August 29, 2014

Feature Focus

Feature Focus: Playoff Odds

by Rob McQuown

Playoff odds are based on three things:

1. Playing time estimates for each player for the rest of the season (as found in the Depth Charts).

2. PECOTA projections for each player for the rest of the season, with playing time taken from depth charts.

3. A simulation of a high number of seasons, where each matchup on the actual schedule is "played" (simulated).

After these seasons have been simulated, the playoff odds report simply tallies the number of times each outcome occurred, such as a team winning its division, winning a wild card spot, or winning the World Series.

As we reminded you in the past, 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*."

-- Colin Wyers, 2013

*ed - presumably unless your favorite team is the Houston Astros.

Okay, already, show me the odds!

Simply click on the pulldown menu option within the "Standings" category:

Oh, no! What happened to the Astros chances, Colin?

Here are some details on some of the columns (much of the following explanation taken directly from Colin Wyers' past explanation, reprinted here for convenience):

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:

Div Pct + (WC Pct * AdjWinPct)

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.

Note, for example, that while Atlanta has almost a 40% chance for postseason play, their odds of reaching the NLDS is just over 20%:

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.

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Note: Clicking on a team name on this page takes you to the data-packed Team Audit page for the team selected, which starts with basics, such as this Angels page:

We'll have more on other features, including Team Audit, in upcoming weeks. We hope you enjoy Playoff Odds, and feel free to pose any questions you have about them here.

Rob McQuown is an author of Baseball Prospectus. Follow @robmcquown
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