So here we go. Losers of 13 straight, our beloved Royals head into New York to face a shaky Yankee team thats managing to win, in a stadium wherein the Royals literally haven't won in years.
You might remember the awful game from yesterday, for those that like numbers and bad memories, here's the Win Expectancy graph:
Last season, as the Royals lost 19 straight, James Click at Baseball Prospectus ran the numbers on the likelihood of losing that many. Assuming the Royals were a .325 team there's about a 3% chance that the team would lose 13-straight at any given point. You can find the article here (reg req'd).
Perhaps some interpid reader would like to run the numbers for the current team. Here's the formula,
As Rany Jazayerli pointed out, "In other words, it's not accurate to say that the odds of not losing 18 in a row on Day X is (1-.000984) = .999016, and (.999016)^144 = the odds of not losing 18 in a row over an entire season. On Opening Day, the odds of starting an 18-game losing streak is .000984; from that day on, the odds are (.000984) * (.319)." (He also pointed out that a 162-game season provides 145 opportunities to lose 18 games, not 144.)
A more accurate formula to answer the question we were asking--how likely is a team of a given winning percentage to lose a certain number of games in a row at some point during the season?--would be this:
Where W% is the team's "true" winning percentage and G is the number of games in the streak. Let's break this down into pieces to get a better idea of what's going on. 1-W% is the odds a team will lose a game, so (1-W%)^G is the odds they will lose the required number of games in a row. Then, 1--((1-W%)^G)*W% is the likelihood that a team will start a losing streak of the required number of games after winning the game before. This is the key component that Rany identified that prevents us from counting streaks of G+1 games as two streaks of G games and thus inappropriately doubling the odds of a team losing that many games in a row. Raising 1--((1-W%)^G)*W% to the power of (163-G) gives us the odds that a team will not encounter the required streak and thus we finish by subtracting from one. (We use 163 instead of 162 because any number of games X is X+1 chances to have the required streak; for example, if we wanted to know how many chances a team has to lose one game in two games, we wouldn't raise it to 2-1, we'd raise it to 3-1 since there are two chances to lose.) In effect, it's the same formula from last week, but we've multiplied the odds of the streak in any given number of games by the team's winning percentage before running it for the full season.
So for the current team it would look something like this?
I have no idea how to do that, especially since I don't own a calculator.
When a team is as bad as the Royals (a .222 winning % !?!?!?) its not that far-fetched that the team will lose 13 straight. Hell, the Royals already came close once this season, and we've only played 45 games.
The Royals send Self-Appointed Team Effort Inspector Scott Elarton to the mound, with his awe-inspiring, respect inducing 0-5, 4.71 ERA line. Elarton is 2-0 in 3 career starts against the Yankees, albeit with a 4.74 ERA. The Royals square off against a Mike Mussina (6-1, 2.57 ERA) whos having something of a renaissance season.
Should be an incredible game.