Letter distributions in Bananagrams and other games

What determines how many of each letter there are in various word games? The inventor of Scrabble designed the frequency of his tiles around the frequency of letters used on the front page of the New York Times. (Somebody must have sat and done a lot of counting back in 1938.) The distribution for Snatch is said to be based on the frequency distribution of letters in the English language as calculated by World War II cryptographers.

This photograph visually displays the letter distribution for Bananagrams. (Click for a larger version.)
The following table gives the letter distributions for Bananagrams, Scrabble (without the blanks), and Snatch:

Game	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Bananag.	13	3	3	6	18	3	4	3	12	2	2	5	3	8	11	3	2	9	6	9	6	3	3	2	3	2
Scrabble	9	2	2	4	12	2	3	2	9	1	1	4	2	6	8	2	1	6	4	6	4	2	2	1	2	1
Snatch	5	2	4	4	12	4	2	5	5	1	1	5	4	5	6	3	1	5	5	7	4	2	3	1	3	1

By comparing the Bananagrams and Scrabble sets, we learn that the Bananagrams set of tiles is a superset of the Scrabble set of tiles (except for the blanks). In fact, for each letter of the alphabet, the Bananagrams set has at least one more tile than the Scrabble set. Since there are 100 Scrabble tiles and 144 Bananagrams tiles, this additional 26 tiles explains a lot of the discrepancy. It also gives a hint as to how the inventors of Bananagrams may have derived their distribution.


The Snatch set, on the other hand, is NOT a subset of the Bananagrams set. If you want to try to play Snatch with a Bananagrams set of tiles (and if you are kind of a stickler), you can get close to the right distribution by throwing out these letters in these numbers: (A,7), (E,5), (I,6), (O,4), (R,3). (I am reducing each difference by one to allow for a slightly larger Bananasnatch set (121 tiles instead of 100).) You can remember this with the mnemonic lAttIcEwORk and noting that you start by throwing out 7 tiles lettered A, decreasing the number by one for each of the vowels, and finally setting aside 3 tiles with the letter R on them.

UPDATE:
I found the letter distribution for Spanish Bananagrams here and the French Bananagrams letter distribution here.

Here is the revised table, in vertical format (to accommodate the extra letters):

	B a n a n a g r a m s	S p a n i s h B G	F r e n c h B G	S c r a b b l e	S n a t c h
A	13	17	13	9	5
B	3	3	3	2	2
C	3	5	4	2	4
D	6	7	6	4	4
E	18	17	18	12	12
F	3	2	3	2	4
G	4	3	2	3	2
H	3	3	2	2	5
I	12	8	12	9	5
J	2	2	2	1	1
K	2	1	1	1	1
L	5	5	6	4	5
M	3	3	4	2	4
N	8	7	9	6	5
O	11	12	12	8	6
P	3	3	4	2	3
Q	2	2	2	1	1
R	9	7	10	6	5
S	6	8	6	4	5
T	9	6	10	6	7
U	6	7	6	4	4
V	3	2	4	2	2
W	3	1	1	2	3
X	2	1	2	1	1
Y	3	2	1	2	3
Z	2	2	1	1	1
CH		2
LL		2
Ñ		2
RR		2

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Suggested reading:

• The Boggle cube redesign and its effect on the difficulty of Boggle
• The longest word that you can make in Bananagrams