The (almost really) Complete Works of Lewis Carroll

To the Editor of the St. James’s Gazette

Sir,—Players of Lawn Tennis, and those interested in other kinds of sport in which Tournaments occur, have no doubt often realized the very unsatisfactory way in which the prizes are at present adjudged. I propose to deal with the subject mathematically, and to point out, first, the extraordinary injustice of the existing laws; and secondly, a method of adjudging the prizes which would, as I hope, really carry out the principle of detur digniori.

Suppose there are 32 competitors. These are arranged as 16 pairs for the contest of the first day: on the second day, the 16 winners are arranged as 8 pairs, the losers being excluded from further competition: similarly, on the third day, there are 4 pairs, and the 4 winners (supposing 4 prizes to be given) are now known to be the price-winners. In order to settle their claims, 2 pairs contend on the fourth day, and the 2 winners have a final contest on the fith day, to decide which is to take the first prize and which the second: the two losers have no further contest, since the third and fourth prize are of equal value.

The injustice of this system needs few words to prove it. Any one of your readers, who will write down 32 numbers, and bracket them in 16 couples, and then, after marking the supposed winner in each couple, will bracket these winners in 8 couples, and so on, will easily convince himself that the result is really as follows: if the original list be divided into 4 quarters, the best man in each quater is a winner of the 4 prizes—the best in each half wins one of the first 2 prizes—and the best in the whole list (it would indeed be a strange system which failed to secure this!) wins the first prize. Now suppose the original list chanced to be arranged in the order of merit: in this case it will be found that the 17th best player gets the second prize, while the 9th and 25th best get the third and fourth!

This, of course, is an extreme case: but, in every case, the 2nd best player has only 16-31ths of a chance of getting the prize he deserves, and the chance, that the best 4 players shall get their prizes, is almost exactly 19-250ths: i. e. the odds are more than 12 to 1 against it!

Now, if any Lawn-Tennis-player is content that the element of pure chance should so largely enter into a contest of skill, I have nothing to say against it: every one to his taste: but to those who think, with me, that a Tournament would give more general satisfaction if the prizes were always given to those who played best, the following suggestions may prove interesting.

It is quite unimportant how the names are bracketed for the first set of contests: but, after that, the contests should be arranged thus:—the 16 winners (I am taking, as before, 32 competitors and 4 prizes) should be bracketed together, and the 16 losers should also be bracketed together. A list should be kept of the players, and against each man’s name should be entered the names of those who have been proven superior to him, either by actually beating him or by beating those who have done so (e. g. if A beats B, and B beats C, both A and B are “superiors” of C). The contests should all be arranged on the principle of bracketing together, as far as possible, those who have the same number of superiors but have no common superior (e. g. if A has been beaten by K and L, B by K and R, C by L and S, D by S and T, we should bracket A with D, and B with C). It would not be at all necessary to have only one set of contests each day: as soon as any court was finished with, the committee would assign it to any two disengaged players, who could be properly bracketed together.

The 4 prizes would be assigned thus:—so soon as any player had 4 superiors entered against his name, he would be struck out of the list: so soon as all, but one, had at least one superior, that one would be marked as “first prize:” of the remainder, so soon as all, but one, had at least 2 superiors, that one would be marked as “second prize:” and, of those then remaining, so soon as all, but two, had at least 4 superiors, those two would receive the remaining prizes.

This system would require many more contests than the present one does, so that there would be much more spectacle for the public to see: but, since the courts would usually be filled up as fast as vacated, I do not think that the whole Tournament would be likely to occupy more time than under the present most unsatisfactory system, which may often result in the 2nd, 3rd, and 4th best players all returning home empty-handed, while their prizes are carried off by players known to be far inferior the them.—I am, Sir, your obedient servant,