What Scrabble tiles would be worth today
Alfred Butts priced the tiles in the 1930s by counting letters in newspaper text. We priced them again from the words players actually use: NWL2023, the North American tournament list of 196,601 words, measuring how hard each letter is to play. Butts mostly got it right. J should be the 10 and Z an 8.
The price list, re-dealt
We kept Butts's own price list (ten 1-point tiles, two 2s, four 3s, five 4s, one 5, two 8s and two 10s) and handed the prices out again, hardest letter first. 6 letters change for clear reasons: G 2 → 3, H 4 → 3, J 8 → 10, K 5 → 4, V 4 → 5 and Z 10 → 8. Two more are close calls: C 3 → 4 and P 3 → 2.
Every letter, hardest first
The difficulty index runs from 0 (E, the easiest letter to play) to 100 (Q). It averages three measures, each on a log scale: how rare the letter is in words of 2 to 8 letters, how many two- and three-letter words contain it, and how often it can be used in a random seven-tile rack.
| Letter | Today | Re-priced | Change | Difficulty | Share of letters | 2–3 letter words | Usable in rack |
|---|---|---|---|---|---|---|---|
| Q | 10 | 10 | same | 0.18% | 5 | 62.4% | |
| J | 8 | 10 | +2 clear | 0.27% | 27 | 93.3% | |
| Z | 10 | 8 | -2 clear | 0.46% | 31 | 93.0% | |
| X | 8 | 8 | same | 0.34% | 46 | 97.3% | |
| V | 4 | 5 | +1 clear | 0.95% | 42 | 93.0% | |
| K | 5 | 4 | -1 clear | 1.49% | 61 | 97.5% | |
| W | 4 | 4 | same | 1.20% | 92 | 97.1% | |
| F | 4 | 4 | same | 1.52% | 81 | 97.5% | |
| C | 3 | 4 | +1 close call | 3.57% | 75 | 97.3% | |
| Y | 4 | 4 | same | 1.84% | 111 | 99.7% | |
| B | 3 | 3 | same | 2.32% | 116 | 98.0% | |
| H | 4 | 3 | -1 clear | 2.47% | 114 | 99.3% | |
| G | 2 | 3 | +1 clear | 2.97% | 121 | 97.8% | |
| M | 3 | 3 | same | 2.86% | 132 | 98.4% | |
| P | 3 | 2 | -1 close call | 2.96% | 141 | 98.5% | |
| D | 2 | 2 | same | 4.07% | 132 | 97.6% | |
| L | 1 | 1 | same | 5.52% | 105 | 97.7% | |
| U | 1 | 1 | same | 3.67% | 159 | 99.2% | |
| N | 1 | 1 | same | 5.76% | 136 | 98.1% | |
| R | 1 | 1 | same | 7.11% | 137 | 98.1% | |
| T | 1 | 1 | same | 5.70% | 162 | 98.3% | |
| I | 1 | 1 | same | 7.50% | 205 | 100.0% | |
| S | 1 | 1 | same | 9.37% | 176 | 98.6% | |
| O | 1 | 1 | same | 6.17% | 288 | 100.0% | |
| A | 1 | 1 | same | 8.10% | 360 | 100.0% | |
| E | 1 | 1 | same | 11.63% | 293 | 100.0% |
Share of letters: in NWL2023 words of 2 to 8 letters. Usable in rack: share of 1,000,000 random seven-tile racks holding the letter where it fits into at least one word made from that rack. "Clear" means the change holds when any one of the three measures is left out.
Why the letters move
J makes up 0.27% of the letters in today's words, Z 0.46%. J sits in 27 two- and three-letter words, Z in 31. In a random rack the two are about equally playable (93.3% and 93.0%), so rarity and short words decide it.
of racks holding a Q can't use it in any word from that rack. For every other letter that figure is 7.0% or less. Only 5 two- and three-letter words contain Q: QI, QAT, QIS, QUA and SUQ. On a fair scale Q would be worth far more than 10; the price list stops there.
V has no two-letter word at all and turns up in 42 short words, against 61 for K. Racks holding a V use it 93.0% of the time, K 97.5%.
H is in 114 short words and fits 99.3% of racks, close to the 3-point letters. G was priced with D at 2, but it is the harder of the two to place (index 20 against 17) and moves up to 3.
Score a word both ways
Across all 196,601 words, 35% would score more under the new prices and 28% less. QUIZ 22 → 20, JAVELIN 17 → 20, WIZARD 19 → 17, SCRABBLE 14 → 15, OXYPHENBUTAZONE 41 → 37.
If the bag followed the dictionary too
Tile counts are a separate decision from values. Shared out in proportion to today's letters (98 lettered tiles, at least one of each), the bag would change like this. Butts kept S scarce on purpose, by most accounts to stop plurals making the game too easy, which is why S moves most.
- S4 → 9
- C2 → 3
- L4 → 5
- M2 → 3
- P2 → 3
- R6 → 7
- I9 → 7
- O8 → 6
- A9 → 8
- E12 → 11
- F2 → 1
- T6 → 5
- V2 → 1
- W2 → 1
How we priced the letters
- Rarity. Each letter's share of all letters in NWL2023 words of 2 to 8 letters, the lengths most plays use. Long words are rarely played, so they are left out of this count.
- Short words. How many two- and three-letter words contain the letter. These are what let a player dump an awkward tile or play alongside another word.
- Racks. 1,000,000 seven-tile racks drawn at random from the 98 lettered tiles. For each letter in a rack we check whether at least one word can be made from the rack using that letter.
- Index. Each measure is turned into a difficulty from 0 (easiest letter) to 1 (hardest) on a log scale, and the three are averaged with equal weights. Nothing was tuned.
- Prices. Butts's 26 values are handed out again in order of difficulty. A change counts as clear when it survives leaving out any one of the three measures.
Not modelled: playing through tiles already on the board, blanks, premium squares and strategy. Those would change the index, but they would not make a letter easier to place for a player holding it.
Use this data
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Questions, a spreadsheet of the figures or a figure for your own state or town: Adrian Talvik, adrian@unscramblex.com.