Variance Decomposition and Replication In Scrabble: When You Can Blame Your Tiles?

TL;DR

This paper introduces a new tile drawing method in Scrabble that enables consistent replication of tile patterns across matches, facilitating better comparison of player performance and analyzing the impact of tile variance on game outcomes.

Contribution

It proposes a novel tile drawing scheme for Scrabble that allows for replicable tile patterns, enabling more accurate assessment of player skill and tile influence.

Findings

Variance from tile order matches board pattern variability

Tile placement significantly affects player scores

Simulations show the impact of tile distribution on game outcomes

Abstract

In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match against a superior player, and more difficult to determine the true ability of a player in a tournament or contest. I propose a new format for drawing tiles in a two-player game that allows for the same tile pattern (though not the same board) to be replicated over multiple matches, so that a player's result can be better compared against others, yet is indistinguishable from the bag-based draw within a game. A large number of simulations conducted with Scrabble software shows that the variance from the tile order in this scheme accounts for as much variance as the different patterns of letters on the board as the game progresses. I use these simulations as well as the experimental design to show how much various tiles are able to affect player scores depending on their placement in the tile seeding.