Vowel-consonant Ratio

This article is the second post in my series “No Tile Left Behind” focusing on leaves. For a list of articles on this topic, click here.

One common adjustment that we make is for vowel-consonant ratio. While EI is a positive leave when you add the value of the tiles together, nearly every expert will agree that EI is not a good leave. In my book, I recommend subtracting 4 points for each tile off from ideal vowel-consonant ratio, which is approximately 3 consonants for every two vowels.  When assessing vowel-consonant ratio, there are numerous factors at work:

  1. Words inherently involve more consonants than vowels at a slightly greater effect than the 56-42 breakdown of consonants to vowels inherent in the tile bag.
  2. Consonants are worth more points: thus, it is easier to play through too many consonants. There are many times when you can score well with consonant heavy racks. On the other hand, scoring well with vowel heavy racks is much more difficult.
  3. It is easier to get rid of a surplus of consonants than a surplus of vowels. Many more words have 75% or more consonants than vowels, so making a 16 point dump using 4 or 5 consonants is a lot easier than a 16 point dump using 4 or five vowels.
  4. Duplication is a bigger issue with vowels, resulting in fewer permutations and less potential to make words.
  5. The dampening effect: Exchange racks are exchange racks. There really isn’t any difference between AAIOUVW and IIIIUUU. Both are exchange racks even though the first rack is clearly better than the second. Even the difference between AEEIOTU and IIIIUUU is fairly small, since in the first rack you can either exchange or make a play that is only slightly better than exchanging (most of the time)

My book recommends that it costs about 4 points if you’re 1 tile off in vowel-consonant ratio. This comes from a statistical fact based on the opening rack. For other situations (3 vowel racks, or later in the game) it is trivial to use the same method to approximate the problem.

2 vowels saved

# Vowels drawn Frequency Expected valuation
0 .07 35
1 .25 41
2 .36 33
3 .24 19
4 .07 9
5 .01 3

.07(35) + .25(41) + .36(33) + .24(19) + .07(9) + .01 (3) = 29.8

1 vowel, 1 consonant saved

# Vowels drawn Frequency Expected valuation
0 .07 23
1 .25 35
2 .36 41
3 .24 33
4 .07 19
5 .01 9

.07(23) + .25(35) + .36(41) + .24(33) + .07(19) + .01(9) = 34

34 – 29.8 = 4.2

Thus, it is about a 4.2 deduction on average to keep vowel/vowel, relative to consonant/consonant. Using the same technique you will get 7.3 for three vowels, 9.4 for 4 vowels, 3.1 for 3 consonants, and 5.2 for 4 consonants. From this, I created the rule as mentioned above: a rough guideline as to how to adjust for vowel-consonant ratio.