In general, it should take L about the same amount of work, in a Bayesian sense, to gather one more bit of information regardless of how many he currently has. Thus, quantifying Light's mistakes in terms of bits conceded is probably the best way to do it.
I don't know if this is a little too afar field for even a Discussion post, but people seemed to enjoy my previous articles (Girl Scouts financial filings, video game console insurance, philosophy of identity/abortion, & prediction market fees), so...
I recently wrote up an idea that has been bouncing around my head ever since I watched Death Note years ago - can we quantify Light Yagami's mistakes? Which mistake was the greatest? How could one do better? We can shed some light on the matter by examining DN with... basic information theory.
Presented for LessWrong's consideration: Death Note & Anonymity.