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| Content Provider | ACM Digital Library |
|---|---|
| Author | Scheid, Francis |
| Abstract | Suppose that two competitors A and B have symmetric score distributions. If B's mean score is greater than A's subtract the difference in means to obtain B's net scores. The result is suggested by Figure 1, in which B's net scores show greater variability. In a particular competition the actual net scores shot might be a and b. Assuming the objective is to score low, A wins this match. But for any such pair of scores there is a symmetric pair a', b' of equal probability for which B is the winner, so clearly each player ought to win Just as often as the other. The competition is fair. Put in another way, the mean score is a perfectly accurate measure of ability in this situation. The same can, of course, be said of the median. With B's game having wider spread there is the somewhat unfortunate fact that A can play his very best and still lose, but in compensation he can also play his very worst and still win. Things are about as fair as a cruel world allows. In most types of competition scores are not symmetrically distributed. In golf, for example, it is well known that poor scores range farther from the mean than good scores do, and more so for weak golfers than for strong ones. The question arises, what is then the most accurate measure of ability and do the mean and median still perform well? To find the answers to this and related questions in a golf setting the following experiments were carried out. |
| Starting Page | 889 |
| Ending Page | 896 |
| Page Count | 8 |
| File Format | |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 1978-12-01 |
| Access Restriction | Subscribed |
| Content Type | Text |
| Resource Type | Article |
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