Maybe it’s because I’m cranky today, maybe it is because the represenation, or lack thereof, of mathematics in popular and high culture is a constant annoyance to me. Or maybe it is because it is deeply mystifying to me how someone as learned as David Foster Wallace can screw up so badly with numbers; anywho.
I’ve advanced to page 259 of Infinite Jest now, the book gets better and better, but then this: “a 54 match conclusion [of a 108 match tournament] is extremely unlikely – odds being 1 in 227“. Whoa, hold on. Really?
So Wallace gets the binomial distribution wrong, big deal, you might say – the correct probability for a draw is about 0.0766 or 1 in 13, by the way – but that’s not what irks me. How could a number so wildly implausible sail unchecked past both his and his editor’s critical skills? In a tournament with 108 matches, there is 109 possible outcomes (from team A loses all, to team A wins all). The average probability of each outcome then is 1/109. Now if the two teams are equally matched, a draw is the most likely of all these outcomes, making their average (1/109) a lower limit on the actual probability. For this kind of reasoning you need no binomial, no probability distribution, just a little bit of mathematical common sense. Which, for some odd reason, seems to be a rather rare commodity.