Today, we’re launching the first iteration of our Playoff Odds Report for 2013.
Before we get underway, some notes. PECOTA does not hate your favorite team. PECOTA is a collection of algorithms, written in computer code and run by an unfeeling machine. It cannot hate, or love. It can do only what it is told to do, nothing more or less.
I’m the one that hates your favorite team.
No, but seriously. These odds are based on preliminary depth charts, with teams still having many roster moves to make before the season starts. Thus, they aren’t etched in stone, they’re etched in sand. And these are PECOTA’s estimates of what would happen if the season were played thousands of times. PECOTA is not infallible, and the season is played but once. It is a prediction, not destiny.
Which brings us to the changes we’ve made to the methodology of the Playoff Odds. We recognize that PECOTA is not infallible, which is why we use a Monte Carlo sim with random numbers instead of just ranking teams by the output of the Depth Charts. But in examining the Playoff Odds Report, we found that the randomness was pretty symmetrical. So what we’ve done is skew the randomness toward the mean a bit more, so that we no longer have playoff percentages above 90 percent before spring training games are even underway. What this also means is that you’ll see a smaller spread of SimWin and SimLoss than what you see in the Depth Charts and other products.
As you might have noticed, we’ve added two new columns to the Playoff Odds Report, just to the left of the one- and seven-day deltas: Adjusted Playoff Percentage and World Series Win Percentage.
Adjusted Playoff Percentage, which we abbreviate as Playoff Pct (Adj), is scaled more like Playoff Percentage used to be when there was only one Wild Card in each league. It’s the chance that a team will make it to the Division Series round (in other words, the odds that it will win the division plus the odds that it will win the Wild Card and win the play-in game), and it’s figured as so:
To determine the adjusted WinPct, we use the odds ratio method to figure out the odds of a team winning a matchup against the other Wild Card team. To calculate the winning percentage of the other Wild Card team, we take an average of all other teams in that league, weighted by their odds of winning the Wild Card. This way, the better your team is, the weaker your expected Wild Card opponent.
(We have to apply a slight adjustment to the odds ratio method to get everything to work out correctly; instead of assuming that the league average is .500, we figure out what the league average would be if we removed the team in question. Otherwise we end up overestimating the Wild Card advancement rate.)
The benefit of the Adjusted Playoff Percentage is that it allows us to compare teams across divisions and leagues more readily because it places a greater emphasis on a team’s chances of winning the division (which in the current playoff format is much more valuable than winning the Wild Card). If you have two teams with otherwise equal Playoff Percentages, the team that is more likely to win its division instead of a Wild Card berth is in a better situation, and our Adjusted Playoff Percentage reflects that.
We also have our WS Win Pct, which tells us the odds of a team winning the World Series given its Adj. Playoff Pct and its expected win percentage. What we first do is come up with an expected win percentage for the Division Series round, using the team’s expected win percentage and the odds ratio method outlined above. Then we use the binomial probability mass function to figure out the odds of winning a five-game series. We multiply the Adjusted Playoff Percentage by that to figure the odds of advancing to the Championship Series round, and then start the process all over again (except we use the probability mass function for a seven-game series this time). Then we repeat the process one more time to get the odds of winning the World Series.
This World Series percentage is useful, again, because it helps put a team’s playoff chances in perspective. Because we use a league-quality adjustment, an AL team with the same Adjusted Playoff Percentage is favored in the World Series Win Percentage.
(The astute among you may notice that these odds will be uniformly lower than the odds of winning the World Series given out by sportsbooks. This is not because we hate your team, but because sportsbooks include something called the vigorish. When adding up the implied probabilities from one sportsbook, the total came out to nearly 140 percent. Because of a pernicious reality-based bias we have, our World Series odds instead add up to 100 percent.)
You can view the Playoff Odds Report through this link and also from the dropdown list accessible by mousing over the "Standings" button on the navbar at the top of any BP page. We will continue to update the odds up until the start of the season (as well as daily during the season), as the Depth Charts continue to be updated to reflect roster moves and the like. But for now, we hope that you find these useful, and that the new additions help to further illuminate the playoff races in the early going.