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What do the Kansas City Royals and my iPod have in common?

On the surface, not much. The Kansas City Royals have lost 19 straight games and are threatening to break the all-time record for futility in major league baseball. My iPod, on the other hand, has quickly become one of my most beloved material possessions.

So what do they have in common? They both can teach us a lesson about randomness.

The human mind does badly with randomness. If you ask the typical person to generate a series of “heads” and “tails” to mimic a random sequence of coin tosses, the series doesn’t really look like a randomly generated sequence at all. You can try at yourself. First, before you read further, write down what you expect a random series of 20 coin tosses to look like. Then spend 15-20 minutes flipping coins (or use a random number generator in Excel). If you are like the typical person, the “random” sequence you generated will have many fewer long streaks of “all heads” or “all tails” than actually arise in real life.

My iPod shuffle reminds me of this every time I use it. I’m consistently surprised at how often it plays two, three, or even four songs by the same artist, even though I have songs by dozens of different artists on it. On a number of occasions, I’ve even become mistakenly convinced I don’t have the iPod on shuffle, but rather, I’m playing all the songs by one artist. (If someone is really bored, maybe they can repeatedly have iPod shuffle the songs, record the data, and see if shuffle really is random. My guess is that it is random, because what would be the point of Apple doing something different? I have a friend, Tim Groseclose who is a professor of Political Science at UCLA, who was convinced that the random button on his CD player knew which songs were his favorites and disproportionally played those. So I bet him one day, made him name his favorite songs in advance, and won lunch.)

Which brings us to the Kansas City Royals. It seems like, when a team loses 19 games, that is so extreme that it can’t reasonably be the result of randomness. Clearly coaches, sports writers and most fans believe that to be true. How often have you heard of a coach holding a closed-door meeting to try to turn a team around? But if you look at it statistically, you expect 19 game losing streaks to occur, simply by randomness, about as often as they do.

The following calculations are admittedly crude, but they give you the basic idea. Each year, there are about two teams in the major leagues that have a winning percentage of around 35%. (Sometimes no team is that bad, in other years there are real stinkers like Detroit in 2003 — they won only 26.5% of their games.) The chance of a team that has a 35% of winning each game losing their next 19 games is about one in 4,000. Each team plays 162 games a year, so has 162 chances to start such a streak. (They count streaks that begin in one year and end in the next year, so it is correct to use all 162 games.) So each year, for these two bad teams that win 35% of their games, there are a total of 324 chances to have a 19 game losing streak. It takes about 12-13 years for these two bad teams to have a total of 4,000 chances for a 19 game losing streak. Thus we would expect a losing streak this long a little less than once a decade. In practice, we see, if anything, slightly fewer long losing streaks than expected based on these calculations. The last really long losing streak was by the Cubs in 1996-1997 — 16 games. (There is actually a good reason that long streaks occur a little less than in the simple model I was using. It is because a team that wins 35% doesn’t have the same likelihood of winning every game: sometimes it has a 50% chance and sometimes a 20% chance…that sort of variability lessens the likelihood of long streaks.)

So, one doesn’t need to resort to explanations like “lack of concentration,” being “snakebit,” or demoralized to explain why the Royals are losing so many games in a row, just that they are a bad team getting some bad luck.