Friday, January 31, 2014

Super Bowl Prediction

Seahawks 31, Broncos 17

At the beginning of the year, I would not have expected to be picking against Denver. They were playing as well as any football team ever, and it didn't look like anyone would come close. But due to the nonlinear nature of my metric, their ranking was based on a value that could come down pretty fast. And it did. Not out of the top few teams in the league, mind you, but when there's a cubic term, there can be a big difference between first by a lot and first by a little. And half way through the season, the Seahawks pulled ahead. And never looked back. They snuck into the number one spot defensively only in the last week of the season. But what went unnoticed to the mainstream was their offense. They may not have piled up a lot of yards, which happens when you run the ball a lot. But still, only seven teams managed to score more points. In fact, a lot of fans would be shocked to learn that neither the Saints nor the Chargers were able to score as much as the offenseless Seahawks. And those teams didn't have to face the Cardinals and 49ers twice. The Seahawks have the skill to dominate on offense as much as any team sitting at home. When they open up the passing game, they're lethal. And they will. Darrell Bevell finally showed a willingness to make non-horrendous decisions during the conference championship game. Against a defense that has Terrance Knighton in the middle, he'd be hard pressed not to do it again. And exploiting this mismatch is going to be the big difference in the game. The Seahawks are actually the team with the practically unstoppable offense. Bevell was the only thing stopping them all season.

As we can see with my rankings, the Seahawks are the much better team. The gap between them and the Broncos was almost twice the gap between the league's third place team, the Patriots, and its last place team, the Texans (ok, that's more of a function of the luck (or lack thereof) for the Pats and Texans, but the Seahawks are clearly superior to Denver).

...

But something's being overlooked. Injuries. And the fact is, the Seahawks are a much healthier team. I want to talk about two players specifically. To do this, I'll take us back to a time when we could see both of them playing healthy for an extended period of time. Specifically, midway through the 2012 season. Let's go.

So it's the start of November now, and we're trying to decide on the ten best players in the league. The Broncos aren't very far into that 11 game winning streak, but Peyton still makes it. We realize he's back. Adrian Peterson has been good, but his first half just isn't at MVP level yet. But it turns out we're lying to ourselves, because the top two MVP candidates in the future aren't the two best players right now. In fact, they AREN'T THE BEST PLAYERS ON THEIR OWN TEAMS. That's right. Other than JJ Watt, the two best players in the world are their teammates: Von Miller and Percy Harvin. And on that note, we come back to the present, when one of these two players is about to be a world champion. But one of them isn't playing. That .1 difference between the Seahawks and Broncos? That was with a top 3 player in the NFL playing half the season. And more importantly, with another top 3 player not playing (pretty much) at all. But it's all switched now. And the Seahawks have a huge advantage.

I will acknowledge the variance in football, and I will acknowledge that my predicted score does not, by any means, represent an actual, calculated, median score, or even average score, for each team. But it's no fun to give a real prediction, like: the Seahawks' score will be (approximately) normally distributed with mean 26 and standard deviation 8, and the Broncos' score will be (even more approximately) normally distributed with mean 21 and standard deviation 12. Which leads to a probability .64 for the Seahawks winning. If you want to judge me based on a prediction, judge me based on this one. And don't give me credit for my first one. I did that to grab attention. And show the strength of my convictions about my model. And that's all any "expert" on espn is doing as well. The probability that the final score is 31-17 is pretty much identical to the probability that it's 26-21 (In fact, it's higher, because 26 isn't that common a football score.). And wouldn't it be wonderful if I were right?

Wednesday, January 29, 2014

A Super Matchup (Part 2: Rushing)

Rushing. Like that matters. Yeah, right.

A Super Matchup (Part 1: Passing)

Here, I'm just going to look at the passing games. Clearly, the Broncos' passing offense is better. But that doesn't matter. The Seahawks passing defense is better. But that doesn't matter either. This will be a look into the passing game in today's NFL. And we'll see why it's the Seahawks, not the Broncos, who should be wishing the game were played in a dome.

Normally, the offense dictates the passing game. Good quarterbacks put up good numbers. Peyton Manning dominates pretty much everyone. And good defenses get carved up by good quarterbacks. Nowadays, it's just too hard to stop someone who can consistently make the right read and put the ball on the money. Passing games have taken off. So normally, we should be placing much more weight on the Broncos' offensive strength rather than the Seahawks' defensive advantage.

But these Seahawks are different. It's not just how good they are. It's not just that they allow an average passer rating of 63.4 (The Bengals are second, allowing an average passer rating that's more than 10 points higher.). It's that they have transcended the norm. In the Seahawks' case, the first sentence of the second paragraph doesn't hold.

For a typical defense like the Broncos, the correlation between passer rating allowed and opponent's season passer rating is about .6 (I did the exact calculation, going through each game including postseason and looking at the opponent's starting quarterback's passer rating in the specific game and for the whole season, and r=.605.). Since r^2 = .6^2 = .36, this means that 36% of the variation in an opposing QB's passer rating vs. the Broncos can be explained by the variation in his actual season-long passer rating. Most of the rest of the variation can be attributed to luck*. For the Bengals, r^2 was .18: much lower, but still a reasonably significant factor. However, for the Seahawks, that r^2 value was less than .1 (!). They were so good at defense that the success of their opponent's passing game was almost entirely attributable to luck, and only as important as the Seahawks' own defensive skill.

This leads to a least squares regression line for the Seahawks' passer-rating-against of:
RatingAgainst = .874*opponentSeasonRating - 8.187.
For the Broncos, it's:
RatingAgainst = 1.28*opponentSeasonRating - 21.167
For Peyton Manning, we have:
PasserRating = .6024*opponentSeasonRatingAgainst + 58.8
And finally, for Russell Wilson, we have:
PasserRating = 1.535*opponentSeasonRatingAgainst - 34.1

Each of these, respectively, predict passer ratings of:
Peyton Manning rating of 92.42
Russell Wilson rating of 108.41
Peyton Manning rating of 96.99
Russell Wilson rating of 95.66

Manning's average is 94.7, Wilson's is 102. These predictions not only took into account the skills of the offenses and defenses, but how much each depended on the other team's skill. After doing that, we see that it is in fact the Seahawks that have a huge advantage in the passing game, mainly due to a defense that dominates good quarterbacks almost as well as it dominates bad ones. Given how strongly passer rating correlates with winning, this is a good sign for the Seattle Seahawks.

And it makes sense. Normally, a passing attack involves a set of receivers that more talented secondaries will shut down more effectively. The more solid defensive backs a defense has, the fewer receivers that will be open consistently. Similarly, and more importantly, the more stacked a receiving core is (and the more accurate their QB is), the more consistently those receivers will be open enough against overmatched secondaries. There will always be variance, and as I've talked about many times before, way more of it than most people assume, but an overmatched DB is an overmatched DB, and when the probability of some receiver getting open gets close to 1, the variance decreases. Let's look more closely at this. No defense allows less than a 50% completion percentage, so we don't see the variance drop-off from a lower-than-.5 probability of someone getting open (again, open enough. Because the quarterback matters.). If p is the probability that someone gets open enough for a completion, then the variance of completion percentage is attempts*p*(1-p), which clearly gets smaller as completion percentage (p) increases (again, note that in what we're looking at p is always above .5.). So that's one element. But it's not just that. Every quarterback in the NFL can hit an open slant pretty consistently, and every receiver can get open on a slant reasonably often. This will happen against the Seahawks, too. Because some things are just unstoppable (or at least close). What the Seahawks do with their secondary, which is probably the best secondary of all time, is they take away the stuff that's not unstoppable. Which also happens to be the stuff that separates good passing offenses from bad ones. When every offense is reduced to doing something that every offense does pretty well, the good ones don't stand out any more. And this is probably the bigger reason. Getting open deep against Sherman, Maxwell, Thurmond, or Thomas isn't a sign that you're good. It's just a fluke that happens on a blown coverage a couple times a year, irrespective of how good the receiver or quarterback is. And that's why the Seahawks are such a roadblock for good passing games.

*For a typical quarterback, like Andy Dalton (We were talking about the Bengals, and Peyton and Russell are too good to be considered typical), the correlation between passer rating in a given game and that opponent's passer rating allowed (over the season) is about .3 (This was the calculated r value for Dalton. It was only .25 for Manning.), so only about 9% of the variation is due to defense. That's a fourth as much as the variation due to QB against an average defense like the Broncos.

Wednesday, January 8, 2014

New Playoff Simulation

It's interesting that the two worst teams remaining have been matched up against each other in each of the first two rounds. And it will actually happen again in the next round if the Chargers beat the Broncos. And clearly it will be true for the Super Bowl by virtue of the fact that there are only two teams remaining.

Seahawks
Championship %: 36.1921985
Making Super Bowl %: 56.7616887
Conference Championship Game Appearance %: 74.3278182

Broncos
Championship %: 34.5214005
Making Super Bowl %: 66.2177433
Conference Championship Game Appearance %: 76.473966

49ers
Championship %: 9.318069399999999
Making Super Bowl %: 18.6722192
Conference Championship Game Appearance %: 51.2433869

Panthers
Championship %: 5.3916135
Making Super Bowl %: 13.2613655
Conference Championship Game Appearance %: 48.7566131

Saints
Championship %: 5.363147
Making Super Bowl %: 11.304726599999999
Conference Championship Game Appearance %: 25.6721818

Chargers
Championship %: 4.1272912
Making Super Bowl %: 12.2613634
Conference Championship Game Appearance %: 23.526034000000003

Patriots
Championship %: 3.4121841
Making Super Bowl %: 13.820838599999998
Conference Championship Game Appearance %: 60.9514125

Colts
Championship %: 1.6740958
Making Super Bowl %: 7.7000547
Conference Championship Game Appearance %: 39.0485875