06 October 2010

Why 2:1 Odds for the Phillies Is Overly Optimistic

Yesterday I posted the results of a log(5) postseason odds simulation that I'll be updating throughout the playoffs. As Tom Tango notes, my simulation is at serious odds (pun intended) with the crowd. While I have the Phillies at about 15:2 to win it all, Bodog has them a whopping 2:1 favorite! As I noted yesterday, my model is probably short-changing the Phils, but for Philadelphia--or just about any team--to post at 2:1 is quite silly. Patriot helps explain why:
To have even a 50/50 chance [of winning the LCS], a team must be a .606 (98 win) team--relative to its playoff opponents. Even if the playoff opponents are of just .525 true quality, Log5 estimates that the .606 team would be a true quality .630 (102 win) team.
Of course, to average a 33% shot at winning it all, you need a 50% shot at winning the pennant. How does he know this? Basically by running the same type of simulation I did with generic numbers. What this means is that the market is pricing the Phillies as a .630 team even though they've played the full season as a .553 true quality (read, third-order win percentage) team.

This doesn't mean that the market's wrong, but it does hint that the market is probably suffering a bit of recency bias. For another perspective, I thought I'd take a look at the historical relationship between true quality and playoff success, running a logistic regression on all playoff teams from 1999-2009. This is the graph of those results:

The top line indicates probability of winning the LDS, while the next two represent the LCS and World Series, respectively. Historically, in order to have a 2:1 shot to win it all, a team would require a third-order win percentage about 0.125 higher than the 2009 Phils.

The dots indicate where this year's playoff teams fall along those lines. Let's zoom in for a closer look:

Since the Yanks lead in third-order percentage, they lead the pack again. The numbers are a bit different than what the log(5) simulation indicates. The chart below lists the historical chances of each team winning each series based on third-order percentage, compared to the Bodog odds as well as yesterday's simulated odds:

WP3 P(LDS) P(LCS) P(WS) Historical Log(5) Sim Bodog
Yankees 0.590 52.9% 26.9% 13.3% 15:2 11:2 7:2
Rays 0.564 46.9% 20.8% 10.2% 10:1 7:1 9:2
Braves 0.562 46.6% 20.6% 10.1% 10:1 15:2 12:1
Phillies 0.553 44.5% 18.7% 9.2% 11:1 15:2 2:1
Reds 0.548 43.4% 17.8% 8.8% 23:2 9:1 11:1
Twins 0.546 42.8% 17.3% 8.6% 23:2 10:1 17:2
Rangers 0.546 42.8% 17.3% 8.6% 23:2 21:2 10:1
Giants 0.540 41.4% 16.3% 8.0% 25:2 10:1 7:1

In short, the Phils may be a great team. They may even win the World Series. However, based on what we know about the historical relationship between true talent and playoff success, 2:1 seems a bit outlandish.

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