Max Wasserman, the numbers fanatic from Cornell who earlier this week broke down college football, today takes a stab at the NBA. The Spurs have won four NBA titles in the brief 32-year history of the franchise. Here’s what’s quirky – they’ve all come in odd-numbered years. What are the odds? No, really, how random is that? Incredibly. Max breaks out a calculator after the jump.

After crunching the numbers on college football my last post, this post I worked on something a little more in-season. As we all know, the San Antonio Spurs have won four NBA Championships in their 32-year history, all of which came in the last 10 years and all of which occurred in odd-numbered years. TBL was pondering what is the probability of this happening randomly. Well, with the semester over and the Nationals recent dominance of the Mets putting me in a positive mood, I set to working on the problem.

First, assuming 32 seasons, (the Spurs’ tenure in the NBA) and an equal chance for each team to win an NBA title in each year. With these parameters it turns out the expected probability of winning at least one NBA title with all titles coming in odd-numbered years to be 24.86% (variance 0.044). Of course, that includes the situation that a team wins one NBA title in an odd-numbered year. Keeping with the Spurs motif, the expected probability of winning at least four NBA titles, all in odd-numbered years, to be 0.14% (variance 6.61*10^-5).

But as we all know, NBA teams do not all have equal chances of winning an NBA title, no matter how much Pacers fans may hope. So I changed the parameters of the situation, this time looking at 11 seasons (Tim Duncan’s time in the NBA) and a more Spurs-appropriate probability for an NBA title each year (12.5%). With these parameters in place, the expected probability of winning at least four NBA titles, all in odd-numbered years, to be 0.049% (variance 7.05*10^-6). Not very likely at all (duh).

There you have it. The expected probability of a Spurs-with-Tim-Duncan-quality team winning at least four titles in 11 years with all titles coming in odd-numbered years and everything being random: 0.049%.

Do you have any other random/intriguing/pointlessly intriguing sports probability problems? Such as an expected value of how many appearances until Aaron Heilman doesn’t ruin a game for the Mets?