JSM 2011 Online Program

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Abstract Details

Activity Number: 329
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistics in Sports
Abstract - #302054
Title: The ABCs of Xqjkz: A New Scrabble Rating System Based on a Statistical Model for Tile-by-Tile Play
Author(s): Kenneth Shirley*+
Companies: AT&T Labs Research
Address: 180 Park Ave, Florham Park, NJ, 07932,
Keywords: Scrabble ; Rating system ; Hierarchical Bayes
Abstract:

We develop a statistical model for Scrabble in which we model the number of points scored on each turn as a function of the individual tiles in a player's rack. The result is a detailed model that describes a player's Scrabble skill in terms of dozens of player-specific variables related to interpretable Scrabble skills such as how often a player plays each tile, how many points he earns per tile, and how much he augments his score by incorporating tiles already on the board into his play. Our data comes from a public database of about 600 games of Scrabble played at the expert level. We find that most of the variation in points scored is explained by the frequency with which tiles are played and the frequency with which players get a "bingo" (playing all 7 tiles in the rack on a single turn). The player-specific model parameters can be used as the basis of a much more detailed player rating system than is currently in use. This work also sheds light on the degree to which the outcomes of Scrabble games depend on the randomness inherent in drawing tiles, as opposed to player skill. The largest component of the model consists of a hierarchical Bayesian logistic regression model.


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