Making a smash hit anime involves a number of steps. Typically you have to have to get solid source material, assemble the right staff, and do well on the PR front. But most importantly of all, you have to, to some extent, simply get lucky in getting engaged with your target demographic. This is at the heart of the discussion regarding the recent dearth of hit anime this past Fall and current Winter being the first shows in a while to potentially have no series averaging above 20k and 10k in disk sales, respectively. But how unexpected is that outcome really?

Recently, hit shows (shows with sales averages at 10k and above) have made up about 10% of the total number of anime released, so let’s go ahead and say that the odds of one occurring are roughly 1/10. Put another way, the naive vacuum odds of a show not being a hit are about 9/10. There are about 30 shows in your average modern season, give or take 5 or so. In this case, the odds that not one of those is a hit are fairly simple to calculate; .9^30=.042, or about 4.2 percent. This suggests that, even with the highest frequency of hits as a function of total shows the industry has had at any point since 1995, one should expect to see one season without a 10k hit at least once every 25 seasons, or a tad less often than every 6 years. The last time a season without a 10k average happened was in Winter of 2007, when Nodame Cantabile topped the charts with an 8787 average. 7 years is a tad longer than 6.

For 20k hits, the frequency is obviously a bit lower. In 2011 (8 20k shows) and 2012 (7 20k shows), there were a total of around 250 shows to air, a little more than 30 per season. (235/250)^30=.156=15.6%, so one would expect this to happen once every 6.5 seasons, or a little more than once every two years. We’ve gone without such a season for a good 2.5 years (the last time was in Summer of 2010).

Also, if 20k hits are a lock, one would expect to see series in any season putting up well in excess of that total. But we’ve had some near misses in the not-so-distant past. In Summer 2011, the top averager Idolm@ster was below 28k. This isn’t quite a skin-of-the-teeth miss, but it’s not unfeasible that things could have gone south for one or more of those series and led to a non-20k season. What if Im@s decided not to package itself with Gravure for You? In Spring 2012, the top averager Fate/Zero season 2 put up a hefty 46k, and Kuroko’s Basketball was the only other 20k+ show in the season. What if Fate/Zero was aired in one chunk and finished up over Winter, and Kuroko’s Basketball was slightly less well-made? The point here is that very feasible situations could have made non-20k seasons considerably less rare.

This is all without even counting stuff like source material strength for a given season.* For one, Nou-Rin and The Pilot’s Love Song aren’t exactly on the same tier of light novel popularity as Sword Art Online or Ha Ga Nai. For another, the odds in favor of Winter and Summer are typically lower due to a lower total number of shows airing in those seasons. It’s worth it to consider how this season and the last will end up in the long-term legacy column. But for a Spring season containing a strong field, including at least 3 followups to 10k+ shows (JJBA, Love Live, and Mushishi) plus an LN adaptation of a series that handily eclipsed Sword Art Online’s pre-anime figures this past June in Mahouka Koukou no Rettousei, the bet on one show hitting it big is a relatively safe one.**

*Though I admit, I was rather bullish on the dark horse chances for some of its content.

**Just don’t be stupid and bet your ear on it or anything.