"More broadly, I think Valett can provide the foundation for answering other interesting questions in word games, such as how to quantify the difficulty of Boggle boards."<p>Well, you can already quantify the difficulty of Boggle boards pretty well just by counting up all the points you can make on them (it's a small enough problem that you can do that pretty fast). I think the topology of the board is important enough (whether those I N and G blocks are next to each other or not makes a _big_ difference) that a simple histogram of letters isn't going to be sufficient.
For valuing Scrabble tiles, Valett also needs to include the representation of the letter in common prefixes and suffixes that can be prepended or appended to existing words. I believe that one reason that G is so playable is the common -ING suffix.
Competitive Scrabble player here :) -- the reason the C goes down to two points despite having no two-letter words is that it is actually a very good letter - basically, it's in a lot of high-probability bingos. In contrast, the V is one of the worst tiles in the game. It's telling that the Q stays at 10 despite QI -- the Q is by far the worst tile in the game.<p>In any case I've always wondered what the values of tiles should be if we were to use our current word list rather than the NY Times - thanks for this analysis. The blank is missing though, it would probably have a significantly negative value (-25 to -30?).<p>At the end of it all I'd rather keep the values what they are. Part of the beauty of Scrabble is the fact that there is chance. Despite the Z and the Q both being worth 10 points, one realizes pretty quickly how much worse the Q is.
as a competitive scrabble player, one mistake that I think he might have made is overweighting corpus-based probability versus game playability. his transition-in and transition-out weights are a good start, but there's also the fact that n+1 letter words that can be made by "hooking" (adding a single letter before or after) n letter words are far more useful than those that cannot. also the layout of the premium squares, and the letter distribution of the bag, factor into how playable certain tiles are. intuitively, at the least I'd expect one more point for the U, and for the V to catch up with the Z, though of course it's very easy to fool yourself about these things when using strategies based on the current letter values.
The problem, of course, is convincing us "old hat" Scrabble fanatics to change our minds on the point values. "Only 5 points for an 'X'? Nonsense!". Then again, competitive Scrabble and the original foundation of the game have little in common, methinks. Rather frequently I think about the Scrabble-likes (Words with Friends, Literati, etc) and the boards themselves. I am more curious about the designs and placements of the premium squares than the value of the tiles.<p>Interesting analysis though.
Little known is the fact that Butts actually did some manual fine-tuning of the frequencies he obtained from NYTimes. E.g., he decreased the number of S's to four in order to mitigate its affixability to almost every singular noun and enhance the gameplay.
One advantage of using the NY Times over the full OSPD for determining letter scores is that it gives precedence to words that people know and use. Casual players don't memorise lists of two letter words. Having imperfect letter scores adds an element of luck to the game which can make it more fun.