Code and Football

To explain the columns below, 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. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

New England  is atop the Median measure, followed by Green Bay and Houston. Topping Pythagoreans is Green Bay, followed closely by San Francisco and Houston. Green Bay is leading by plenty in both MOV and SRS, as MOV is one metric where they separate substantially from the rest of the NFL.

There are three interesting sites doing the dirty job of forecasting playoff probabilities.  The first is Cool Standings, which is using Pythagorean expectations to calculate the odds of successive wins and losses, and thus, the likelihood of a team making it to the playoffs. The second is a page on the Football Outsiders’s site named DVOA Playoff Odds Report, which is using their signature DVOA stat – a “success” stat – to  generate the probability of a team making it to the playoffs. Then there is the site NFL Forecast, which has a page that predicts playoff winners using Brian Burke’s predictive model.

Of the three, Cool Standings is the most reliable in terms of updates. Whose model is actually most accurate is something any individual reader should try and take into consideration. Pythagoreans, in my opinion, are an underrated predictive stat. DVOA will tend to emphasize consistency and has large turnover penalties. BB’s metrics have tended to emphasize explosiveness, and now recently, running consistency, as determined by Brian’s version of the run success stat.

I’ve found these sites to be more reliable than local media (in particular Atlanta sports radio) in analyzing playoff possibilities. For a couple weeks now it’s been clear, for example, that Dallas pretty much has to win its division to have any playoff chances at all, while the Atlanta airwaves have been talking about how Atlanta’s wild card chances run through (among other teams) Dallas. Uh, no they don’t. These sites, my radio friends, are more clued in than you.

To explain the columns below, 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. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

Presently, New England,  Houston, and Green Bay are at the top of the medians, San Francisco, Green Bay, and Houston own the Pythagroreans, and leading SRS are Green Bay, San Francisco, and Houston. In most statistical scoring measures, Green Bay and San Francisco are separating themselves. Matt Leinert has a challenge duplicating the success of Matt Schaub in Houston. And the Giants: a team outperforming its own metrics. Though Tim Tebow is the clutch quarterback of the moment, just where would New York be without their quarterback?

The recent success of DeMarco Murray has energized the Dallas fan base. Felix Jones is being spoken of as if he’s some kind of leftover (I know, a 5.1 YPC over a career is such a drag), and people are taking Murray’s 6.7 YPA for granted. That wasn’t the thing that got me in the fan circles. It’s that Julius Jones was becoming a whipping boy again, the source of every running back sin there is, and so I wanted to build some tools to help analyze Julius’s career, and at the same time, look at Marion Barber III’s numbers, since these two are historically linked.

We’ll start with this database, and a bit of sql, something to let us find running plays. The sql is:

select down, togo, description from nfl_pbp where season = 2007 and gameid LIKE "%DAL%" and description like "%J.Jones%" and not description LIKE '%pass%' and not description LIKE '%PENALTY on DAL%' and not description like '%kick%' and not description LIKE '%sacked%'

It’s not perfect. I’m not picking up plays where a QB is sacked and the RB recovers the ball. A better bit of SQL might help, but that’s a place to start. We bury this SQL into a program that then parses the description string for the statement “for X yards”, or alternatively, “for no gain”, and adds them all up. From this, we could calculate yards per carry, but more importantly, we’ll calculate run success and we’ll also calculate something I’m going to call a failure rate.

For our purposes, a failure rate is the number of plays that gained 2 yards or less, divided by the total number of running attempts, multiplied by 100. The purpose of the failure rate is to investigate whether Julius, in 2007, became the master of the 1 and 2 yard run. One common fan conception of his style of play in his last year in Dallas is that “he had plenty of long runs but had so many 1 and 2 yards runs as to be useless.” I wish to investigate that.

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To explain the columns below, 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. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

In median point spreads, the top three are Green Bay, Houston, and New England. Pythagoreans favor Green Bay, San Francisco, and Houston. On top of SRS are Green Bay and San Francisco, no other teams are even close. The third highest is now Chicago, still sporting the highest strength of schedule of them all.

Yes, the question is abstract, but reasonably important. Some statistical comparisons are transitive. That is, if a probability is expressed as a ratio, x:y, then if x:y and y:z, then you can assume x:z. You see it used here, for example, but things like nontransitive dice and general discussions of transitivity and intransitivity suggest that you just can’t assume it to be true.

Image from Wikimedia. Rock-Scissors-Paper is an example of an intransitive relation.

Enter the Pythagorean formula. Though originally an ad hoc formula penned by Bill James in baseball, people keep finding ways to derive this fomula under certain limiting conditions (a recent discussion of a Sloan MIT paper is here). On this blog, we’ve done our share of analysis of Pythagoreans, and we have been calculating them weekly this year.

Why is this question important? Because if Pythagoreans were transitive, you could calculate the winning percentage easily between a team A and team B. Assume team A has a 65% pythagorean. Assume team B has a 80% pythagorean. Then you can set up these two ratios: 65:35 and 20:80. Since Y isn’t common between the two, you multiply 20:80 by 35 and 65:35 by 20. You end up with 65×20:35×20 and 35×20:35×85, and so A:B becomes 65×20:35×80 or 1300:2800.

The odds of A winning become 1300/4100 and the odds of B winning become 2800/4100. Expressed as percentages, the odds of A winning would become 31.7% and the odds of B winning would become 68.3% .

At this point, such a calculation could be refined. You could add in home field advantage, typically around 0.59 to 0.6. You could use a logistic regression to figure out if the SRS variable strength of schedule is significant in the regular season. I’m pretty sure Brian Burke’s predictive model has a strength of schedule component. I haven’t figured out yet whether I can see a correlation between winning and the simple ranking SOS variable in the regular season, but there sure is one in the playoffs.

To throw in some numbers, to perhaps whet your appetite, I wrote a piece of code to calculate transitivities, and count in home field advantage, and not having a logistic value for the regular season, I  used the postseason SOS to do some rough calculations on the recent (Nov 7, 2011) Chicago Philadelphia game. And what I saw was this:

And the question that was occurring to me in all the pre-game hoopla, were the analysts really taking into account Chicago’s exceptionally tough schedule?

So in conclusion, I’m really interested in this question, whether it can be answered yes or no, or if it can’t really be totally answered, can it be tested, perhaps experimentally, in some useful way. Knowing this would help those of us doing back of the envelope calculations of winning in the NFL.

Update

If Pythagorean expectation probabilities are treated as real numbers, with all the properties of real numbers, and if ratios can be treated as fractions, then transitivity becomes equivalent to: if A/B and B/C, then A/C. This statement can be proven by multiplying A/B and B/C.

Another way of looking at this is as follows: Team A has a probability of winning and one of losing, a_W and a_L, that total to 1.0. Team B has a probability of winning and a probability of losing, b_W and b_L, that also total to 1.0.

Multiplying the two pairs of terms yields: a_Wb_W +  a_Lb_W + a_Wb_L + a_Lb_L. Since the win-win terms and the lose-lose terms don’t count, the remaining terms of consequence are the cross terms, whose ratio is the same as those invoked by transitivity.

If you use a random number generator to model this process, and insist that when a win-win or a lose-lose is calculated, you recalculate the whole equation until a win-loss or loss-win term is obtained, then we note the following. This process is geometrically equivalent to drawing a square on each iteration, within which there are two squares ( a_Wb_W and a_Lb_L ) and two rectangles ( a_Lb_W and a_Wb_L). In the first iteration, the area of the large square is 1, every iteration after, the area of the large square will be ( a_Wb_W + a_Lb_L )^N-1, where N is the number of the iteration. The area ratio of the two rectangular regions will never change, the ratio of areas will remain the same. As trials approach infinity, the cumulative ratio of the “score” terms will approach a_Lb_W : a_Wb_L.

To explain the columns below, 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. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

It has been interesting watching various teams land atop various metrics. Medians favor Houston, Baltimore, and Green Bay. SRS favors Houston, Green Bay, and San Francisco. Pythagoreans favor San Francisco, Detroit, and Baltimore.

The Stathead blog is now defunct and so, evidently, is the Pro Football Reference blog. I’m not too sure what “business decision” led to that action, but it does mean one of the more neutral and popular meeting grounds for football analytics folks is now gone. It also means that Joe Reader has even less of a chance of understanding any particular change in PFR. Chase Stuart of PFR is now posting on Chris Brown’s blog, Smart Football.

The author of the Armchair Analysis blog, Jeff Cross, has tweeted me telling me that a new play by play data set is available, which he says is larger than that of Brian Burke.

Early T formations, or not?

Currently the Wikipedia is claiming that Bernie Bierman of the University of Minnesota was a T formation aficionado

U Minnesota ran the T in the 1930s? Really?

I’ve been doing my best to confirm or deny that. I ordered a couple books..

No mention of Bernie's T in this book.

I've skimmed this book, and haven't seen any diagrams with the T or any long discussion of the T formation. There are a lot of unbalanced single wing diagrams, though.

I also wrote Coach Hugh Wyatt, who sent me two nice letters, both of which state that Coach Bierman was a true blue single wing guy. In his book, “Winning Football”, I have yet to find any mention of the T, and in Rick Moore’s “University of Minnesota Football Vault”, there is no mention of Bernie’s T either.

I suspect an overzealous Wikipedia editor had a hand in that one. Given that Bud Wilkinson was one of Bernie’s players, a biography of Bud Wilkinson could be checked to see if the T formation was really the University of Minnesota’s major weapon.

To explain the columns below, 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. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

Today, Philadelphia is the only team with a losing record and a winning Pythagorean. Medians favor Baltimore, Green Bay and Cinncinnati, while SRS “likes” Detroit, San Francisco, and Green Bay.