My system went 3-0-1 last weekend (Or 3-1 if you consider my prediction in the Bengals – Chargers game a loss, as opposed to “too close to pick”), so time to present playoff odds for the second round of the playoffs.

Divisional Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Seattle Seahawks New Orleans Saints 0.676 0.663 5.0
Carolina Panthers SF 49ers -0.157 0.461 -1.2
Denver Broncos San Diego Chargers 0.411 0.601 3.0
New England Patriots Indianapolis Colts -0.060 0.485 -0.4

 

Odds that differ by less than a point in estimated point spread are probably not significant, and from my POV, a suggestion that you don’t bet that particular game.

The regular season has ended and the playoffs have begun. It would be useful to have a set of playoff grade data to do playoff probabilities, and though I’ve been down and out this season (no job at times, foot stress fracture at times, and a bad right shoulder), I currently have some time off my new job, a new laptop, and enough time to grind through some playoff numbers.

NFL stats at the end of the regular season:

week_17_2013_stats

To explain the columns above, Median is a median point spread, and can be used to get a feel for how good a team is without overly weighting a blowout win or blowout loss. HS is Brian Burke’s Homemade Sagarin, as implemented in Maggie Xiong’s PDL::Stats. Pred is the predicted Pythagorean expectation. The exponent for this measure is fitted to the data set itself. SOS, SRS, and MOV are the simple ranking components, analyzed via this Perl implementation. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

Playoff Odds are calculated according to this model:

logit P  =  0.668 + 0.348*(delta SOS) + 0.434*(delta Playoff Experience)

The results are given below, as a “score” in logits:

2013 NFL Playoff Teams, C&F Playoff Model Worksheet.
NFC
Rank Name Home Field Advantage Prev. Playoff Experience Strength of Schedule Total Score
1 Seattle Seahawks 0.406 0.434 0.494 1.334
2 Carolina Panthers 0.406 0.0 0.484 0.889
3 Philadelphia Eagles 0.406 0.0 -0.661 -0.256
4 Green Bay Packers 0.406 0.434 -0.842 -0.003
5 San Francisco 49ers 0.0 0.434 0.612 1.046
6 New Orleans Saints 0.0 0.0 0.658 0.658
AFC
1 Denver Broncos 0.406 0.434 -0.546 0.293
2 NE Patriots 0.406 0.434 -0.258 0.582
3 Cancinnati Bengals 0.406 0.434 -0.856 -0.017
4 Indianapolis Colts 0.406 0.434 0.209 1.048
5 Kansas City Chiefs 0.0 0.0 -0.602 -0.602
6 San Diego Chargers 0.0 0.0 -0.118 -0.118

 

The total score of a particular team is used as a base. Subtract the score of the opponent and the result is the logit of the win probability for that game. You can use the inverse logit (see Wolfram Alpha to do this easily) to get the probability, and you can multiply the logit of the win probability by 7.4 to get the estimated point spread.

For the first week of the playoffs, I’ve done all this for you, in the table below. Odds are presented from the home team’s point of view.

First Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Philadelphia Eagles New Orleans Saints -0.914 0.286 -6.8
Green Bay Packers SF 49ers -1.049 0.259 -7.8
Cincinnati Bengals San Diego Chargers 0.101 0.525 0.7
Indianapolis Colts Kansas City Chiefs 1.650 0.839 12.2

 

Some general conclusions from the data above: the teams my model favors most are the Seattle Seahawks, the Indianapolis Colts, the 49ers, the Carolina Panthers, and then the New Orleans Saints, mostly NFC teams. Since the Super Bowl itself does not have a home team, the odds change once you actually reach the Super Bowl. The sum of the SOS column and the Previous Playoff Experience column can be used to estimate odds of winning “the big one”. The strongest team in a Super Bowl setting would be the San Francisco 49ers, with a total score, less HFA, of 1.049. The Indianapolis Colts, with a total score of 0.643 less HFA, would be the strongest possible AFC contender.

A point I’d like the reader to consider is this question: should the New Orleans Saints be granted an exception to the previous playoff experience rule of “last year only counts” and given the 0.434 advantage of a playoff team? 2012 was an aberration as the coach was suspended. I’m not calculating this variation into the formula at this point, but I’ll note that this is an issue that you, the reader, need to resolve for yourself.

The road to the playoffs is not easy, a topic that can be studied by trying to calculate the path to the playoffs of the Indianapolis colts, a team that would be favored in every matchup along the way. Let’s calculate the odds of Indianapolis actually winning all three games.

Odds of Indianapolis reaching the Super Bowl
WP versus Kansas City WP versus Denver Broncos WP versus NE Pats Cume Probability
0.839 0.586 0.515 0.253

 

Three teams from the NFC would be favored over any possible AFC contender. Those are San Francisco, Seattle, and the New Orleans Saints. Carolina would be favored over any AFC contender except the Indianapolis Colts.

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.

The three sites we noted last year: Cool Standings, Football Outsiders, and NFL Forecast, are at it again, providing predictions of who is going to be in the playoffs.

 

Cool Standings uses Pythagoreans to do their predictions (and for some reason in 2011, ignored home field advantage), FO uses their proprietary DVOA stats, and NFL Forecast uses Brian Burke’s predictive model.

Blogging the Beast has a terrific article on “the play”. If you watched any Dallas-Philadelphia games in 2011, you’ll know exactly what I mean, the way with a simple counter trap, LeSean McCoy treated the Cowboys line as if it were Swiss cheese.

Most important new link, perhaps, is a new Grantland article by Chris Brown of Smart Football. This article on Chip Kelly is really good. Not only is the writing good, but I love the photos:

Not my photo. This is from Chris Brown’s Chip Kelly article (see link in text).

as an example. Have you ever seen a better photo of the gap assignments of a defense?

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