Tennis Tournaments
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Text length: 2,100 words
Excerpted from 'Lawn Tennis Tournaments'
By Lewis Carroll
, 1883
Talent is not enough - the rules of the competition determine the characteristics of the prize winners: the winners may be the best players, or there may be a significant random component
The structure of the space influences the results - something that seems intangible like the structure of a space can have dramatic and often unappreciated consequences
Keywords:
Tennis, competition, tournament, space, structure, talent, skill, luck, fairness, winner, loser, prize
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Summary
When we watch a sporting event like a tennis tournament we might hope for a favorite player to win and even feel upset if he loses. However, we don’t often question the rules of the tournament. Lewis Carroll, better known as the author of Alice in Wonderland, explains why the typical tournament structure often fails to award best players the top prizes and offers an alternative method.
In an elimination tournament, each player can only advance along a certain path toward the final. As each player moves through this space, the field is narrowed, until the top prizes are determined. The structure of the space critically influences who finishes well in the tournament. A competition that seems at first glance to be fairly structured to filter out the weaker players may, in fact, not be good at all at selecting the best competitors. In any competition it is not just skill and lucky breaks that determine the winners; the rules of the competition itself determine who will finish well. Many competitions are structured to correctly determine only first place; the second and third prizes are very much subject to chance.
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Introductory
At a Lawn Tennis Tournament, where I chanced, some while ago, to be a spectator, the present method of assigning prizes was brought to my notice by the lamentations of one of the Players, who had been beaten (and had thus lost all chance of a prize) early in the contest, and who had had the mortification of seeing the 2nd prize carried off by a Player whom he knew to be quite inferior to himself. The results of the investigations, which I was led to make, I propose to lay before the reader…
A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning…
A system of rules for conducting Tournaments, which, while requiring even less time than the present system, shall secure equitable results…
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A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning
Let us take, as an example of the present method, a Tournament of 32 competitors with 4 prizes.
On the 1st day, these contend in 16 pairs: on the 2nd day, the 16 Winners contend in 8 pairs, the Losers being excluded from further competition: on the 3rd day, the 8 Winners contend in 4 pairs: on the 4th day, the 4 Winners (who are now known to be the 4 Prize-Men) contend in 2 pairs; and on the 5th day, the 2 Winners contend together to decide which is to take the 1st prize and which the 2nd -- the two Losers having no further contest, as the 3rd and 4th prizes are of equal value.
Now, if we divide the list of competitors, arranged in the order in which they are paired, into 4 sections, we may see that all that this method really does is to ascertain who is best in each section, then who is best in each half of the list, and then who is best of all. The best of all (and this is the only equitable result arrived at) wins the 1st prize: the best in the other half of the list wins the 2nd: and the best men in the two sections not yet represented by a champion win the other two prizes. If the Players had chanced to be paired in the order of merit, the 17th best Player would necessarily carry off the 2nd prize, and the 9th and 25th best the 3rd and 4th! This of course is an extreme case: but anything within these limits is possible: e.g. any competitor, from the 3rd best to the 17th best, may, by the mere accidental arrangement of pairs, and by no means as a result of his own skill, carry off the 2nd prize. As a mathematical fact, the chance that the 2nd best Player will get the prize he deserves is only 16/31sts; while the chance that the best 4 shall get their proper prizes is so small, that the odds are 12 to 1 against its happening!
If any one thinks that, after all, we are merely introducing another element of chance into the game, and that no one can fairly object to that, let him try the experiment in a rifle competition. Let him interpose when the man, who has made the 2nd best score, is going to receive his prize, and propose that he shall draw a counter from a bag containing 16 white and 15 black, and only have his prize in case he draw a white one: and let him observe the expression of that rifleman's face.
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