The exact quote is "Lies, damn lies, and statistics." Benjamin Disraeli is the first one to have said it, although it's often attributed to Mark Twain, who was really quoting Disraeli. I don't know where Will Rogers comes in, except that he's known for saying witty things too.
Anyway, I don't want to bore anyone here with a discussion of probability theory, but I just wanted to say that TheNiceOne needs brush up on his probabilty calculations, especially something called "binomial distribution". Cracker was much closer to the truth.
I guess that you are technically correct in discussing the odds for any particular permutation, but nobody really cares about the probability for a specific permutation. What they are really interested in is the sum of probabilities for a set of permutations.
Note that there's a big difference between asking "What are the odds of getting one head out of five flips of a coin?" and "What are the odds of flipping a tail, tail, tail, heads, and then a tail, in that specific order?" You answered the latter question, but the former is more relevant.
If I had a game where I won 40 elite battles, which is close to my experience on a standard map with a fair amount of warmongering, then the odds of me not getting a single leader in that game is 7.5%. Or conversely, I'd have a 92.5% chance of getting at least one leader. (This is assumingly that the odds of an elite win generating a leader is 1 out of 16.)
If we break the odds down even more, the odds of getting exactly one leader is about 20%, the odds of getting exactly two goes up to 26%, the odds of getting exactly three falls to 22%, and continues to decrease after that. So with 40 elite wins, the most likely scenario is that I'll get 2 leaders.
The numbers change depending on how many elite wins that I have, and there's no easy way to scale the above 40-win result to another number of wins. That's the tricky thing about binomial distributions but this calculator is real handy to use in other cases.
http://faculty.vassar.edu/lowry/binom_stats.html
Although it may not seem intuitive, with 10 elite wins the odds are about the same that you'll get a leader (48%) as not (52%). If you have more than 10 elite wins in a game, then you're more likely than not to get at least one leader. But as I stated above, even in a game with 40 elite wins, it wouldn't be all that unusual (7.5%) to not get a single leader during the entire game.
I do agree with your contention that a game with zero leaders is much more likely to stick out in a person's mind, and thus we'll hear about it in the forums. Even though a game with 40 wins is much more likely to produce at least one leader (92.5%) than not (7.5%), we tend to hear about all the games where people whine about not having a leader, and it comes across as a common event, even though it's fairly rare.
Anyway, sorry for the boring lesson on statistics, this stuff interests me.
Rimpy
P.S. In any case, Firaxis should have told us about the "one leader per elite unit" thing a long time ago. I can think of several games that I would've played differently.