Chess, football and the Bilbao Rule

Chess, football and the Bilbao Rule

By Josu Fernández

Looking for the victory exclusively by valid means ist a cornerstone of all sport competition. In the sport world, personal best and the spirit of sacrifice are all important to achieve victory and to triumph, principally for oneself, but also for others. Without doubt, the most beautiful moments that sport history has provided are closely related with the many great efforts made to reach that victory.

However, in high competition sport it often happens that the final ranking of a competition is more important than the competitiveness itself in a particular game or competition. When competing in order not to lose instead of winning it means that regrettably, something goes wrong. The consequences of this practise can be very harmful to the sport itself, but also to sportsmen, sportswomen, managers, sponsors and fans.

The implement of rules that promote and encourage competitiviness and the desire of victory in the sport world must be therefore a strategic aim of the responsibles of sport events. The unsporting conservatism, that is to say the defensive systems that marginalize the searching of victory weaken the spirit of the sport and the enthusiasm for it.

This sporting “illness” occurs often in sports like football, in which there is relatively little difference in scoreboard terms between victory and defeat. In football, it is possible to play on the defensive, not to lose, but in basketball as example, it is only possible to play to win.

The Associated Football International Federation, hereinafter referred FIFA (Fédération Internationale de Football Association) was aware of this danger and of the fact that football matches were reaching a stalemate. Consequently, they implemented a change in the scoring system of the matches, in order that the value of the victory became three times greater than a draw. Football managers all over the world resolutely supported the attack strategy for the game; in others words, to encourage the sporting spirit in the football world.

The Spanish Football League agreed to adopt the FIFA recommendations in the year 1995-96. From that season onwards, a victory would score 3 points, a draw, 1 point and a defeat, 0 points. Up to that moment, a victory scored 2 points, a draw 1 point and a defeat 0 points. In England, this rule was already in use (1982). Nowadays it is the current system for all the Leagues throughout the world and for all FIFA Competitions.

In order to analyse the effect of this new rule, we have compared the 7,706 matches that were played in the Spanish football first division during the ten previous years before the adoption of the new scoring system, to the matches played during the following ten years.

The conclusion is extremely enlightening: applying the new goals coefficient per match, with the new rule, the number of goals has risen in 965, a 10% increase in relative terms compared with the previous rule (10,595-2.43*3,964). It is significant that, an important part of this increase of goals occurs during the last 20 minutes of a match. This is the consequence of the points incentive that encourages the search for victory instead of a draw and the possibility of defeat.

As afore-mentioned, the rules applied to football are reflected with more intensity in the highly competitive chess world. Firstly, because both in chess and football, unlike basketball, as we previously remarked, it is possible to play not to lose. Furthermore, and most importantly, with the current scoring system, playing not to lose can be the best strategy for both adversaries in a chess game. In chess league tournaments it often occurs, depending on the ranking of the player and his adversaries in the competition, that the strategies of two players in a game can lead to each of them realising that the best choice is to reach a draw.

This behaviour has been studied in Games Theory: John Harsanyi, Reinhard Seiten and John Nash were awarded the Nobel Economic Prize in 1994 for a study based in the Games Theory using chess as a theoretical model for taking decisions. From the several decision strategies, the one that consists in minimising the maximum possible loss is a solution called Minimax.When the players play according to the Minimax theory, it is due to the risk of incurring a bigger loss than the benefits that the victory could give. Therefore, the game will end with a high probability of drawing.

In others words, if both players independently arrive at the conclusion that the best strategy to guarantee a safer position is to reach a draw without taking any risk and play consequently in order to reach this result, then draws are practically unavoidable. This is evident even before starting the game. At other times, players are determined to assume a higher risk and do not play defensively. However, when during the game they find themselves in an unsteady position then the Minimax strategy appears and the game ends with a draw in the middle of the game. Sometimes adversaries persistently fight for the victory up to the end, as they do not have “external” determining factors. Although the games end with a draw, they have been an example of combat and sportsmanship.

The following charts demonstrate what occurred in the Mexico World Championship and in the main world tournaments during the years 2006-2007:

Sixty one percent of the 532 games that took place in these tournaments have ended in draws, and the performance is more or less the same in all of them. Further on, we will analyse in greater detail the competitive performance of each of them.

We will define games that end in a draw with scarcely a fight, in other words without fighting enough (in some cases without fighting at all, for example, games finishing in less than 15 moves) as those that have ended in draws in less than 31 moves. We could call draws with a number of moves between 31 and 45 “semi-fought draws”, and those with more than 45 moves we could call “fought draws”.

The percentage of draws without a fight rises up to a 27% over the total played games. It is important to note that here there are significant differences. In the Sofia Tournament, only 3% of games in 2006 and 7% in 2007 were drawn before 31 moves. Sofia also has the highest percentage of games that ended in draws in more than 45 moves, 23% in 2006 and 33% in 2007.

Josu Fernández is and economist and graduate in statistics and operative research. He is the Organisation Director of the International Chess Festival “Villa de Bilbao”.

The origin of this great result is what has become known as the Sofia Rule which takes its name from being the first implemented in this tournament. This Rule mainly indicates that players are not allowed to offer draws directly to their opponents. Draw offers are allowed only through the arbiter in the following three cases: triple repetitions of the position, perpetual check and in theoretically drawn positions.

The Sofia Rule is without doubt a great advance in the chess world, but more is needed, since in our opinion the number of draws in less than 45 moves continues to be excessive. Games must be in the framework of sport competition and draws can only be made after a great fight between the players.

The Sofia Rule guarantees that draws can not be agreed, but does not ensure that players play to draw, play without taking risks, or that both players play with the intention of reaching a draw, therefore arriving at a balanced situation that will obviously lead to draws. In other words, short draws without fighting can be avoided by public agreement between both players. Nevertheless, the fact remains that both players could develop a conservative strategy according to the methodology Minimax that leads inexorably to a theoretical drawn position.

Mark Galeck, Sunnyvale, California

Hello, I am a PhD in Theoretical Mathematics by training, and so perhaps I have some insight into the somewhat abstract problem of scoring the game of chess. As some people point, the system used in the Bilbao tournament (3/1/0) may encourage swapping wins, but also, the ratio 3 to 1 of winning to drawing is arbitrary. Why not 4? As an aside, this ratio is the only distinguishing characteristic of such a system - some people propose systems such as 2/0/-1, without realising that mathematically this is exactly equivalent to 3/1/0.

OK, here is my proposal. To prevent possible win swapping, one should have 2 draws equal one win, I think. In other words, you always split one point between white and black. But in case of draw, not evenly! Black gets x, white gets 1-x, and x is probably more than 1/2.

I think this will reduce the number of draws. Why? I think if white gets less than 1/2 point for a draw, white will fight harder and attack more aggressively. This is comparable to a situation, currently, where one side really needs a win and pushes for a win. I don't have the statistics, one would have to study this, but I think, in cases currently where one player really needs a win and pushes for it, if you look at such games, I bet that the percentage of draws in such games is lower than in all games (and the win is not necessarily for the player who chases it). Correct me if I am wrong.

OK, how to determine x? This is a separate problem, and the best and most elegant way to solve it, is to put it up for auction. Suppose Kramnik and Topalov are to play, and we want to decide x. Both players submit what they think is the fair value for x. Suppose Kramnik thinks black deserves .7 points for draw, and Topalov, being a more aggressive player, thinks that .6 points for black is the right amount. OK, then we assign the average, .65 points for black draw (and .35 for white), and Topalov plays black. Both players are happy: Topalov likes to play black and get even more than he wanted; Kramnik likes to play white because he too gets more than he wanted (.3 for white). If they agree exactly on x, the colors are drawn randomly and both will be happy too.

This system would have another advantage - most tournaments nowadays are with even number of players, and half of them are penalised by having one less game with white. The above system would completely eliminate that problem. In other words, the advantage of playing white in chess would disappear completely, by using the auction system.

The similar system can be used in "sudden death" games - right now often a tiebreak in a match is decided where white has, for example, 5 minutes to black 6, and white must win. The ratio of 5 to 6 is arbitrary and may not be fair, who knows? Let it be up to auction - say we play a game with 5 minutes for white, and both player submit, how much is fair time for black. Just like above, we play with the average of their proposals, and the person who wanted less time for black, plays black. This is far superior to the current system.

Mr. Friedel, I admire you very much for what you are doing to the world of chess, and you can use my proposal in any way you want, including submitting to any deciding body (or dumping it); all I ask is that you include my name, but no "copyright" of any kind, the idea is freely given. Whatever your opinion, I think you have to say, my idea is very elegant (like the best of mathematical proofs!).

Bruce Harper, Vancouver, Canada

I read the e-mails about draws with interest. In Vancouver we have experimented with a system of "overtime" games (as in hockey – what can I say?), which can be employed in chess using the following rules:

1. At the start of each round, each player receives a set amount of time (such as 90 minutes), plus a 10-second increment each move.
2. If the first game is drawn, each player receives one-third of a point.
3. The players then switch colours and play a second game, using their remaining time. If this playoff game is drawn, the players again switch colours and play another game, using their remaining time, repeating this as often as necessary until either:
        a. One player wins, which ends the round; or
        b. The time allocated for the round has elapsed.
4. If one player wins a playoff game (3.a.), that player receives an additional one-third of a point. The other player still receives one-third of a point.
5. If there is no decisive result before the time limit for the round expires, each player receives only one-third of a point, and the remaining one-third of a point is not allocated.
6. The five possible results of each individual round are 1:0 or 0:1 (if the initial game is decisive); 2/3:1/3 or 1/3:2/3 (if a playoff game is decisive); or 1/3-1/3 (if there is no decisive result).

In practice, there is always a decisive game. Without increments, this is ensured. In other words, if you draw, keep playing until you don't (for the other 1/3 of a point). Cautious players would net at least 1/3 a point each round, and maybe 2/3, but they would be passed by those who won the first game (which would be worth an entire point).

Iman Khandaker, Watford

I'm amazed by the number of responses from chess players, who appear to have no friends. They seem to dismiss the idea of collusion because they cannot believe that anyone could show sufficient trust to lose first. A concrete example of someone throwing a half point to honour his word with a prearranged (but not concocted) draw:

Miles,Anthony J (2585) - Christiansen,Larry Mark (2575) [C42]
San Francisco San Francisco, 1987
1.e4 e5 2.Nf3 Nf6 3.Nxe5 d6 4.Nf3 Nxe4 5.Nc3 Bf5

Miles spotted 6.Qe2. He spent time polishing the square, waited until Christiansen blushed ... and played Nxe4 anyway. The game continued 6.Nxe4 Bxe4 7.d3 Bg6 8.Bg5 Be7 9.Bxe7 Qxe7+ 10.Be2 Nc6 11.0-0 0-0 12.Re1 Rae8 13.Qd2 Ne5 14.d4 Nxf3+ 15.Bxf3 Qd7 16.c3 b6 17.Rxe8 Rxe8 18.Re1 Rxe1+ 19.Qxe1 Kf8 20.g3 ½-½. Incidentally Anand lost to Zapata with 5...Bf5 in 1988, and eleven other players fell into the same trap in the intervening years.

Aside from friendship there is a logical reason not to break an agreement to collude. Under a 3-1-0 system colluders would have a major long term advantage over fair players, so breaking an agreement might win you one tournament, but this advantage would be lost for all subsequent events.

As for those who dismiss collusion on the basis of personal pride – don't professional players concoct sharp looking games which peter out into theoretical draws? And don't all professional players know what is happening when they read the scoresheets? These concoted games do not contain a single competitive move and are just as dishonest as concocted losses – though commonly accepted by organisers because they aren't obvious to the amateur.

I don't believe that the success of the 3-1-0 system in soccer is any guarantee of sucess in chess. It is a great deal more difficult to corrupt several dozen multi-millionaires subjected to global TV scrutiny than it is to corrupt two or three chess professionals living out of a suitcase.

However, Joseph Ellis makes an excellent suggestion his scoring system reflecting statistical expectation:

Draw with white = .45 points
Draw with black = .55 points
Win with white = 1.0 points
Win with black = 1.1 points
Loss with white = –0.1 points
Loss with black = 0.0 points

This doesn't just address the draw issue, it would sort out tiebreaks and make the rating system more accurate by taking into account any imbalances in drawn colours.

Evan Post, Philadelphia, PA, USA
It's easy to exorcize the hobgoblin of "GM draws" in tournament chess without grossly distorting the historic culture of the game. Simply require the (significantly) higher rated player to play for a win! Award one point for a win and half a point to the lower-rated player if the game is drawn, and zero points to the loser or higher-rated draw player. In cases of little or no rating difference award each player half a point.

Ingemar Falk, Stockholm
My proposal: players who draw before 30th move have to play the next round with just half the thinking time. For example: 40 moves in 90 min and 30 increment will be 45 min and 15 inc. Those who agree draw before move 30 for the second time in row have to play the next round with time 22.30 inc 7.5 next round and so on. If you win or lose or draw a game after 30th move you will recieve the original time 90/30 the next round. The rule for this can also be set above 30 move, say 40 or 45.

Wijnand Engelkes, Zeist
In a tournament where the Bilbao 3/1/0 system was used I've seen two players in a drawn postion flipping a coin to determine who had to resign. Certainly at the bottom of the tournament this is a threat: you can earn 1.5 point on average by flipping a coin in drawn situations, instead of the one point you get for the draw.

Knut Jarle Hjørnevik, Bryne, Norway
A good way to solve the problem with "grandmaster draws" is to give the players 0.1 points each if they spend less than 10 moves on the entire game, 0.2 points if the game lasts for less than 20 moves, 0.3 points if the game lasts for less than 30 moves. etc. Only when a game lasts more than 40 moves the players are given 0.5 points. This would probably help the fighting spirit among lazy chessplayers.

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