Le'Veon Bell's decision to sit out game 1 of the NFL season led to the inevitable discussion in gambling circles about the impact of running backs on the NFL point spread. There was a significant line move in favor of the Browns after the announcement and I personally had the Browns as well, although it had nothing to do with the Bell sit-out. It also led to one of the more obvious picks in the history of daily fantasy football in James Conner, who was only around ~28% owned, suggesting DFS is still extremely beatable. In the end Conner had a huge game on the back of great game flow, run-friendly weather conditions, and an extra quarter of football to pick up yards, while the Browns got outplayed as usual but picked up some lucky breaks and turnovers to...tie the game.
To measure the potential value of running backs in the NFL we will turn to one of our favorite tools, the Madden ratings. In using the Madden ratings we will break down rosters into five "units": starting QB, defense, o-Line, WR/TE, and the starting RB. For this study, using a list of all players who played in the game, we take the average overall rating of the starting QB, the top 11 defensive players, the top 5 offensive linemen, the top 3 WR/TE, and the top rating of the RB.
We begin with a linear regression, with our independent variable being the scoring margin between the home and away team, and our dependent variables being the difference in average rating across all five of these categories:
In this regression model, the coefficient can be defined as having units of points per average Madden rating. For example, according to the model above, a team with a QB with a rating 20 points higher than their opponent can be expected to outscore them by 0.31*20 = 6.2 points per game. For those not familiar with the Madden ratings, they are typically between 70-99 for most starting players. The average starting defensive unit in any one game has a rating around 82, with the biggest mismatches on defense being in the ~10 overall range (or 10*0.74 = 7.4 points per game) and at QB in the ~25 overall (25*0.31 = 7.8 points per game) range in any one year.
We can see that QB and defense are highly significant in our model, with WR/TE also having a minor influence; a top unit with a rating in the high-80s can make as much as a two point per game difference over a poor mid-70s rated unit. However, O-Line and RB make no difference at all. No reasonable difference in ratings can ever make more than a difference of one tenth of a point in our predictions, and neither of the variables are statistically significant.
While I think most winning handicappers would agree that RBs are over-rated, I don't think any would suggest they have no value at all. And certainly the offensive line is very important. The most obvious explanation is that the Madden ratings don't do a very good job of rating the true skill of players at the RB and offensive line positions, leading to our model not placing much value on the ratings at these positions. Still, it is odd that these ratings have a ton of predictive value at QB and defense and have some value at WR/TE, but don't seem to work at offensive line or RB at all.
Let's go further and instead of modeling scoring margin, model rush yards per play. If these Madden ratings have any value at all, we should see it in the form of improved rushing outcomes on teams with a highly rated RB and offensive line:
We do see that the running back and offensive line seem to have a minor influence on yards per rush. The best RBs with a 99 overall rating would be expected to average about 0.2 YPC more than an 80 overall rating, and a top O-Line with a 10 rating-point difference would also make a difference of around 0.2 YPC. The opposing defense has more influence than either. Overall, the impact is not all that high - a few tenths of a yard per rush is still not going to have a major influence on the point spread.
We can measure one other thing with the Madden ratings, which is how teams with a given roster tend to play on offense. Teams with a highly-rated RB and offensive line might just be teams that have a more run-focused game plan. This would lead to better fantasy production and more "big games" at the RB position, which would probably flow back into higher ratings, since the Madden ratings probably heavily leverage stats at these skill positions. To test this we model the difference in percentage of rushing plays per game by home vs. away, as a function of difference in Madden ratings at each position:
The numbers do seem to support the idea that teams with "good" RBs and offensive lines run the ball more. The top-rated rushing teams will run the ball about 3-4% more often as a percentage of all plays given the above model. However, the reason there should be a home advantage or defensive influence on rushing percentage is less obvious, until one recalls that teams tend to run the ball more in games where they have the lead. We may be able to improve the above model and make a fairer comparison by including the final game score, to account for these differences in game flow:
When the final score is included we can better see the overall impact of team roster composition on how often a team runs the ball. For a given difference in scoring margin, teams with highly rated QBs and WR/TEs run the ball less, while teams with highly rated offensive lines and RBs run the ball more. The common range of influence of Madden ratings at each position is somewhere between 2 and 7%.
The above chart may explain why Madden ratings don't have much handicapping value when it comes to RB and offensive line, even though they seem to have a lot of value at many other positions. Rather than measuring the influence players have on their team winning the game, the ratings instead seem to be heavily tied to usage, which is probably caused by the ratings being set based on statistics. On defense and in the passing game, this is fine, because statistical production is highly correlated to winning. More sacks or turnovers forced on defense really do win more games, and effectiveness in the passing game is also one of the best predictors of future success.
The problem is that past rushing production, particularly rushing fantasy production, is not tied to winning and in fact the opposite is probably true. Pretty much every study ever has concluded that running the ball is usually worse than passing, especially on first down. Part of this probably comes from a sample bias where teams with a better passing game pass more often, as we can see above. Still, passing is better by enough that a run-focused attack can almost never be right unless one has a truly terrible QB and strong running game. Most of the value that running the ball does have is from higher success rates in short-yardage situations, which fantasy stats and Madden ratings don't measure well.
Going beyond Madden ratings, there is one final chart I like to use whenever I begin to believe that the running back position might be extremely important in the NFL. In this chart I have split running backs up into the starting, second-string, and third-string roles, based on their percentage of carries in past games, and measured their yards per carry in that particular game:
We can see that starters do tend to have slightly higher past yards per carry, but this doesn't seem to continue into the current game. Running against the same opposition, with the same offensive line, backup running backs actually outperform the starters. Part of this is probably because the backup is better rested and less likely to come in during short-yardage situations, but in any case, the difference between the two is unlikely to be large.
In the end there may be a sort of Moneyball effect at running back, where teams who have a good running back and offensive line feel like they have to use these players. This leads to teams with a lot of talent at these positions running the ball more when they would still be better off passing. When a top RB falls out of the lineup, the team may be slightly less efficient in the running game and perhaps the passing game as well, but they run less and benefit as a result. In any event, since the Madden ratings don't mean much, the question is then to decide how to handicap these games, and what value to place on the running back and offensive line positions.
In my own handicapping, I rate offensive line injuries as being similar to those on defense, and assume that the Madden ratings are just bad at rating the offensive line. My justification is that offensive linemen are paid similar salaries to defensive players, meaning they should have around the same value. This means that a typical starting player is worth around half a point per game, with the best linemen in the league being worth perhaps one point. I don't put much value on the running back at all - I assume that teams will just run the ball less, meaning they will play better strategically as a result of the injury, making the impact mostly a wash.