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Sunday, May 5, 2013

Randomness and Winning (and Losing) Streaks

A few years back the folks at Radio Lab visited Deborah Nolan's statistics class in order to explore that nature of randomness ("Stochasticity: A Very Luck Wind"). When there Nolan divided the class into two sections. She gave one section a coin and asked them to flip the coin 100 times and record whether it was a head or a tail. She asked the other class to simply imagine flipping a coin 100 times and then record whether each flip was a head or a tail. She then left the room and didn't return until both sections had finished "flipping" their coins. After glancing at what the two sections had recorded, she correctly guessed which record represented the section that flipped the actual coin and which one had not.

Why? Because when most people think of randomness, they don't imagine that long streaks of heads or tails occur, but they do and more often than they think. It is not unusual to for a head (or a tail) to appear 4, 5, 6 or more times in a row. However, if you ask someone (or a class) to imagine flipping a coin 100 times and recording whether each flip was a head or a tail, you typically get something like this:


Such a pattern, however, is anything but random. There's a pattern to it. Instead, a series of coin flips is more likely to look something like this:


Of course, if you flip a coin over the long run you will get heads about 50% of the time and tails about 50% of the time, but there's no guarantee that in the short run you will. This is captured by the graph below, which plots the percentage of heads over 100 coin flips. As you can see, the first flip was a head, but then a series of tails occurred before a number of heads (and only a few tails). And by 100, the percentage of heads is approaching 50%.

Unfortunately, we often mistakenly see patterns in random events and interpret them in terms of cause and effect when there is none. This often occurs in the world of sports. A team will go on a 5-game losing streak, and fans will start asking what's wrong when, in fact, there is nothing wrong. Randomness has simply played a role. For example, a basketball team, which typically makes 50% of its shots, has a series of games where an unusual number of shots roll in and out. Or a baseball team keeps hitting line drives at the other team's players, while their bloop hits keep falling in.

To illustrate this, I simulated one hundred 162 game seasons for a team that wins 58% of its games. That is, a team that on average will win 94 games a year, which is typically enough to make the playoffs. However, as the graph below shows, the number of wins that such a team could have ranges from 78 to 109 (although the extremes are improbable). Needless to say, if a team won 94 games one year and 78 the next, its fans and owners would probably ask, "What Went Wrong?", when it's possible that nothing went wrong, except that the team had a really bad run of luck. However, even if the owners sense this, if they do nothing, their fans will throw a hissy fit and the rest of league will heap scorn on them.

Now consider the streaks that such a team could experience in a given season. The first graph below presents the range of the longest win streak the team would have during a season; the second, the range of the longest losing streak the team would have. In other words, in an average season, the longest winning streak of a team that wins 58% of its games will be 8 and the longest losing streak will be 4 or 5. As you can see, however, the range of possibilities (from pure randomness) is quite large although the extremes (i.e., an 18-game winning streak and a 11-game losing streak) are highly unlikely.

Is there a moral to the story? Possibly. At least for owners, managers, and players: Don't push the panic button too quick. You may just be experiencing a run of bad luck. Nothing more.

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