The title drought

My posts from a week ago mocking the Miami Heat's downfall might have my three readers thinking that I'm more of a negative fan than I really am. In fact, I consider myself a very positive fan - as much as I enjoyed the outcome of the 2011 NBA Finals, I'd trade it in a second for even an AL Central title for the Indians. Sure, I root fervently against my archrivals when they advance in the playoffs, and relish their defeats, but I really don't want to see them there in the first place. I want the Cleveland teams there.

As you may or may not have heard, however, the Cleveland teams haven't experienced a whole lot of championship success in recent years. I know, it's surprising, especially since national TV never mentions it every time Cleveland makes the postseason. Nevertheless, it's true - we haven't been on top since the Browns' NFL title in '64. The Indians have baseball's second-longest winless streak, having not won since '48. And the Cavs have yet to take home the NBA's top honors. These are the facts.

But what should we have seen by now? What's a reasonable expectation for the number of championships a fan of my seasoning and experience in a three-sport town should have seen by now? We can safely say it's more than zero without even running the numbers, but hey, I like running the numbers. Let's answer two questions: how many championships should I have enjoyed by now, and what are the odds of the current championship-less scenario having developed?

We'll make one key assumption at the outset: every team, every year, has an equal probability of winning it all. I realize that this is not true, for several reasons, but it's an appropriate basis for this sort of calculation. We will also assume that I started watching sports in the summer of '86, because this is indeed what happened. We will also omit the Buckeyes (not pro) and Penguins (not Cleveland) from my analysis.

First, let's look at the number of seasons. I've been through 25 Indians campaigns (1986-2010), 25 Cavaliers seasons (ending 1987-2011), and 22 Browns seasons (1986-1995, 1999-2010). If we wanted to do a quick and dirty analysis, we say that's 72 aggregate seasons, estimate 30 teams per league each year, and say that Clevelanders should have had two or three victory parades during this span. I suspect this won't be far off from the actual answer.

Calculating the expected value of total wins is actually as simple as summing the expected value of a championship for each team-season (i.e. 1/30 for the 2011 Indians) - the only real legwork is figuring out exactly how many teams populated a given league in a given year. Stupidly, I actually did this, and it came out to 2.50. I could have left it at "two or three" and saved us all some time.

Calculating the odds of never having won a title is done a little differently. The approach I take is to determine the product of the odds of not winning a championship for each season. What we're saying is that, every season, our favorite club's expectation of not taking home the title is, let's approximate again, 29/30. The odds of them doing so in n consecutive years, treating each season as an independent event, is (29/30)ⁿ. Using our league estimate of 30 teams per league per season, a quick approximation of us having lost for every one of the 72 seasons that I've been a fan is (29/30)⁷². This works out to 8.7% (8.3% using actual numbers of teams, again proving the utility of my estimate).

Didn't you think that would be a bit lower? Doesn't it seem a bit more improbable than a 1/12 shot that we would never have taken home a title? Think about how many Boston, Chicago, and New York have - granted, they have four or more teams, but still. This surprised me. Meanwhile, readers in Buffalo, San Diego, and Kansas City are trying to figure out what I'm confused about.

What does this mean for the next decade of Cleveland sports? Well, if you tack on the rest of the '10's to my original calculation, bringing us up to 100 total seasons or so, the odds of not claiming a title during the entire span are around 3.3%, or just a 1/30 shot. That sounds better to me. But wait! Unfortunately, the previous 72 are already in the books - if we were predicting the next 35 years, this would be accurate, but a lot of the heavy lifting has already been done. Just isolating the next decade of activity, we're looking at a 36% chance, a bit greater than 1/3, of extending the drought even further.

And for the record, the odds of the current streak having happened are slightly less than half a percent.