Bowling a 300: An Exercise in Probability and Statistics

February 8 will mark the 24th anniversary of my first and only sanctioned 300 game of bowling. I like to tell people I got mine back when it "meant something," which is mostly true, although most bowling historians (can I get a job like that?) will tell you that even in 1988, a 300 meant less than it did even only years prior, and in 1983, it meant less than five years prior to that. But at least it meant enough to feel like a once-in-a-lifetime event when it happened to this 21-year-old, a whole house full of bowlers stopped what they were doing to watch, and the 12th strike strike was met with a huge roar.

The problem with joke-boasting about having done it when it "meant something" is that one would expect that I'd have no trouble doing it again (and again, and again, ...). I expect it will come, but the closest I've come since "getting back into" bowling in recent years and actually keeping up with technology has been a 296 game (left the bucket...too much speed on the final shot). I've also had 15 in a row over the course of two games (Andy Veripapa, anyone?)

So the other day I was wondering, what would the mathematical odds be of me bowling a 300 game on any particular night? If I treated my bowling like a dice game, I could calculate this. Luckily, if a bit geekily, I keep stats for fun, and can indeed calculate this.

Among stats I keep are strike percentage and double percentage (how often I follow a strike with another strike). Over the past two season, with 72 games logged, my strike percentage is 64.71%. My double percentage is 63.25% (which means I might be inclined to let the nerves get to me knowing how important it is to follow a strike with another one).

So, if we had a 10,000-sided die to roll (take that, D&D fans), we could mimic my game by saying that everything between 1 and 6471 would be a strike, and in a frame following a strike, everything between 1 and 6325 would be a strike.

The odds, then, of a 300 game would be .6471 * .6325^11 = .004194, or .42% rounded off. Put another way, you could expect a 300 game every 238 games or so.

There was a time in my life where I bowled that many sanctioned games in a season. If I still were, I might be one of those guys with several 300 games to his credit. Still, the top bowlers in the Twin Cities area have scores of 300 scores (see what I did there?), so they are doing more than just bowling more. They are indeed bowling better. The former does tend to beget the latter, but there's more to bowling closer to your potential than simply bowling more.

If I were to improve my strike and double percentages to 65% each, my likelihood of a 300 game becomes 1 in 176. Improve them to 66.67% each (2 strikes in every 3 shots), and it's 1 in 130. At 70% each, it's 1 in 72.

The "dice" game version of course does not factor in the human element of pressure. The die would not know that it had just rolled 11 strikes in a row. So how does a human combat this? Knowledge is power, I say. Knowing that my time will come if I am just patient should, in theory, allow me to relax more when a game gets into the "nervous zone" of 8 or 9 strikes in a row. I just need to wait it out, and it will happen. Maybe not within the 238-game span, but it will, eventually.

Yeah, I know, easier said than done.

One other thing is clear from the statistics: Since I'm not likely to get permission from the better half to bowl 238, 176, or even 130 games a year, it behooves me to try to improve with the relatively few games I am able to bowl and practice, if I am to not only get that next 300 soon, but even more to come.