I suspect  to a first approximation almost no one other than Baltimore fans, such as Brian Burke, and this blog really believed that Baltimore had much of a chance(+). Well, I should mention Aaron Freeman of Falc Fans, who was rooting for Baltimore but still felt Denver would win. Looking, his article is no longer on the Falcfans site. Pity..

WP graph of Baltimore versus Denver. I tweeted that this graph was going to resemble a seismic chart of an earthquake. Not my work, just a screen shot off the excellent site Advanced NFL Stats.

WP graph of Baltimore versus Denver. I tweeted that this graph was going to resemble a seismic chart of an earthquake. Not my work, just a screen shot off the excellent site Advanced NFL Stats.

After a double overtime victory by 3 points, it’s awfully tempting to say, “I predicted this”, and if you look at the teams I’ve  favored, to this point* the streak of picks is 6-0. Let me point out though, that you can make a limiting assumption and from that assumption figure out how accurate I should have been. The limiting assumption is to assume the playoff model is 100% accurate** and see how well it predicted play. If the model is 100% accurate, the real results and the predicted results should merge.

I can tell you without adding up anything that only one of my favored picks had more than a 70% chance, and at least two were around 52-53%. So 6 times 70 percent is 4.2, and my model, in a perfect world, should have picked no more than 4 winners and 2 losers. A perfect model in a probabilistic world, where teams rarely have 65% chances to win, much less 100%, should be wrong sometimes. Instead, so far it’s on a 6-0 run. That means that luck is driving my success so far.

Is it possible, as I have argued, that strength of schedule is an under appreciated playoff stat, a playoff “Moneyball” stat, that teams that go through tough times are better than their offense and defensive stats suggest? It’s possible at this point. It’s also without question that I’ve been lucky in both the 2012 playoffs and the 2013 playoffs so far.

Potential Championship Scenarios:

 

Conference Championship Possibilities
Home Team Visiting Team Home Win Pct Est. Point Spread
NE BAL 0.523 0.7
HOU BAL 0.383 -3.5
ATL SF 0.306 -6.1
SF SEA 0.745 7.9

 

My model likes Seattle, which has the second best strength of schedule metric of all the playoff teams, but it absolutely loves San Francisco. It also likes Baltimore,  but not enough to say it has a free run throughout the playoffs. Like many modelers, I’m predicting that Atlanta and Seattle will be a close game.

~~~

+ I should also mention  that Bryan  Broaddus tweeted about a colleague of his who predicted a BAL victory.

* Sunday, January 13, 2013, about 10:00am.

** Such a limiting assumption is similar to assuming the NFL draft is rational; that the customers (NFL teams) have all the information they should, that they understand everything about the product they consume  (draft picks), and that their estimates of draft value thus form a normal distribution around the real value of draft picks, and that irrational exuberance, or trends, or GMs falling in love with players play no role in picking players. This, it turns out, makes model simulations much easier.

Though the results for the divisional round are embedded in the image of my playoff spreadsheet in my previous article, the table below is certainly easier to read.

 

Divisional Playoff Round
Home Team Visiting Team Home Win Pct Est. Point Spread
DEN BAL 0.477 -0.7
NE HOU 0.638 4.2
ATL SEA 0.462 -1.1
SF GB 0.700 6.3

 

I suspect other systems will rank Seattle as stronger than mine does, and Baltimore as weaker. That said, the Vegas line as of this Sunday gives Atlanta a 2 point advantage over Seattle, and my system slightly favors Seattle. We can calculate odds and points via other mechanisms, say, Pythagoreans, SRS and median point spreads, and if we do, what do we get?

 

Atlanta Versus Seattle
Technique Home Win Pct Est. Point Spread
Median Point Spread 0.632 4.0
Simple Ranking System 0.407 -2.8
Pythagorean Expectation 0.486 -0.4

 

Certainly different systems yield different emphases. For me, the one lasting impression I had was the Washington Seattle game was an almost picture perfect demonstration that home field advantage is strongest in the first quarter.

Of all the teams playing, my system likes San Francisco the best. I suspect it likes it more than others. We’ll learn more as other analytics oriented folks post their odds for the divisional round.

We can’t work with my playoff model without having a set of week 17 strength of schedule numbers, so we’ll present those first.

2012_stats_week_17

Between a difficult work schedule this last December and a very welcome vacation (I keep my stats on a stay at home machine), I haven’t been giving weekly updates recently. Hopefully some of my various thoughts will begin to make up for that.

Though with SOS values, you could crunch all the playoff numbers yourselves, this set of data should help in working out the possibilities:

Odds as calculated by my formula

Odds as calculated by my formula, with home field advantage adjusted to 60%. Point spread calculated with formula 3.0*logit(win probability)/logit(0.60). Click on image twice to expand.

What I find interesting is the difference between Vegas style lines, and my numbers, and the numbers recently posted by Brian Burke on the New York Times Fifth Down blog. My model is very different from Brian’s, but in three of the four wild card games, our percentage odds to win are within 2-3 percent of each other.

Point spreads were estimated as follows: if an effect of 60% were valued at 3 points (i.e. playoff home field advantage is about 60% and home field advantage is usually judged to be worth 3 points), then two effects of that magnitude should be worth 6 points. But it’s only on a logit scale that these effects can be added, so it only makes sense to relate probabilities of winning through their logits. As the logit of 0.60 is about 0.405465, then an estimated point spread can be had with the formula

point spread = 3.0*logit(win probability)/0.405465

Update (1/9/2012) – even simpler is:

est. point spread = 7.4*logit(win probability)

A simplified table of the wild card games, with percentages and estimated point spreads is:

Wild Card Playoff Round
Home Team Visiting Team Home Win Pct Est. Point Spread
GB MIN 0.682 5.6
WAS SEA 0.482 -0.5
HOU CIN 0.642 4.3
BAL IND 0.841 12.3

How many successes is a touchdown worth?

We’ve spoken about the potential relationships between success rates, adjusted yards per attempt, and stats like DVOA here, but to make any progress, you need to consider possible relationships between successes and yards. Let me point out the lower bound of the relationship is known, as 3 consecutive successes must yield at least 10 yards, and 30 consecutive successes must end up scoring a touchdown. In this case, the relationship is 1 success is equal to or greater than 3 1/3 yards.

Thus, if the surplus value of a touchdown is 20 yards, that’s 6 successes. If a turnover is worth 45 yards, that’s about 13.5 successes.

A smarter way to get at the mean value of this kind of relationship, as opposed to a limiting value, would be to add up the yards of all successful plays in the NFL and divide by the number of those plays. For now, that’s something to be pursued later.

Things that are easy to note: the teams with at least 9 wins are either guaranteed a playoff birth, or have, at worst, a 99% chance of making the playoffs. The teams with 8 wins have a very good chance of entering the playoffs. Those teams with 7 wins have at least a 50% chance of making the playoffs. Those with 6 wins have between a 5% to 30% chance of making the playoffs. Let’s say they are hoping to get in.

Data from week 12

2012_stats_week_12

Data from week 13

2012_stats_week_13

The methodology of these stats is discussed in previous posts in this series. If you’re wondering where I’m getting odds to go into the playoffs, see this post. If you’re wondering what chance your team has of winning in the playoffs, see this post on my logistic regression methods, based on studies of playoff games. How would your ranking in the playoffs affect your chances of getting into the Super Bowl? We studied that here.

I am not a proponent of the notion that regular season offensive stats are predictive in the post season. My studies suggest p on the order of 0.15 for offensive stats in the post season, and thus aren’t predictive enough for my tastes ( p <= 0.05). That hasn't stopped Football Outsiders from pretending that their proprietary stats are predictive and calculating playoff odds with their tools.

One of the nice things about Madden’s book, “One Knee Equals Two Feet”, is that it does understand the importance of Preston Pearson, and the notion of the third down back in general. A lot of this influence is a consequence of a single game. In 1975, the Dallas Cowboys were a wild-card team, a 10-4 team advancing into the second round of the playoffs against a very good and well coached Chuck Knox team, the Los Angeles Rams, with a record of 12-2. They were led by the excellent Lawrence McCutcheon at running back and featured one of the best defensive lines ever in professional football, featuring Fred Dean and Jack Youngblood at defensive ends, Merlin Olson at defensive tackle, and Jack Reynolds and Isiah Robertson at linebacker. The Rams were the #1 defense in football, allowing less than 10 points a game.

By the end of this game, Dallas had won 37-7. Roger Staubach called it “the most perfect football game we ever had as Cowboys.”  Preston Pearson had gained 20 yards rushing, but 123 yards passing, including three touchdowns.

It wasn’t as if he was given easy passes to catch, either.

second touchdown

reaching for the ball.

The most famous catch was his third touchdown, the shovel pass.

Video of this game is here.

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