Multi-opponent James functions
-
Christopher N. B. Hammond
and
Warren P. Johnson
Abstract
The James function, also known as the “log5 method”, assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, explores the analogous situation where a single team or player competes simultaneously against multiple opponents.
(Communicated by Tomasz Natkaniec)
Acknowledgement
We would like to thank Maximillian C. W. Bender for his many valuable suggestions, particularly relating to the structure of Section 4.
References
[1] Chartrand, G.—Zhang, P.: A First Course in Graph Theory, Dover Publications, Mineola, NY, 2012.Search in Google Scholar
[2] Hammond, C. N. B.—Johnson, W. P.—Miller, S. J.: The James function, Math. Mag. 88(1) (2015), 54–71.10.4169/math.mag.88.1.54Search in Google Scholar
[3] James, B.: 1981 Baseball Abstract, self-published, Lawrence, KS, 1981.Search in Google Scholar
[4] Luce, R. D.: Individual Choice Behavior: A Theoretical Analysis, John Wiley and Sons, New York, 1959.Search in Google Scholar
[5] Luce, R. D.: The choice axiom after twenty years, J. Mathematical Psychology 15(3) (1977), 215–233.10.1016/0022-2496(77)90032-3Search in Google Scholar
[6] Stamatis, N.: On the representation of involutive Jamesian functions, Math. Slovaca 68(6) (2018), 1421–1430.10.1515/ms-2017-0191Search in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
