## What Does the Season Series Tell Us About Playoff Matchups?

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 | |||||||||
---|---|---|---|---|---|---|---|---|---|

Rk | Tm | Year | Date | Opp | W# | G# | Day | Result | |

1 | NWE | 2010 | 2010-12-06 | NYJ | 13 | 12 | Mon | W 45-3 | |

2 | NWE | 2010 | 2010-09-19 | @ | NYJ | 2 | 2 | Sun | L 14-28 |

Steelers vs. Ravens | |||||||||
---|---|---|---|---|---|---|---|---|---|

Rk | Tm | Year | Date | Opp | W# | G# | Day | Result | |

1 | PIT | 2010 | 2010-12-05 | @ | BAL | 13 | 12 | Sun | W 13-10 |

2 | PIT | 2010 | 2010-10-03 | BAL | 4 | 4 | Sun | L 14-17 |

Falcons vs. Packers | |||||||||
---|---|---|---|---|---|---|---|---|---|

Rk | Tm | Year | Date | Opp | W# | G# | Day | Result | |

1 | ATL | 2010 | 2010-11-28 | GNB | 12 | 11 | Sun | W 20-17 |

Bears vs. Seahawks | |||||||||
---|---|---|---|---|---|---|---|---|---|

Rk | Tm | Year | Date | Opp | W# | G# | Day | Result | |

1 | CHI | 2010 | 2010-10-17 | SEA | 6 | 6 | Sun | L 20-23 |

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.

If so, this actually lends bizarre credence to Chase's tongue-in-cheek tweets during the Pats' shellacking of New York in December:

"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

"Can not believe how much Belichick continues to tip his hand. #amateur" - 10:58 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?

Pure luck?

On a serious note, injuries might be messing with the data a little bit.

I'm also wondering if the timing of the meeting might be significant--for example, imo, the GB vs. PHI game in week one didn't tell us much about the game last week. GB prepared for Kolb in the earlier meeting, PHI prepared for Ryan Grant at RB, etc. Whereas, if my Saints had bothered to take their defense to SEA, I wasn't worried about going to ATL (thinking that PHI would prob. beat GB because of GB's injuries), since we had just gone there a couple of weeks ago and beat ATL on the Mon PM after Christmas--in a playoff-type atmosphere (given that ATL winning that game would have secured the division & HFA).

Regarding divisional foes (AFC games), I think that the only significant advantage MIGHT be HFA--but, considering that divisional foes play in each other's stadium every year, that advantage is probably minimized.

Statistical noise. Seems pretty clear to me that the conclusion should be "margin of victory in the regular season doesn't significantly predict playoff wins against the same opponent.."

Regression to the mean? If you blow out a playoff-quality opponent by 42 pts in the regular season, that ain't likely to happen again. You were lucky or something. But the +42 goes into your SRS, inflating it (and equally deflating the opponent's). Then when the two of you meet in the playoffs, your inflated SRS combined with the opponent's deflated SRS "overpredicts" your chance of winning. (With only 16 games in a season, pro football stats are always cursed by small sample size.) In the end, the bigger the blowout the less you will actually win compared to what straight SRS predicts.

The last element of your formula seems to be making that correction, via "+ 0.01757894*(-x + y)))" which is added to the divisor of 1.

That is, in the Pats/Jets example "-11.3 + 39.3" (from the 42-point blowout) or 28 is the net of the x,y, increasing the divisor of one, reducing the resulting win% computed from using "Home Team SRS - Road Team SRS + 2.7" accordingly.

In contrast, in the Atlanta/Green Bay game the corresponding amount added to the divisor is "0.3" which is basically nothing. So "Home Team SRS - Road Team SRS + 2.7" rules unchallenged.

Or maybe not. If I don't correctly understand what your equation is doing, never mind. Looking at it again, I'm not sure I do.

I'll try to make my comment above clearer using plain English. Correct me if I am misinterpreting.

I believe you are trying to determine a team's probablility of winning using SRS ("SRSDiff = (Home Team SRS - Road Team SRS + 2.7") then adding the result from the individual game(s) between the two teams to see if it adds any extra information (via "y*TotMOV")

So the probability of winning is 1/ (x* SRSDiff+y*TotMov)

Well, the results of the games between the two teams are already included in SRSDiff, so if they are within normal bounds counting them again via TotMov adds no information. Atlanta beat Green Bay by 3 at home, that equals out to near 0 after HFA, at the very center of normality, setting y*TotMov at basically zero -- so the win probability determined using SRSDiff is unaffected.

But the Pats beat the Jets by 42. Many Jets fans consider that the center or normality too, but in reality no playoff team is 42 better than another. The betting line indicates the money people think the Pats are better by about 6 on the merits on a neutral field. If so, then in the SRS computation that game gives the Pats 36 too many points and the Jets 36 too few, 72 total, divided by 16 = 4.5 net in the SRS tally. This will cause SRSDIff to significantly overpredict a NE victory.

But your regression, which counts the actual historical wins resulting from such relationsips, catches this by now adding a significant positive number into TotMove, and since TotMov is in the divisor, it reduces NE's computed chance of victory ... appropriately. (At least the computer thinks appropriately).

So, yes, your formula does result in one team's calculated chance of winning being reduced if it as has whomped the other earlier -- and correctly so.

If during the regular season two playoff teams played close games against each other, TotMov has no information to add to SRSDIff and doesn't matter, it equals near zero.

But if one team walloped the other by 40, TotMov identifies the game as an outlier that distorts SRSDiff, and corrects the situation by reducing the winning team's calculated chance of winning again, to offset the SRSDiff distortion. The bigger the outlier, the more TotMov reduces the calculated chance of winning.

I think. But ten I may be TotConfused.

That sounds plausible. We know the results aren't due to chance (or at least there's better than a 95% probability that they aren't). However, what you describe is a pitfall I've fallen into because the variables are at least partially linearly correlated (in the sense that totMOV already goes into the SRS calculation). One depends on the other to a degree, which defeats the purpose of having variables where you can change one and keep the other constant.

The better thing to do is probably to regress everyone's SRS to the mean, which will deal with

alloutliers (not just specific ones against the playoff opponent) and then re-run the logit with just SRSDiff as the predictor. I don't think it's going to change much, though: Doug's formula from 5 years ago has the Pats winning 76% of the time.I'm trying to follow the statistics here... In order to have a confidence level, you must be testing against a null hypothesis of some sort, yes? What's the null hypothesis we're testing against here?

What's the formula for p(W) when you don't have the second term with head to head MOV? Are the results really any worse than having the second term? I'd expect them to be very marginally worse simply due to a second term being there, but...

Is there any chance we can get the 206 games with SRS, MOV, results, etc.?

Oh, and sometimes your head-to-head MOV is one game, sometimes 2. I'd expect some sort of SNR issue here, where your coefficient would be higher when you look at the 2-game setups but lower with the 1-game setups.

How about keeping it simple? For every instance where Team A plays Team B in the postseason, how often does Team A win when it was:

1-0

0-1

2-0

1-1

0-2

vs. Team B in the regular season? I'm supposing we can ignore ties, due to the very small sample size.

It may be simpler than that - pride. A team that is blown out, especially against a bitter rival, is going to froth at the mouth for a chance at redemption. And expectations are lower for them because of the previous loss, so they can just come out and play loose.

It's particularly true in this case as the Jets demonstrated they were capable of beating the Pats at least at one point.

Re: Mattie -

The null hypothesis here would be that cumulative MOV against your opponent has no predictive relationship with W-L after taking SRS into account.

If you take out TotMOV, you end up with this equation:

p(W) ~ 1 / (1 + EXP(-0.11425*SRSDiff))

I also tested for head-to-head MOV per game, but it wasn't significant while TotMOV was.

Here's the dataset I used.

The Gambler's fallacy is real? Maybe?