are abbreviations for the five players who participated in the event: Botvinnik, Euwe, Keres, Reshevsky, and Smyslov; the blank cells (e.g. Botvinnik in Rd.1) show who had the bye in a round; and the dark horizontal lines show the end of each round-robin stage and the beginning of the next.

The 1948 event didn't appear to be particularly suspenseful. Botvinnik took the lead during the first stage, never relinquished it, and was assured of first place after the 22nd round. There was, however, a tight battle for second place, where Reshevsky missed his chance by losing in the 24th round (to Botvinnik).

A cumulative score is useful for understanding first person narratives like that by Keres in 'Grandmaster of Chess - The Complete Games of Paul Keres' (p.295). It started,

In the spring of 1948 I went to Holland in order to contest, at long last, the highest chess title in the world. For various reasons Fine declined to participate and so this left five of us to embark on this momentous conflict. From the very first rounds a fierce struggle developed and this continued right to the very last games. I began the tournament with two wins, against Euwe and Smyslov, but then lost in the ensuing rounds against Reshevsky and Botvinnik and at the end of the first tour I stood equal with Smyslov in third and fourth places.

About the third stage he wrote,

I came to within 1.5 points of Botvinnik and now everything hung on our individual encounter. In the event of a win I would come to within half a point of the leader and the issue of the tournament would be once again wide open.

This deciding encounter had a most complicated and exciting course and constituted a stiff test for the nerves of both players. Out of a complicated middlegame I succeeded in evolving a position of the most promising kind. Then, however, I failed to utilize my opportunities to the best advantage and the scales tipped over in Botvinnik's favor. Then there ensued a whole series of inaccuracies committed by both sides and when the game was eventually adjourned a double Rook endgame with an extra Pawn for Botvinnik had arisen.

When play was resumed Botvinnik did not find the best line and a Rook ending resulted that should have been easily drawn. But the vicissitudes of the game were by no means ended. Both sides conducted the game imprecisely and it was I who made the last mistake. By the time the second adjournment came Botvinnik had an easily won position and I suffered a bitter defeat. With this win Botvinnik had in practice ensured for himself victory in the tournament since with only eight more games to be played he already had a lead of 2.5 points.

The cumulative score indicates that this was the game played in round 15. Keres' description of its 'vicissitudes' is hard to reconcile with conspiracy theorists who claim he was under orders to let Botvinnik win the tournament. Keres' account also shows that the event was more suspenseful than the crosstable alone would indicate.

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