C M D A? Try H G D O.
I have been watching Wheel of Fortune for more than 20 years now–my parents even tell me that the game taught me how to read. And all the while I have unquestionably thought that the best letters to call during the bonus round are C M D and A. But watching the program last night, I realized I had no factual basis for that. It was a belief. It was not science.
So I figured I would do some quick Googling and find out what the best letters actually were. Turns out, it seems no one has figured this out yet. (The best result was some dude on Yahoo! Answers, which wasn’t exactly reassuring.)
No problem. I found this website, which archives Wheel of Fortune bonus round puzzles and other associated information. It has a complete record from 2007-2012, or 1166 total puzzles. I scraped the data and began my analysis. Here are some of the important findings:
1) I am not a lone in my belief: C M D A are the four most frequently called letters at 64.6%, 59.9%, 57.9%, and 48.3%, respectively.
2) P H O G are the next four in order at 38.2%, 34.5%, 31.1%, and 21.0%.
3) O is the most common letter to appear in puzzles, consuming 9.5% of all letters. This just goes to show you that the bonus round puzzles are not a random sample of words from the English language–in real life, O is the fourth most common letter after E, T, and A.
4) Despite being the most common letter in English, E is the fourth most common letter in the puzzles after O, I, and A. Ostensibly, they give you R S T L N E for free because they are common letters. However, the producers intentionally pick puzzles where those letters don’t show up. Like cake, the value of R S T L N E is a lie.
5) M is an awful pick, ranking 21st on the list. It only accounts for 2.1% of the letters. Only V, J, Q, Z, and X are less frequent. No one ever calls V, J, Q, Z, or X unless they already know the answer to the puzzle and want to show off. Yet 57.9% of players pick M. Go figure.
6) H is a great selection. It has a frequency of 4.6%, placing the highest among non-R S T L N consonants. It ranks just slightly below the least frequent vowel (U, 4.7%) but higher than N (4.5%), S (3.8%) and L (3.7%).
7) If you solely want to maximize the number of letters that are revealed, H G D O is the best selection. D (3.5%) is very close to P and B (both 3.4%), so there is some wiggle room here.
To hammer home the point, the plot below shows the frequency of called letters versus what appears on the board (click to enlarge):
The mess on the bottom left corner is the V, J, Q, Z, X trash.
A couple of notes before I wrap this up. First, I want to emphasize the distinction between “most frequent letters” versus “best letters.” What shows up most frequently might not be the most useful in terms of actually solving the puzzle. G’s frequency might be overrated since a lot of those come from -ING suffixes, which you could reasonably guess if you see a word like _ _ _ _ _ N _. Letters like C, B, or P might have an advantage in that they could appear at the beginning of words more frequently and are thus more valuable. This is something I could check on later.
This segues to the second point nicely. There are a bunch of interesting questions we can now answer now that I have this dataset. Expect more investigative posts like this in the future.
 The category What Are You Doing? only appears 9 out of 1166 times. Since this category always begins with a word ending in -ING, having the G be revealed in that slot is worthless to a contestant. But even if you remove those puzzles from the sample, G ranks much higher than the nearest alternatives.