5 ms·

Rethinking the value of Scrabble tiles

112 points by jlewis_st 14y ago

ChuckMcM 14y ago
That is a very nicely done analysis. I too have wondered what a 'modern' valuation of letters might look like, this approach seems reasonable.
dfan 14y ago
"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." 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.
- jlewis_st 14y ago
  I was thinking that you could sum up the transition probabilities from the actual transitions available on the board as the main measure. Then you could use frequency by length to weight legal Boggle plays (3/4 letters and up, so 2-letter words wouldn't even count). You're right that with a Boggle board you could just count up the available Boggle points by finding all the possible words, but that might miss some aspects of how hard the words are for a human to find.
  - robryan 14y ago
    If you had enough real games data you could see how often a word is found when present and use that is a weighing factor. Although the arrangement if a word might also impact the likelihood to be found.
    - Tloewald 14y ago
      Changing the values of tiles will change the game, so you'll have a new mismatch. I think that a simpler fix would be to ban plays of fewer than three or four tiles are placed (I'd say four since three is still too easy). You can still score off the stupid two letter gotchas, but you have to place a three or four letter word down to score anything. The game would end when all players had two few tiles to play.
      - robryan 14y ago
        I am speaking of Boggle, where the scoring is based on unique words.
StevenRayOrr 14y ago
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. Interesting analysis though.
deleted 14y ago
[deleted]
transfire 14y ago
2-letter Scrabble words are more offensive than curse words, and anyone who insists on them deserves only two: "F" and "U".
- dfan 14y ago
  Sorry, they're part of the game. It's like getting offended at a chess player for castling.
  - RyJones 14y ago
    I'd guess en passant is more surprising to neophytes than castling
    - jacquesm 14y ago
      At a guess check-mate is the most surprising to neophytes. It gets them every time no matter how often it happens.
      - lmm 14y ago
        Huh? If checkmate is confusing you can just play until you take the opponent's king, with minimal difference to the game.
    - mediocregopher 14y ago
      I had never even heard of that (although I'm by no means an avid chess player). I think I'll have a hard time convincing my friends that's a real rule.
      - jspthrowaway2 14y ago
        The Wikipedia article is good at explaining the rationale. According to it, it was added around the time the two-space opening move for a pawn was added to balance the game. Oddly, though Wikipedia deletes programming languages like Factor due to non-notability[1], editors get to go nuts on everything chess or Star Trek without recourse. If you want to know more about why things in chess are the way they are, Wikipedia is your pal. [1]: http://en.wikipedia.org/wiki/Talk:Factor_(programming_language) http://en.wikipedia.org/wiki/Talk:Factor_(programming_langua...
zem 14y ago
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.
- javajosh 14y ago
  Maybe you and the OP should petition the Words With Friends people to give you a statistically significant data-dump of real games so you can analyze and revalue the letters. It would be a service to us all.
  - furyofantares 14y ago
    That would be really interesting data to look at. There would be a lot of factors to consider that might make it hard to apply to re-valuing Scrabble, though: 1. Most Words With Friends play is casual, and casual players are likely to play very differently than competitive players. 2. The data would show you what words players play given the current scoring system, and wouldn't necessarily translate to another scoring system. 3. Words With Friends is a different game than Scrabble (different board layout, different bingo scoring, different number of tiles and different tile frequency). 4. Players end up playing the majority of the tiles they draw, so the frequency with which they play a letter may have a closer relationship to how many of the printed tiles have that letter than it is to the frequency of the letter in the corpus.
    - hdevalence 14y ago
      Regarding 1: perhaps one could segment the players based on their scores --- the people I know who play scrabble competitively generally have a significantly higher average word score.
caf 14y ago
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.
- DLWormwood 14y ago
  I believe that is part of what his definition of “ingoing and outgoing entropy” is refering to. That said, it does seem weird to heavily bias for the 2-3 letter and 7-8 cases. I would think the moderate length words should not get such short shrift, since these words tend to be the ones used to determine when the various letter and words value tiles get hit in any given game. (Full disclosure: not a regular Scrabble player.)
  - zem 14y ago
    regular scrabble player here. 2, 3, 7 and 8 are absolutely way more valuable than all the other lengths.
BasDirks 14y ago
article claims to be written 1 year from now: "30 DEC 2013 - JOSHUA LEWIS"
nathell 14y ago
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.
- jlewis_st 14y ago
  I did simple analysis of overall letter frequency and how that would map to a 98 tile set (not counting the blanks) and this is what I got: A: 7 B: 2 C: 4 D: 3 E: 11 F: 1 G: 3 H: 2 I: 8 J: 1 K: 1 L: 5 M: 3 N: 6 O: 6 P: 3 Q: 1 R: 7 S: 9 T: 6 U: 3 V: 1 W: 1 X: 1 Y: 2 Z: 1 It makes a lot of sense to reduce the number of Ss for the sake of gameplay, and it seems like Butts redistributed those extra tiles amongst the vowels.
cdelsolar 14y ago
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. 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?). 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.
- jlewis_st 14y ago
  Yes, my distaste for C is probably because I'm not a good enough player, haha. I received an email mentioning the CLARINETS heuristic for choosing tiles to leave in one's rack, and in that context the drop in C's value makes sense, as you say.
opk 14y ago
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.

112 points by jlewis_st 14y ago

That is a very nicely done analysis. I too have wondered what a 'modern' valuation of letters might look like, this approach seems reasonable.

dfan 14y ago

"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." 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.

jlewis_st 14y ago
I was thinking that you could sum up the transition probabilities from the actual transitions available on the board as the main measure. Then you could use frequency by length to weight legal Boggle plays (3/4 letters and up, so 2-letter words wouldn't even count). You're right that with a Boggle board you could just count up the available Boggle points by finding all the possible words, but that might miss some aspects of how hard the words are for a human to find.
- robryan 14y ago
  If you had enough real games data you could see how often a word is found when present and use that is a weighing factor. Although the arrangement if a word might also impact the likelihood to be found.
  - Tloewald 14y ago
    Changing the values of tiles will change the game, so you'll have a new mismatch. I think that a simpler fix would be to ban plays of fewer than three or four tiles are placed (I'd say four since three is still too easy). You can still score off the stupid two letter gotchas, but you have to place a three or four letter word down to score anything. The game would end when all players had two few tiles to play.
    - robryan 14y ago
      I am speaking of Boggle, where the scoring is based on unique words.

StevenRayOrr 14y ago

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. Interesting analysis though.

deleted 14y ago

[deleted]

transfire 14y ago

2-letter Scrabble words are more offensive than curse words, and anyone who insists on them deserves only two: "F" and "U".

dfan 14y ago
Sorry, they're part of the game. It's like getting offended at a chess player for castling.
- RyJones 14y ago
  I'd guess en passant is more surprising to neophytes than castling
  - jacquesm 14y ago
    At a guess check-mate is the most surprising to neophytes. It gets them every time no matter how often it happens.
    - lmm 14y ago
      Huh? If checkmate is confusing you can just play until you take the opponent's king, with minimal difference to the game.
  - mediocregopher 14y ago
    I had never even heard of that (although I'm by no means an avid chess player). I think I'll have a hard time convincing my friends that's a real rule.
    - jspthrowaway2 14y ago
      The Wikipedia article is good at explaining the rationale. According to it, it was added around the time the two-space opening move for a pawn was added to balance the game. Oddly, though Wikipedia deletes programming languages like Factor due to non-notability[1], editors get to go nuts on everything chess or Star Trek without recourse. If you want to know more about why things in chess are the way they are, Wikipedia is your pal. [1]: http://en.wikipedia.org/wiki/Talk:Factor_(programming_language) http://en.wikipedia.org/wiki/Talk:Factor_(programming_langua...

zem 14y ago

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.

javajosh 14y ago
Maybe you and the OP should petition the Words With Friends people to give you a statistically significant data-dump of real games so you can analyze and revalue the letters. It would be a service to us all.
- furyofantares 14y ago
  That would be really interesting data to look at. There would be a lot of factors to consider that might make it hard to apply to re-valuing Scrabble, though: 1. Most Words With Friends play is casual, and casual players are likely to play very differently than competitive players. 2. The data would show you what words players play given the current scoring system, and wouldn't necessarily translate to another scoring system. 3. Words With Friends is a different game than Scrabble (different board layout, different bingo scoring, different number of tiles and different tile frequency). 4. Players end up playing the majority of the tiles they draw, so the frequency with which they play a letter may have a closer relationship to how many of the printed tiles have that letter than it is to the frequency of the letter in the corpus.
  - hdevalence 14y ago
    Regarding 1: perhaps one could segment the players based on their scores --- the people I know who play scrabble competitively generally have a significantly higher average word score.

caf 14y ago

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.

DLWormwood 14y ago
I believe that is part of what his definition of “ingoing and outgoing entropy” is refering to. That said, it does seem weird to heavily bias for the 2-3 letter and 7-8 cases. I would think the moderate length words should not get such short shrift, since these words tend to be the ones used to determine when the various letter and words value tiles get hit in any given game. (Full disclosure: not a regular Scrabble player.)
- zem 14y ago
  regular scrabble player here. 2, 3, 7 and 8 are absolutely way more valuable than all the other lengths.

BasDirks 14y ago

article claims to be written 1 year from now: "30 DEC 2013 - JOSHUA LEWIS"

nathell 14y ago

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.

jlewis_st 14y ago
I did simple analysis of overall letter frequency and how that would map to a 98 tile set (not counting the blanks) and this is what I got: A: 7 B: 2 C: 4 D: 3 E: 11 F: 1 G: 3 H: 2 I: 8 J: 1 K: 1 L: 5 M: 3 N: 6 O: 6 P: 3 Q: 1 R: 7 S: 9 T: 6 U: 3 V: 1 W: 1 X: 1 Y: 2 Z: 1 It makes a lot of sense to reduce the number of Ss for the sake of gameplay, and it seems like Butts redistributed those extra tiles amongst the vowels.

cdelsolar 14y ago

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. 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?). 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.

jlewis_st 14y ago
Yes, my distaste for C is probably because I'm not a good enough player, haha. I received an email mentioning the CLARINETS heuristic for choosing tiles to leave in one's rack, and in that context the drop in C's value makes sense, as you say.

opk 14y ago

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.