Are the Mariners really that bad?

Baseball prides itself on its obsession with statistics. I can't count the number of times I've heard an announcer tell me "Joe DiMaggio is hitting .376 with runners on first and third, less than 2 outs, against a left-handed pitcher from Venezuela, playing outdoors in an afternoon game after being shut out the night before by a right-hander." But statistics don't always tell the tale, I'm afraid.

Commentators love to use the phrase 'He's due' to explain why a person suffering a slump should be expected to get a hit his next time up. Let's consider an example. Consider a player, we'll call him Ichiro, with a lifetime batting average of .300. That means that over his career, he's gotten a 3 hits for every 10 times up to bat. We won't get into what constitutes an official at bat here - just assume he gets 3 hits every 10 times up. The problem is that Ichiro is mired in a slump. Here is what you could hear from an announcer:

"Ichiro steps to the plate in the middle of a 2-20 slump the past 5 games. He is due to break out of that slump and have a big night."

Ever heard that phrase before? It suggests a deep understanding of statistics and probability. And it's wrong. When Ichiro steps to the plate, he's going to do one of two things - he'll either get a hit, or he won't. Some people consider that a 50/50 proposition, but in baseball, the chances of getting a hit on a given at-bat are far worse than 50/50. Anyone who can get 3 hits in 10 tries will be a millionaire. So Ichiro, who hasn't been able to get a hit, faces two options: He continues on his streak of futility, or he manages to get a hit. The question is, which is more likely BEFORE he steps to the plate?

To understand this better, let's consider a coin-tossing experiment. In this experiment we toss a coin 10 times and count the number of heads we see. After 10 tosses, we predict the outcome of the 11th toss. Sounds easy, right? Most people would say the probability of getting a head on the 11th toss is 50%.

Now imagine tossing the coin 10 times and seeing all 10 come up heads. What do you predict now? Some people will say 'Heads' because after all, if it came up heads 10 times in a row, it probably will come up heads again. Some will say 'Tails' because "it's due". Finally others will say 'It's 50/50' because that's what coins do. Who is right here?

What we are seeing is a case of the Law of Small Numbers versus the Law of Large Numbers. One is statistically valid, the other is bogus. We are a culture that lives in the moment - what have you done lately, how many games have you won this year, what did you get on your last test? But using small numbers to make significant predictions about future events is dangerous. Small numbers (such as 10 tosses of a coin) sometimes show up with unexpected 'patterns' that cause us to believe something is not right. If you track the performance of a single stock for 4 straight days, you may see it drop each day and conclude that it's overpriced and that you shouldn't buy it. However, this little run of bad luck might be sandwiched between significant growth over time that you miss by looking at the small numbers. A bank CEO might see his bank's value drop over a couple of years after stunning growth the previous 10. Did the CEO suddenly lose the ability to lead the bank? Or is this just a hiccup on the long road of financial development?

The Law of Large Numbers accommodates small fluctuations in performance and doesn't panic. It sees strings of success and failures come and go, and only over time does a clear pattern emerge from the apparent chaos of random events. Those that invest in the stock market for the long haul tend to do better than those who buy and sell on a whim. Baseball takes 162 games to determine a winner. So, too, do statisticians wait for performance over a long period of time and a large number of trials to determine whether a situation is significant or not. And that brings me to my question:

On April 30, the Seattle Mariners were one bunt away from moving into first place in their division. It was the 11th inning, Cliff Lee had pitched a masterpiece, and all they had to do was lay down the bunt. They missed it and Ichiro was tagged out at home. They went on to lose that game. And the next. And the next. All told, they lost 8 straight games to fall well behind the pack in the AL West. So today is Mother's Day, and the question is, what are the M's chances of winning the game? If you are a Small Numbers person, you might think 'they are bound to win eventually, so I think their chances are good.' If you have already jumped off the bandwagon of fan support, you might think 'they are terrible again, and are destined to lose.' Or you might say 'they aren't that good, but they have a chance of winning this one.'

The question is, when a team suffers a long losing streak, do the chances of the team finally winning go up, go down, or stay the same?




By the way, the Mariners won today, 8-1, and are currently 12-19, 5 1/2 games out of first place.