On Any Given Sunday: Fair Competitor Orderings with Maximum Likelihood Methods
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This article addresses the analytic problem of obtaining fair and accurate comparisons among competitors when many pairs of them have never met and where the average quality of opposition faced may vary widely. The context studied is the National Football League's regular season of 1973. A maximum likelihood methodology is developed which simultaneously: (1) ranks all teams and (2) estimates the probabilities of upsets of various sizes. The methodology is compared with alternative approaches and is modified with experimental extensions.