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.

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  1. Stephen Jay Gould wrote a classic essay on the application of statistical reasoning to baseball streaks (my version is “Streak of Streaks” in “Bully for Brontosaurus” but I know it was published previously under another name).

    Maybe it’s the fact that I was actually paying attention in the couple of statistics classes I took, or maybe I’m just a computer geek, but if you asked me to generate a random sequence of heads and tails the FIRST thing I would do is open Excel.

    It would be interesting to see what random sequence generator iPod and other consumer electronics use to create their shuffle mode and whether it is truly random.

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  2. CK says:

    So each baseball game is an independent event having neither been effected by the previous game nor having any effect on the subsequent game?

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  3. Well, that’s the really interesting question, CK. If we suppose that each game is an independent event, can we generate a team’s pattern of wins and losses that reasonably matches the data?

    But perhaps teams are streaky. That is, perhaps winning one game increases the probability that the team will win the next game, and losing a game moves lowers the probability that they will win the next one. Teams move back and forth between probability states (a hot state, a neutral state, or a cold state), and their wins and losses are generated accordingly. Are the sequences of wins and losses generated from this process better fits for the data than the sequence generated by independent games?

    This sort of idea crops up in Albert and Bennett’s book “Curve Ball”, which is worth reading.

    Oh, and Steve ….. while we’re on the topic of baseball, did you ever do anything else with the Moral Hazard / DH Rule? I really liked your critique of that idea.

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  4. CK

    My point is that, to a first order, you can adequately model the data as if what happened yesterday doesn’t affect what will happen today anymore than what happened a week or two ago. It is also possible that sometimes losing yesterday helps you win today and other times losing yesterday hurts your chances of winning today. But on average, it looks like a wash.

    Alex –

    I haven’t done anything else on DH/moral hazard.

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  5. elisha says:

    is the winner of the world series also random? is it possible for a team to, by chance, win 100+ games in a season?
    the problem with this perspective is that it removes skill and effort from the equation and leaves success to fate.

    but very interesting perspective. i enjoyed reading it.

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  6. CK says:

    So here I stand with one foot on the burning coals and the other on a block of dry ice, to a first order approximation I am comfortable. Actually since I live near Philadelphia that is probably correct.

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  7. I would like to argue that iPods are random with sporatic moments of being sentient, and personable, creatures. I offer two pieces of evidence for this. Twice I was running late for the bus, and on both occasions, the theme song from Shaft came on. Both times, the song came on at the corner of Lumpkin and Broad Street, and the song perfectly described what I was feeling as I was running to catch the bus.

    A second time, I got up to leave a coffeeshop late one night, popped in my iPod, walked to my car and the radio turned on, blaring loudly. Not only was it the exact same song as the one on my iPod – it was synchronized perfectly with it.

    Almost as if my iPod knew that that song would be on, and wanted to prepare me for the cartrip home…

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  8. I suspect that iPod shuffling is random, with the caveat that the song currently playing is not allowed to be selected to play next. People sort-of understand ‘random’, but they’d be irritated if their iPod played the same song twice in a row.

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