Prooffreader graphed the distribution of letters towards the beginning, middle and end of English words, using a variety of corpora, finding both some obvious truths and some surprising ones. As soon as I saw this, I began to think of the ways that you could use it to design word games -- everything from improved Boggle dice to automated Hangman strategies to altogether new games.
Now then: I became curious about how letters are placed in English while doing many different, often quick, sometimes pointless, pattern analyses of letters for a wide variety of reasons. (One example: for one art project that will hopefully be posted on this blog one day, I found all the anagrams of "Hollywood", and noticed that words beginning with "w" were overrepresented.)
I've had many "oh, yeah" moments looking over the graphs. For example, words almost never begin with "x", but it's quite common as the second letter. There's a little hump near the beginning of "u" that's caused by its proximity to "q", which is most common at the beginning of a word. When you remove "q" from the dataset, the hump disappears. "F" occurs toward the extremes, especially in prepositions ("for", "from", "of", "off") but rarely just before the middle.
A final thought: the most common word in the English language is "the", which makes up about 6% of most corpuses (sorry, corpora). But according to these graphs, the most representative word is "toe".