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# Statistical Pittfalls and Lessons from a Model of Human Decision Making at Chess

## April 2, 2018 @ 2:00 pm - 4:00 pm

**Statistical ****Pittfalls**** and Lessons from a Model of Human Decision Making at Chess**

**Speaker****:** Professor Kenneth Regan

**Date:** April 2nd (Monday), 2018

**Time:** 2:00 PM – 4:00 PM

**Venue:** Davis Hall 338A

**Description:** We describe a predictive analytic model of human move-choice at chess. The sole inputs are numerical values given by strong computer chess programs to all legal moves in millions of chess positions from competitive games by players of all levels. Whereas the game of Go did not have reliable numerical estimation of position value prior to DeepMind AlphaGo, chess programs pump out values at successive rounds of increasing depth of search that quickly surpass the estimation of all human players. The model has only two parameters describing the nature of a (human) player; the struggle to add a third will occupy some of the talk. The model’s sole equation asserts that the ratio of the logarithms of the probabilities of of a given move m and the best move m* is given by a fixed function of the parameters and a certain scaling of the difference in value between m* and m. The equation is fitted by two levels of nonlinear regression. The outputs are projected probabilities for all moves m and both projections and confidence intervals for aggregate stats such as the percentage of agreements between a human player and the computer program and the numerical error judged by the latter when the former deviates. These yield z-scores for hypothesis tests which have been used in cases of alleged or confessed cheating by human players with computers in competitions sanctioned by the World Chess Federation (FIDE) and national federations.

The model and large data have yielded empirical regularities of human play. This talk will emphasize (1) how some of these regularities run so much counter to reasonable modeling expectations that they constitute examples of data-modeling pitfalls, and (2) the model’s wide scope for cross-validation of statistical methods. Two of the pitfalls owe to quirks of the algorithms used by chess programs: stable sorting and search pruning. A third, discovered only this year, yields a hypothesis about deep complexity of games like Chess and Checkers that have frequent draw results versus those like Go and Shogi that do not. The model allows comparing many fitting methods, among which maximum-likelihood estimation has been consistently and demonstrably inferior. Its error bars are theoretical but some are based on assumptions that beg verification by empirical bootstrap methods. The issues will be framed in student-friendly discussion of statistical modeling and what your data means, including interpreting a regularity that allows skill to be inferred solely from moves on which the player made large mistakes