A response to Chew's "Catastrophic Outrage"
16 Jan 2013 - Joshua Lewis
John Chew, copresident of the North American Scrabble Players Association, recently replied to my post on Valett, which suggested altering the point values of some Scrabble tiles based on a statistical analysis of tournament-legal Scrabble words. Chew's post highlights how an intelligent and skilled Scrabble player might misunderstand what Valett does and its intent. I'd like to clarify these issues, if possible, and show how Valett's results suggest changes to Scrabble that are very much in line with its rich tradition and dynamic play.
Fundamentally there are two related but separate aspects of Scrabble: the structure of the game (its rules, board, tile distribution, word list, etc.) and the play of the game (rack composition, board position, remaining tiles in the bag, strategy, etc.). Because essentially all of the formal analysis of Scrabble (mainly via the excellent software package Quackle) is on the play of the game, John mistakenly conflates the goals of Valett and Quackle, and tile value and equity value, when they in fact deal with two separate domains of analysis: structure vs play.
Valett puts two specific aspects of the structure of the game in harmony: the word list and tile values. One could also revisit tile distribution, as John suggests, but that relationship is a bit less formal since you need to artificially limit the number of S tiles.
We could run Quackle on a version of Scrabble where its structure (tile point values) have been changed as per Valett's suggestions, and you'd end up with different equity values. So the concept of equity value and tile value are closely related (tile value partially determines equity value), but they're absolutely not interchangeable. Tile value is a basic component of the structure of the game, and equity value is a calculated value based on extensive simulation of game play taking into account rack composition, board position, and so forth. John ignores the distinction between these values in his reply, "Given that the 'I' currently has a face value of 1, if you wanted to create a 'fair' SCRABBLE game that didn't penalize players for drawing an 'I', you'd want to increase the face value by 2 points to 3." Changing some tile values in Scrabble wouldn't alter equity values in the direct manner Chew suggests.
Later on, Chew mischaracterizes Valett's tile frequency by word length analysis, "Valett's requirement that you specify the rates at which words of each length are played is also problematic..." When weighting frequency by length, Valett is not making any assumptions about how frequently words of those lengths are played, but rather how important words of different lengths are given the rules of Scrabble. Two- and three-letter words are important in Scrabble because it is a crossword game, and the presence of a letter in a two- or three-letter word makes that letter easier to hook off of existing letters on the board. Similarly, because there is a substantial bonus for playing all the tiles in one's rack (which has seven tiles), seven- and eight-letter words are particularly powerful. Without saying anything about how they might be played, Valett allows one to weight the frequency of letters in these word lengths more highly than at less notable lengths like five or twelve.
Chew is also a bit disingenuous here, "If you did this, you'd reduce a little bit of the luck of the draw, but at the same time you'd be reducing the skill involved in recognizing which tiles are good or bad and playing accordingly. You'd end up with a game that was a little closer to just rolling a die to determine the winner." In fact, reducing the luck of the draw by aligning tile values more closely with the word list (and causing the related changes in equity value and game strategy) would make the game less about luck and more about skill, and therefore further from just rolling a die to determine the winner.
Tournament players benefit from a system with a little less luck because it makes tournaments more accurate. While something like Elo is reliable in a game with a lot of luck when it draws from a very large sample of games, in tournaments only a certain number of games can be played due to time and stamina constraints. So the more luck in the game, the less accurate tournaments are in determining who's the best.
Now, one might object that if I want to reduce the luck in the game, why aren't I suggesting to remove the blanks, or have a computer distribute tiles to player's racks fairly. Well, I like Scrabble, and a game without blanks isn't Scrabble. Alfred Butts clearly went to a lot of trouble to get the structure of the game to reflect English use in the 30s, but he wanted the game to have entertaining aspects like blank tiles and the luck of the draw. Slightly modifying tile values to track changes in the set of legal Scrabble plays respects this tradition and maintains the lucky elements of the game, such as drawing a blank, and the unlucky, such as drawing all vowels.
Valett is an attempt to keep the intentional luck in the game, and remove the unintentional luck that has crept in over time as the use of English has changed. I hope Chew and I might see eye to eye on that goal, and I look forward to further spirited discussion.
Joshua Lewis is a cofounder of Ost with Galen Wolfe-Pauly. He received a PhD in Cognitive Science at UC San Diego in 2011. Both his academic and entrepreneurial pursuits help folks to better interact with their data.