Posted by Neil Paine on January 12, 2011
All four of this weekend's playoff matchups feature rematches of regular-season games:
|Patriots vs. Jets|
|Steelers vs. Ravens|
|Falcons vs. Packers|
|Bears vs. Seahawks|
How much extra information (above & beyond the Simple Rating System) can we glean from these previous matchups of playoff foes?
To answer that question, I looked at every playoff game since 1970 that featured teams who played in the regular season, recording their respective SRS scores and the total HFA-adjusted margin of their previous meetings (the HFA adjustment was -2.7 to the home team's margin and +2.7 to the road team). There were 206 such cases, ranging from the Colts and Dolphins' 1971 AFC title-game showdown to the Eagles-Packers game this past Sunday. Plugging the data into a logistic regression model, we arrive at the following formula:
p(W) ~ 1 / (1 + EXP(-0.1319031*SRSDiff + 0.01757894*TotMOV))
Where SRSDiff = (Home Team SRS - Road Team SRS + 2.7), and TotMOV is the cumulative HFA-adjusted margin of victory for the team in all of its regular-season matchups with the playoff opponent. Both variables were significant at the 0.05 level.
Using this equation, we get the following win expectancies for this weekend's games:
New England vs. NY Jets: 1 / (1 + EXP(-0.1319031*(15.4 - 6.5 + 2.7) + 0.01757894*(-11.3 + 39.3))) = 73.8%
Pittsburgh vs. Baltimore: 1 / (1 + EXP(-0.1319031*(10.2 - 6.4 + 2.7) + 0.01757894*(-5.7 + 5.7))) = 70.2%
Atlanta vs. Green Bay: 1 / (1 + EXP(-0.1319031*(6.1 - 10.9 + 2.7) + 0.01757894*(0.3))) = 43.0%
Chicago vs. Seattle: 1 / (1 + EXP(-0.1319031*(4.1 - (-9.4) + 2.7) + 0.01757894*(-5.7))) = 90.4%
An interesting implication of this formula is that the more you cumulatively beat your opponent by in the regular season, the lower your chance is of beating them in the playoff rematch. For instance, holding SRS equal (which admittedly isn't realistic because SRS would change with a change in cumulative MOV -- see below), if the Patriots had a margin of zero vs. New York during the regular season, they would be expected to win the playoff game 82.2% of the time. My only explanation for this is that, holding SRS constant, you gain extra information about your opponent via big losses. Keeping with the Jets-Pats example, perhaps Rex Ryan will receive more information about how to beat the Pats from the 45-3 loss than Bill Belichick received on how to beat NY from the 45-3 win.
"Ryan outcoaches Belichick. Again. Obvious that these two teams will meet in the playoffs when it counts; Jets didn't show anything 2nite" - 10:46 PM Dec 6th, 2010
Of course, it's never really that simple. A decline in cumulative season-series MOV will also lead to a decline in SRS (and an increase in opponent SRS) -- for instance, if the Patriots had tied the Jets on 12/6, their expected W% would be 76.1% because their SRSDiff would drop from 11.6 to 6.9. That said, there still would be a slight positive effect (76% vs. 74%) by erasing the 42-point blowout.
Other than the "increased information" theory, can anyone think of explanations for why this might be the case?