The last question Bill James was asked in this interview was "How many games are the Royals going to win." His answer was 66. They've won their first 8 games. Is there any evidence that Bill underestimated the Royals? Luckily, we can use probability to get a handle on this.

Sixty six wins implies that the Royals would have .4074 winning percentage, or their probability of winning a game is .4074. Now think of a Royals game as a coin toss where the coin isn't fair. Heads only comes up 40.74 percent of the time, and the Royals always call heads. This represents a Bernoulli trial. The outcomes of a series of Bernoulli trials can be described by the binomial distribution. Basically, we can use the binomial distribution to ask, "What is the chance of a team with a .4074 winning percentage winning 8 out of 8 games? The answer is .00076. That's a small number, and you might be saying, "Bill James doesn't know what he's talking about! The Royals are going to win 100." But all we've done is consider the probability of the Royals winning a specific eight games.

During the course of a season, the Royal play a have 155 chances to win eight games in a row (they overlap). So we can set up a new Bernoulli trial, where the trial is:

Over this stretch of eight games, did the Royals win all eight?

From above, we know the chance of 8 in a row is .00076. We can now use this probability to and a binomial distribution to ask the question, "What is the probability of at least one eight-game winning streak in 155 chances for a team who's probability of winning eight in a row is .00076?" And the answer to that question is .11166, or a little over 11%. That's not significant. So they could still reasonably win only 66 games. We'll see what the numbers look like in another week.