What’s a Z Really Worth?
Why efforts to assign Scrabble tiles their “real value” miss the point of the game.
(As with Lexiko, Butts made and sold Criss-Cross Words from his apartment with no success. In 1948, he sold its rights to a small businessman, James Brunot of Newtown, Conn., who renamed, redesigned, and manufactured the game. Five years later, Scrabble became a national sensation. Butts received royalties until 1976. He died in 1993.)
Courtesy National Scrabble® Association.
Lewis and Eifling performed a statistical exercise that can help lay players reconsider particular letters based on the overall lexicon. “Get rid of your J and your Q as quickly as possible, because they’re just damn hard to play and will clog your rack,” Eifling concluded, correctly. A deeper dive would involve valuing each letter based on how it is actually used in Scrabble, because words of certain lengths or lexicographic properties might be more or less useful when playing the game. Lewis’ program didn’t consider, for instance, longer combinations of letters, or the importance of four- and five-letter words. “The game isn’t about drawing words at random from the dictionary,” Chew wrote. “It’s about actually finding places to play them on the board.”
Chew’s and O’Laughlin’s approach to reconsidering the face values of the tiles involves adjusting their equity values. Equity value in Scrabble is similar to advanced baseball stats that compare players to an “average” replacement. Scrabble theorists have been calculating this stat—let’s call it VORT, or Value Over Replacement Tile—since the 1980s. “The Barry Bonds of the Scrabble set,” O’Laughlin said, is the blank, with a VORT of about 25 points. That means a blank plus six random tiles will likely net 25 more points than seven random tiles. At the other end, the Q has the lowest VORT, about -7 points.
To perform a revaluation using VORT, Chew and O’Laughlin would shift the equity value of positive tiles downward and negative tiles upward, have Quackle play thousands of games against itself using those new values, and keep adjusting the values and making Quackle play until the equity of each tile approaches zero. At that point, the tiles could be given corresponding face values, which would be based on how Scrabble is played by the world’s best player.
Chew and O’Laughlin said they aren’t interested in conducting that analysis because it would be time-consuming and wouldn’t add to the understanding of the game. But they have begun trading emails with Lewis, who told me he’s eager to work with the Scrabble quants to learn more and find ways to study the statistical properties of the tiles further. Which shows how, in contrast to the way this story is being framed in the media—Scrabble Controversy!—it’s really just a bunch of curious living-room players and super-smart computer guys swapping ideas about game theory and analysis. Lewis isn’t demanding that the game’s manufacturers change anything, just performing an interesting statistical and intellectual exercise.
Still, he does believe, as he wrote in a new post on Wednesday, that tweaking Scrabble’s tile values would “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.” He’s perplexed as to why competitive Scrabble players wouldn’t favor mediating some of the luck, because that might make the results of games and tournaments more accurate.
I can answer that. Because Scrabble players understand that the game’s inequities are on the margins, and that figuring them out is a crucial part of learning to play well. And we respect, and are in fact awed by, how Alfred Butts, without the benefit of computer programs and language databases, came damn close to nailing both letter distribution and letter valuation, and in the process created a game that exquisitely, often maddeningly, balances skill and luck. Making the X worth six points won’t improve on that.
Correction, Jan. 19, 2013: This article originally misspelled the name of Alfred Butts’ first word game, Lexiko.