jueves, 14 de octubre de 2010

Scientific studies dispute rules in chess and football

Two studies by a Professor in Economics, presented today in Bilbao, dispute certain rules in both chess and football. The studies warn against the “lottery” of the coin toss to decide who starts with the white pieces in a chess tournament or which team shoots first in a tiebreak penalty shootout.

By Gorka Bravo, Bilbao Masters Final

  • The Bilbao organizers of the Grand Slam Chess Masters Final have presented these studies, which will be sent to the main local and international football and chess organizations.
  • University Lecturer Palacios-Huerta has studied both the great chess championships and all of the penalty shootouts in the history of the world’s main football competitions.
  • These studies could have an impact on the rules used in future competitions in these two sports.

Bilbao, October 14, 2010. The organizers of the Grand Slam Chess Masters Final, which is being played for the third consecutive year in Bilbao, have presented two studies carried out by Professor of Economics at the prestigious London School of Economics and Doctor of Economy from the University of Chicago, Bilbao’s Ignacio Palacios-Huerta. These scientific studies, carried out in the disciplines of chess and football, warn against the “lottery” of the coin toss to decide who starts with white in a chess tournament or which team shoots first in a tiebreak penalty shootout.

The traditional way of deciding the order in a penalty shootout in football or who begins a chess match with white, is a coin toss. The winner of the toss shoots first or plays the first game with white. In the second penalty or the second game it becomes the other party’s turn. The order keeps being reversed in this way until all the penalties have been taken or the number of games set for the competition have been played.
The premise of this system, which has been in use for decades in all types of sporting competitions throughout the world, is that a coin is impartial, that it does not favour either of the competitors and that it simply decides an order in which the logical thing to do is to reverse the chances.

However, this scientific study questions this premise. If the order is reversed, the coin does not give each player or team a 50% chance of winning, but instead these chances are distributed 60-40. In other words, whenever the order is reversed, which is what ends up happening, the coin systematically gives a 20% advantage to the team shooting first in the penalties or the player who plays with white first, at least in football and chess, as proved by these studies.

The reason is both subtle and logical and lies in the psychology of the players competing at the highest level. Shooting first during a penalty shootout or playing with white in a chess tournament of many matches, gives one contender a greater chance to move ahead on the scoreboard, and this has considerable psychological effects on players, even elite players, which fundamentally helps their performance.

Research and findings

Ignacio Palacios-Huerta, native of Bilbao and Professor of Economics at the London School of Economics and Doctor of Economics of the University of Chicago (His doctoral thesis was supervised by Nobel Prize winner Gary S. Becker), has studied all of the penalty shootouts in the history of the world’s main football competitions at the selection level (World, Eurocopas, etc.) and team level (Champions League, UEFA Cup, English Cup, Copa del Rey, etc.). To his surprise, “the results show that the team shooting first in a shootout won 60% of the time and the one shooting second, 40%. The hope would be that there would not have been any difference or if there were that it would be minimal. In the end there is always talk of the penalty lottery, as if it were 50-50. Penalties are not a lottery, at least not a 50-50 lottery, but more of a 60-40 one where one out of the two has 20% more tickets, specifically the one shooting first. In other words, tossing a coin and reversing the order introduces a systematic and unfair 20% bias. This is a very significant difference and means that the players are not the only ones playing, but the coin as well. The effect is so geat that the defining moment of a shootout happens even before it begins– at the coin toss”.
Ignacio Palacios-Huerta
Ignacio Palacios-Huerta: 'The players are not the only ones playing, but the coin as well.'
The study containing this discovery (written together with José Apesteguía from the Pompeu Fabra University) is titled “Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment,” and will be published next December in the most prestigious academic journal of economic research, the American Economic Review.

After studying the penalty shootouts, Professor Palacios-Huerta studied a similar situation in which the order is reversed and determined by a coin– chess, through the evaluation of thousands of games played in various rounds. If the situation is in fact similar, there are reasons that would make one think that the psychological effect of the coin and of the reverse in order should not exist:
  1. Unlike footballers, chess players are carrying out a cognitive or intellectual activity, and thinking is very different from kicking a ball.
  2. The subjects play for a long period of time (a match can last up to 4 hours or more), while a penalty only lasts a few seconds.
  3. In chess, at most one match a day is played, and the players have time to rest, calm down and prepare for the next day’s match along with a team of reviewers and trainers. Only a few seconds pass between penalties whith hardly enough time for the psychological effects of emotions (being ahead or behind on the scoreboard) to disappear.
  4. Unlike penalties, which are scored 80% of the time, in chess white wins 28% of matches, black, 17%, and the majority (50%) of matches end in a draw. That is, on most occasions, the player playing as white in the second match ends up drawing and therefore the advantage of playing as white is minimal.
“For these reasons, I was hoping to find that choosing the order by tossing a coin would have no effect in chess. In fact I was convinced it would be that way.” states Palacios-Huerta. The study “Pawns of Emotions: Psychological Elements in Cognitively Sophisticated Humans” (written together with mathematician Julio González Díaz from the University of Santiago de Compostela) finds that the effect is again 60-40– the player starting the first match with white has a 20% advantage over the one who the coin decides must play with white second. Moreover, “the effect is greater the more similar the players are in quality, reaching up to a 35% difference in favour of the person playing the first match as white in the World Championships and with elite players” adds Palacios-Huerta.

The results of these studies could affect the rules used in future sporting competitions throughout the world.
Magnus Carlsen playing football on the rest day of the May 2009 MTel Masters
Magnus Carlsen playing football on the rest day of the May 2009 MTel Masters


Can anything be done? Is there anything fairer than tossing a coin and reversing the order?

Fortunately the answer is in the affirmative. Consider the hypothetical situation of a Spain-Holland World Cup final which ends in a draw at the end of regulation time. Spain wins the toss and shoots first. If shooting first gives an advantage to one of the teams (normally placed in front), the second penalty must be taken by the opposing team. All is well up to this point, the advantage is offset by reversing the order, such as is done in the current system.

But what should be done on the third and fourth penalties?
The reasoning that should be followed is the same as for the first two. If the order of the first two penalties gives an advantage to one team, this advantage should be compensated by reversing the order again on the third and fourth penalties. That is, the order of the first four penalties should be Spain-Holland-Holland-Spain instead of Spain-Holland-Spain-Holland, as is done in the current system. And if we were wrong and the order gave no advantage to either team? Then changing the order would have no effect. That is, changing the order of the 3rd and 4th shots would only have positive effects because it would minimize any possible psychological effects of the results of the coin toss.

What should be done for the next four penalties, the 5th to the 8th?
The answer is the same. The same reasoning should always be followed. The 5th to 8th penalties should be in the reverse order of the first four, that is Holland-Spain-Spain-Holland, and so on. The order would have to be changed every 2 penalties, then every 4, then every 8, etc. The solution of modifying the order in this way minimizes the effect that the coin might have.

This solution is also applicable to chess and to who must play as white or plack in every game of a match.
But is it feasible? Would the public be able to understand the reason for these changes in order?
“I supppose not. The thing is there is a feasible solution that is very easy to implement and that the public will understand immediately– reverse the order once and then repeat the sequence. That is, do Spain-Holland-Spain-Holland (S-H-H-S) in the first 4 penalties and then repeat it in the successive penalties in groups of four– S H H S – S H H S – S H H S etc. That way there will be a sequence just like that of tennis for serving in the tie-breaks– the first player serves once and from then on each player serves twice in a secuence like this one– S H H S S H H S S H H etc”.

The organizers of the Bilbao Grand Slam Chess Masters Final will communicate these studies iabout football and chess within the next few weeks to the main governing bodies of both sports at the local and international levels: FIFA, UEFA and the Spanish Football Federation on one hand, and the European and Spanish Chess Federations, as well as the Grand Slam Association itself, to which Bilbao belongs. These institutions will be urged to evaluate the empirical evidence contained in these studies and it will be proposed that they implement the system that currently exists in tennis, with the aim of organizing the order of play in an optimal and balanced manner.

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