A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation.
A Note on the Pythagorean Theorem of Baseball Production
โ Scribed by John Ruggiero; Lawrence Hadley; Gerry Ruggiero; Scott Knowles
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 93 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0143-6570
No coin nor oath required. For personal study only.
โฆ Synopsis
Recent analyses of baseball managers' performances have employed the so-called Pythagorean Theorem' of baseball. This theorem' states that the ratio of wins to losses can be approximated by the square of the ratio of team runs scored to opposition runs scored. Recent publications assume this approximate relationship can be used to evaluate managers; implicit is the additional assumption that the Pythagorean relationship constitutes a production process. It does not. This paper derives the exact relationship between the wins, losses, runs scored and runs allowed. The result is an identity. We conclude that application of the `Pythagorean Theorem' for manager evaluation is inappropriate.
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