>I'm looking for a list of word lengths with their percentages for
how much they make up the scores in games?
David,
I don't know it based on scoring, but I think playability is a much more reliable measure of a word's value to Scrabble players. So these results were easily computed from John O'Laughlin's march 2006 playability list:
I sorted the groups of words by average playability per word. This assumes the study time is proportional to the number of words alone (and not their length), and so is a rough guide of what order to learn these groups in (if playability is indeed a good measure of word importance, which I have found it to be - although I really suggest studying directly from the entire list).
The 2s make up 15.14% of the dictionary. The 8s make up 24%.
It's interesting that playability suggests the JQXZ fours are more valuable per word than the 3s. And that if you learn any of Mike Baron's bingo lists, you should start with the type III 8s. Also, your time per word is better spent studying the first 1000 most probable 7s and 8s before starting on the 4s. Quite different from Mike's recommended study order. :)
I can easily run more stats for more word groups if anyone is interested. Enjoy.
twos.input.txt
total playability: 365067920
percentage of dictionary: 0.151383539252
playability per word: 3614533.86139
JQXZ fours.input.txt
total playability: 82518801
percentage of dictionary: 0.0342182576607
playability per word: 306761.342007
threes.input.txt
total playability: 269987671
percentage of dictionary: 0.111956397567
playability per word: 265997.705419
JQXZ fives.input.txt
total playability: 85903362
percentage of dictionary: 0.035621741218
playability per word: 123247.291248
type III eights.input.txt
total playability: 12713430
percentage of dictionary: 0.00527190674391
playability per word: 84756.2
first 1000 probable eights.input.txt
total playability: 82582188
percentage of dictionary: 0.0342445424912
playability per word: 82582.188
first 1000 probable sevens.input.txt
total playability: 75138611
percentage of dictionary: 0.031157897598
playability per word: 75138.611
fours.input.txt
total playability: 268405002
percentage of dictionary: 0.111300108637
playability per word: 66601.737469
type I sevens.input.txt
total playability: 100290232
percentage of dictionary: 0.0415875771078
playability per word: 49599.5212661
type II eights.input.txt
total playability: 40653196
percentage of dictionary: 0.0168577526406
playability per word: 45070.0620843
type I eights.input.txt
total playability: 207199188
percentage of dictionary: 0.0859197554516
playability per word: 37032.9201072
highfives.input.txt
total playability: 96288222
percentage of dictionary: 0.0399280545786
playability per word: 36723.1967963
type II sevens.input.txt
total playability: 58078873
percentage of dictionary: 0.0240836974953
playability per word: 36619.7181589
type III sevens.input.txt
total playability: 94362310
percentage of dictionary: 0.039129432298
playability per word: 33833.7432772
fives.input.txt
total playability: 294498122
percentage of dictionary: 0.122120201664
playability per word: 32948.9955247
eights.input.txt
total playability: 580618144
percentage of dictionary: 0.240766237671
playability per word: 19506.085601
sevens.input.txt
total playability: 436826648
percentage of dictionary: 0.18113989313
playability per word: 18179.1438678
sixes.input.txt
total playability: 168069787
percentage of dictionary: 0.0696938783266
playability per word: 10645.4134153
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