1-Play Touchdown Probability

In Week 1 last year, Tom Brady connected with Wes Welker for a 99-yard touchdown against the Dolphins. In an effort to determine whether teams actually protect the ball better as they approach the goal line, we recently looked at 1-play fumble and interception probabilities (also known as transition probabilities from our Markov model). Out of all our absorption probabilities, only fumble, interception and touchdown really make sense to examine on a 1-play basis across downs. Punts and field goals almost always occur on 4th down (turnover on downs always occur on 4th down) and while a safety can occur on any down, they occur extremely infrequently.

In 2011, 37.7% of all offensive touchdowns occurred on 1st down, 33.0% on 2nd down, 25.0% on 3rd down and 4.3% on 4th down. This makes logical sense as there will be more 1st downs than 2nd downs, more 2nd downs than 3rd downs, and so on. But, how does down affect the probability of scoring a touchdown on the next play? Do teams take (and successfully convert) more shots downfield on 1st down than later in the drive?

So You've Got Your Fantasy Draft This Week

So does Andre.

You'd think a stathead like me would be furiously preparing, calculating correlations and running endless mock drafts. There was a time I did all that, but now I don't even pay attention until shortly before draft time. I don't have specific advice for anyone, like take Aaron Hernandez in the 3rd round or don't take a QB until the 4th round, but there are a few concepts that my study of football statistics over the past few years can be applied to fantasy.

1. Fantasy football is overwhelmingly random, and you are not as smart as you think you are. You don't know anything special. You have no special power of analysis and prognostication. None of us do. Admit that now and you'll be doing yourself a favor. Everyone has access to the same information, the same rankings and the same expert predictions. If you're in a 10 team league, you start the day with a 10% chance of winning it. Injuries and unforeseeable developments will determine who wins your league, not your front office acumen. Even if you are God's gift to fantasy football, you have, what, a 15% chance of winning?

2. Ignore your own analysis and trust the crowd. Fantasy football is a great application for the wisdom of crowds. You have your dumb biases and errors, and someone else has theirs, and another guy has his. Average them all together, and as long as they're not correlated, the biases and errors will cancel out. If your fantasy service of choice shows you where players have been drafted so far, and the player hasn't suffered some cataclysmic injury in the last few days, trust the crowd over your own dumb judgment.

Absorptions Over Expectation

Another thing we can look using our updated Markov model is how teams were expected to perform based on where they took over on the field. In other words, based on starting field position, how many touchdowns was a team expected to score on the year? And further, how many touchdowns did they actually score.

Not surprisingly, New Orleans, Green Bay and New England were the top three offenses in terms of touchdowns scored above expectation. Drew Brees and the Saints scored just shy of 26 additional touchdowns above expectation at the start of their drives. That's a whopping 182 points. By comparison, the St. Louis Rams scored 193 points total in 2011.

Click here to see the full table of expected number of each drive-ending state based on starting field position over the course of 2011 for each team.

San Francisco was given the most advantageous starts, which should have resulted in about 31 field goals and 47 touchdowns on average. Akers kicked a record 44 field goals but SF scored a miserable 32 offensive TDs. Other notable expectations are the Broncos' expected 104 punts and Giants' expected 102 punts, the most and second-most in the league.

Modifying The Markov Model

Last season, we revealed our Markov model of a football drive outlined here. 

All of the same math and logic still apply, but this offseason we updated the model to reflect some previous weaknesses.

Check out the Markov Calculator Tool and model results here.

Offensive Line Salary and Performance

Last season I took a cursory look at the importance of depth at offensive line. I highlighted the thinness of the Redskins' line by pointing out that although their total salary spent on their line was in line with most other teams, a large part of their cap space was allocated to a single player, left tackle Trent Williams. Their median salary was less than half of that of the division leading teams at the time, suggesting that the Redskins annual mid-season swoon was due to a lack of replacement talent following inevitable injuries to starting linemen.

This post will go far more in depth and look at correlations between team offensive line (OL) salary and performance. Using salary data from USA Today's database for the 2000 through 2009 seasons, I calculated correlations between OL salary and various advanced offensive performance statistics. (USA Today's database ends at 2009. Additionally, the 2005 season was excluded because USA Today's database appeared incomplete that season, listing half as many players than the other seasons.)

As in my other salary analyses, I relied on cap hit as the truest measure of a player's cost to a team. NFL salary structures are notoriously complex, with base pay, bonuses, guarantees, and other factors. But cap hit comprises most if not all of those considerations, and it represents the cost to most team's most precious resource--its cap space. For each season, I adjusted all salary numbers according to the league's cap for that year to account for salary inflation.

Brees, Rice, and Forte...and Moneyball

Drew Brees signed a record-setting contract extension for $20M per year over five years. That's about what the numbers suggested for a QB averaging 150 EPA per season. The analysis said $18M should be the going rate for Brees at his peak, which is what $20M per year translates to after discounting over five years. That assumes Brees won't decline over that time, which is a risky assumption for a 33 year old QB. In reality, the final year or two of the contract may not be honored, so overall I have to endorse the deal. The Saints absolutely needed Brees on board as the weather a tough 2012 season in the shadow of the bounty scandal.


Ray Rice signed for five years and $40M, $24M of which is guaranteed. I still believe that RBs are paid about double what they should be relative to their impact on game outcomes, but this deal was right at the going rate for RBs. RBs who reliably average 2,000 total yards per season command about $9M per season in 2011 cap dollars. Rice is only 25 and will be in his prime for at least a couple more seasons. In terms of absolute value I can't endorse any top RB contract, but in terms of the market this is a fair deal for both Rice and Baltimore.

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Did you ever get the feeling that this site was designed by a guy who had absolutely no training in web development and had no artistic talent, and that everything he knew about website design he learned from a "For Dummies" book? Yeah, me too.

Now it looks a little less like that.

Paying Free Agent RBs

Ray Rice, Matt Forte, Payton Hillis, Marshawn Lynch, and Arian Foster were all due to become free agents this off-season. Rice and Forte have already been franchise-tagged, and Foster is a restricted free agent. Still, the question of what they're worth in terms of salary and cap space remains.

A couple months ago, I took a look at the safety position and how free agents are paid. And more recently I took a look at how QBs are paid with the intent to eventually establish a rational framework for how they should be paid according to their actual production in terms of wins and points. Like the prior analyses, my primary goal for now is to get a feel for the market.

As in all individual player analysis, it's worth stating up front that football is always a team sport. Like all other positions, a RB's stats are not his alone, as they depend heavily on offensive lines, opponents, scheme, situational variables, passing game strength, and other considerations. We can account for the situational variables with the EPA and WPA models, but we must rely on the tendency for factors beyond the control of the individual player to even out in the long run. They may not even out for any individual RB, but in aggregate, the idea is that some RBs will have above average lines, some will have poor lines, and collectively we can roughly estimate the financial value that a RB brings his team based on production.

First, let's take a look at how RB salaries are actually determined. There are two graphs below. The first plots career total rushing yards vs. career total cap hit. The second plots career Yards Per Carry (YPC) vs. career cap hit. The data include years 2000-2009 and is limited to RB seasons with greater than 6 game appearances and greater than 50 carries. Cap hit is adjusted for NFL inflation. Only players who had a cap hit greater than $1M in year 2000 dollars were considered. This limitation is so that we sample only high-priced RBs, and is necessary to see any relationship at all between performance and pay.