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Friday, July 24, 2009

What makes a good running back? How do you evaluate how good a team's run game is?

The pro-football reference blog recently mentioned something I found fascinating:

What about rushing? . . . .In modern times, most RBs have a median carry length of three yards. I suspect that’s been the case for the majority of RBs for a long time. LenDale White and his 3.9 YPC last season? Median rush of 3 yards. Adrian Peterson and his 4.8 YPC? Median rush of 3 yards.

I think this has powerful implications. If most runningbacks tend to have the same median rush, then those who are more effective -- and hence have higher averages -- would be almost exclusively based on their big-play ability. (That big-play ability could still come in different forms, i.e. the guy who consistently can turn five yarders into 15 yarders, or the guy who can break every 10th or 15th rush into a 50 yarder.)

But this would imply that the powerback, or at least the powerback who is not considered so explosive, is overrated. (Earl Campbell could run you over and break off big gains.) The point is just that the premium would not be on the player's results on the average plays, but instead on the longer ones. Some of this too can be the surrounding cast. Indeed, as Homer Smith has said, a runningback who gets 130 yards on 20 carries plays in a better offense (either because of him or for whatever other reason) than a guy who gets 145 on 35 carries.

But this does all assume that average yards per carry is the most important stat. I'm not sure all would agree that it is. (In fact, I think the PFR Blog folks might not agree, as they ranked runningbacks and included their total carries and pure total yards as a key factor.) I'm not convinced that more carries means a better back or better running game, as that depends on the game situation (does the team get a lot of leads?) and also that the play-calling is optimal. I can also buy that on 3rd and 3, or third and goal, the point is to convert, not to help the average.

Yet then how else can we evaluate running backs, or even a running game more generally? A perusal of the best offenses and running games in college tends to show that the best all have high yards per carry; not too many BCS teams have averaged fewer than 4.5 yards per carry, and several have averaged well over five yards per rush attempt (including sacks, which count against the run game total in college).

So I'm opening the floor to better ideas. IF yards per attempt is the best metric (for either an individual back or a team's run game), and IF the median truly is right around 3 yards for great and average backs alike, then the difference between good and mediocre runningbacks and rushing teams would seem to be wholly in the explosiveness of the upper 50% of plays: a good team or player can rip off big gains, and turn big gains into touchdowns, while the average plays for both is about the same. (And maybe negative plays are overrated.)

But I'm interesting in everyone's thoughts on this question. How do you evaluate the running game?


Richard said...

I think I would agree to use the numbers you have. That is: AYPC-MoYPC=Effectiveness Rank. That's "Average Yards Per Carry, Minus Median of Yards Per Carry, equals Effectiveness".

The theory is that the median indicates the effectiveness of the offensive blocking and play-calling. Assume a median of 2 yards. That would mean the offensive scheme or execution (or both) are poorer than a 3 because a near majority of run plays are getting stuffed at or nearer the line of scrimmage. If the running back does not show a much higher average yards per carry, then he's not much more talented than the playcalling or blocking. But, if the gap is large, that means that when the playcalling (deception?) and/or blocking succeeds in creating an opening beyond the line, the RB can "take it to the house" (a sports metaphor that I personally abhor, but which will have a place of honored disdain in the sports cliche dictionary by Ambrose Bierce).

Chris, since you have much better access to the cumulative running back stats than do I, and probably already have the spreadsheet set up, who are the ranking all-time running backs using *this* mathematic manipulation?

OldSouth said...

On a little reflection, I think any top-notch rushing attack should be good at two qualitative things, which can be looked at relatively easily with quantitative data:

1) They run efficiently.
2) They have multiple threats for the various contexts you might need them for in a game.

1) YPC is pretty obvious here. Instead of just identifying the top YPC teams (which will be skewed by teams like Texas Tech using runs as effective constraint plays), find an agreeable YPC and eliminate teams that don't meet it. That may sound like I'm contradicting the first paragraph, but not really: I think a good YPC is a necessary but not sufficient condition for a good rush offense.
And I don't think you can get around YPC: prima facie, it's hard to believe that you can be a good rushing team without, you knowing, getting a lot of yards when you rush.

2) Identify teams with multiple high YPC rushers who have different standard deviations in yards/rush. I think if you're trying to find a solid rushing offense, you'll want a team who can rush in different ways depending on what you need. E.g., a team like Florida, which doesn't even have a prototypical tailback. Tebow can grind away short yards, while Harvin/James etc. can be more high risk/high reward threats.

The Reggie Bush/ Lendale White and Mcfadden/Felix Jones attacks are two more good recent examples of this.

That's a start but it's not flawless. Some teams can really do well with one "mega-back," as your picture of Barry Sanders hints at.

OldSouth said...

Also, I don't think you can combine the above stats in any meaningful way, nor should you: they're different statistics measuring very different things.

That notion is heresy in ESPN world of easily-digestible moronstats, and it's particularly bad in basketball (e.g., John Hollinger). Those folks attempt to combine a ton of completely independent ideas into one meaningful statistic.

Theoretically, you could be on decent ground if you were to make one of those "uberstats" correlated with a simple second measure (e.g., number of wins or value [relative to salary]).

But that's a different concept than this here. I take your post to mean: how can we identify the best rushing attacks, acknowleging that those attacks involve multiple, independent ideas.

Final thoughts: Chris, I've learned so much from your blog, if you ever feel like watching a Kentucky football game live, I'll supply the ticket (in the law student section no less) and any drinks consumed before- or afterwards. Provided I can pick your mind the whole way (warning: we still run a pro-style offense based out of the I, mr. spreadattack). Lately we've been deviating from our Shakespearian tragedy/comedy attempts at football so it might even be enjoyable.

The Mathlete said...

I've always believed that best way to look at would be in regards to change in expected value based on down distance and LoS. This way, a 1 yard run on 3rd and 1 still has value but a 5 yard run on 3rd and 6 is greatly diminished vs a 5 yard run on 1st and 10.

What's interesting is that based on expected value, running games variance from team to team is much closer than for passing. The top rushers in college last year added about 4 points a game of expected value whereas the worst rushers cost their teams about 3 points per game.

Stan said...

Do you want to evaluate running games (blockers included) or RBs? The best way to evaluate a RB's contribution in the running game is extra yardage, i.e something like yards after contact except you also have to credit the back who can make people miss.

The key question is what did he gain and what would an average back gain from that hole?

Of course, there aren't any conventional stats that will give any kind of real help.

I remember watching Emmett Smith ripping off 7, 8, 9 yards a pop behind a Dallas line that gave him massive holes. Smith was a very, very good RB. At the same time, Barry Sanders made some of the greatest runs in football history just to get back to the line of scrimmage. There isn't any possible way to fold, spindle, or mutilate conventional stats which will effectively illustrate their comparative abilities.

Anonymous said...

For me, situation is the foremost consideration.

Teams with good running games are consistently able to control the ball and run out the clock when they need to -- and even when the other team knows what's going on and is expecting a run.

Same for individual running backs. Can he consistently get the yards needed to convert third down or score a TD when you're inside the redzone? Again, even when the other team is expecting you to hand him the ball?

High averages don't mean a thing if the team or the RB doesn't deliver when the chips are down.

Anonymous said...

I recommend "marginal yards"

MY = total yards - (carries * margfactor)

margfactor would be something like 3 or 4 yards. It would measure total yards gained above the marginal number. 3.33 might be a good factor, that gets you a first down in 3 plays.

That, btw, is also equal to:

MY = carries * (ypc - margfactor)

Tom said...

I don't know if you're familiar with Success Rate, popularized (such as it is) by Football Outsiders but which originally appeared in Hidden Game of Football. In this, rushes (and other plays) are successful if they get 40% of the needed yards on 1st down, 60% on 2nd down, and 100% on 3rd or 4th down. Not to appear on an FO kick, but you should also read this article by Mike Tanier looking at the same topic.

OldSouth said...


In theory, I love what you're saying. Actually, if I could use theory alone to determine a measure, it would be something like "Increase in probability of win from rushing" (ultimately, on a theoretical level, any decision should simply reflect the degree to which is reflects the probability of winning the game).

The problem I see is that EV in football is prohibitively difficult to estimate, let alone calculate. Even the smallest decisions have a staggering amount of factors that would need to incorporated to make a meaningful "value" (e.g., probability of scoring, probability of preventing opponent from scoring by diminishing potential number of plays available to them, as well as field position, morale, plays that help in a "constraint theory" sense, etc.).

Yes, identifying this would be the most useful data we could have. But on a practical level it's impossible. (Except for the last couple of plays at the end of a game where the effect on the probability to win is dramatic and most of the other factors are less, if at all, important. E.g., "touchdown on this play we win; otherwise we lose" type scenarios.

It would take literally hours to figure the EV of one play, let alone every running play for every running back in a season.

Unknown said...

It seems like the best way to quantify the effectiveness of a running back's performance is to measure median YPC but to take into account the skewness of the distribution of YPCs. Assuming a normal (or for that matter any unimodal) distribution, the skewness of the distribution indicates the back's ability to deviate from the median YPC with a big run. Skewness can be quantified by several methods, but Pearson's coefficient of skewness ((3*mean- median)/standard deviation) should suffice. By calculating the ratio of skewness to median we should get an idea of how apt the running back is to bust out a big gain, scaled to their median performance. As you point out, since most backs have equivalent median YPC numbers, this statistic emphasizes the big play ability of the back. Obviously, these statistics are not team or context independent, confounding our interpretation of the data.

If you wanted to look at team independent running statistics, the way that makes the most sense to me, is to assess open field run YPC. This statistic would be based on the median or mean YPC after a runner was sprung from the second level. Again, it may be informative to adjust the median with a ratio of skewness. The idea here is that it takes sound blocking to get a running back past the D-Line and into the second level of defenders, however on many (but not all) plays after a back has broken through the second level he has little to no blocking (to be completely fair, he faces fewer defenders and those that he does face often are defensive backs who don't tackle with the same authority as a linebacker or lineman). The back usually rushes semi-independent of his blockers and thus the YPC after the second level is a more pure (though not perfect) assessment of a backs ability run/avoid defenders. This may be important because excellent blocking schemes/play calling would afford a running back more opportunities of rush for big yardage and thus increase the median YPC and the skewness of the distribution of YPC. However, the question remains: Would a more mediocre running back be able to thrive within the same environment or would our superior running back be able to put up those numbers in a less effective scheme? A team independent measure, be it the one I detail here or another measure, allows us to examine only the running back's performance and is a measure of pure rushing ability. Of course, football is a team sport and thus team independent statistics are great for assessing players for purposes of trade/draft evaluations, etc. but team independent statistics poorly predict game winners or rushing title winners.

Brad said...

I don't think getting long runs is the only way a back can improve his average. He can also do so by getting less short gains.

Think of a back that gets 3 yds minimum on slightly over half of his carries and gets 6 yds on the rest. Then compare him to a back that gets loses a yard on a third of his carries gets 3 yards on a third of his carries and gains 10 yards on a third of his carries.

Both backs have a median rush of 3 yds, but the first back averages around 5 yds per carry while the second one averages only 4. However the second back clearly has more "Big play potential" because he gains 10 yards on 1/3 of his runs.

My point is that a back can improve his average vs median both by getting more long gains OR by having less short runs. Which of these two things that great backs do is a question for the data.

Unknown said...

I'm no statistician, and some of the comments here are totally over my head.

Nonetheless, as I was reading the article, I was thinking that in addition to YPC and MYPC, an effective (and widely available) stat to consider would be 10+ yard runs, 15+ yard runs, etc. Wouldn't that be a good measure of the "explosiveness" of a running back?

In contrast, I think that weighting the RB's progress situationally (i.e. devaluing a gain of 5 on 3rd and 6 vs. weighting a gain of 5 on 2nd and 3) is not as effective of a statistic. I say this because no RB worth a damn is going to aim to gain only 2 yards on 3rd and 2. He's going to try and "take it to the house" every time. Right?

Anonymous said...

RBs and OL performance tends to go hand in hand. If you have great run blocking OL, your RB tends to have success. Obviously, there are exception. There is no good ways of quantifying on evaluating RBs. You have to take everything into account which include rushing yards, YPC, receiving yards and so on.

Unknown said...

Two summers ago, I wrote something up on what Anonymous called marginal yards:

I looked at rushing yards over 3.0 yards per carry. However, as the author has implied, I've begun shifting my focus away from yards per carry.

Rushing first downs is a key part of evaluating a running game. Without play by play information, I'd want to focus on rushing first downs, rushing yards, rushing TDs and carries.

Anonymous said...

Another plug for Football Outsiders, who use context to measure the effectiveness of a run in exactly the way Mathlete suggested, while also taking strength of schedule into account.

Anonymous said...

It seems like most folks have the same idea--perhaps, just like quarterbacks, there ought to be a "run efficiency" statistic. Presumably it should incorporate (in no particular order):
1. Average and/or median yards per carry (can't get around this)
3. Fumble percentage
4. Touchdown percentage
5. First down percentage
6. Percentage of carries resulting in no gain or negative yardage.

We can argue about how to weight each factor to minimize discrepancies across teams in terms of how their offenses employ running backs. But I think we can agree that running backs, when they get the call, should advance the ball, get first downs, score, and not fumble. With respect to weighting the importance of these factors, my feeling is that conversion of first downs and touchdowns should matter enough to more than counteract the fact that the carry might have only gone for one yard (thus reducing the average ypc).

I don't know about yards after contact. It would seem to complicate things since we'd have to factor in whether getting 1 yard after running into the free safety 20 yards downfield indicates a worse back than one who gets 5 after getting jumped by a linebacker at the line of scrimmage. The Barry Sanders illustration in the comments is another illustration--how much should a no-gain play count when the back had to run for his life to get back to the line of scrimmage? Perhaps by not punishing Sanders' efficiency rating as much as if he had a five-yard loss on the carry.

Unknown said...

Chris, you said:

"...IF the median truly is right around 3 yards for great and average backs alike, then the difference between good and mediocre runningbacks and rushing teams would seem to be wholly in the explosiveness of the upper 50% of plays..."

But I have to say I disagree strongly with that statement.

Let's make a baseball comparison. A baseball analyst could say, "For almost every pitcher, the median number of runs allowed per inning is zero." This is a true statement. However, it does NOT imply that the proper way to analyze pitchers is to only look at how much they differ in their big innings, i.e., whether they allow 6 or 8 runs in an inning in which they completely fall apart. Instead, we know that how often a pitcher allows one run in an inning, or two runs, is still extremely important. Also, remember that it often doesn't matter whether a pitcher allows 6 or 8 runs, because by that point, their team is likely to lose anyway.

Similarly, in football, it may be that all backs (or teams) tend to have runs in the vicinity of 3 yards fairly often. But precisely how often they get 5 yards instead of 3, or zero yards instead of 3, is still hugely important and shouldn't be ignored. And remember that the difference between a 40-yard gain and a 50-yard gain might be insignificant anyway, because the length of long gains is often only limited by the distance between from the end zone--who's to say that a 40-yard rushing touchdown wouldn't have been a 70-yard rushing touchdown instead, if only the team hadn't already been so far down the field?

Unknown said...

While I'm here posting comments, let me say this:

Chris, I think your site might be my favorite thing on the entire internet. Seriously. I enjoy it so much that it's downright arousing, like football pornography, and I mean that in the most complimentary way possible.

I guess I can also share my thoughts on the questions you asked:

I think the first task is to make sure we're being completely clear about what it is we're trying to evaluate. Evaluating a single player, i.e., the running back, is a totally different task from trying to evaluate the team's run game as a whole.

Ultimately, I think the first task is virtually impossible from statistics alone. Without game film and a subjective analysis by a human eye, I don't think there's any effective way to consistently separate out the contribution of the ballcarrier from the contribution of his blockers. Sure, we can look at carries over 10 yards or something, but clearly it's possible that a running back will sometimes deserve some of the credit for for a play going 4 yards instead of 2. Ignoring these contributions would be ignoring a valuable running back skill, and so our measure would be inaccurate.

So if we're limited to just the statistical information available, I think the only reliable option is to evaluate a team's run game as a whole. I think the "success rate" concept is a nice idea, but I think it applies more to the passing game than to the run game. It doesn't seem right that a 1-yard gain on 3rd and 1, which counts as a "success," indicates a better run game than a 5-yard gain on 2nd and 10, which counts as a "failure." The value of a run play in a game context is not necessarily the best indicator of a team's running ability. I think run plays differ from pass plays in this respect. The goal of most run plays, as a generalization, is to hit the hole and gain as many yards as possible, whereas the goal of a passing play might depend on the down and distance.

But most people would still agree that yards per carry, by itself, is certainly not the best measure, because it treats all yards equally. This is a big problem when it comes to long runs. Extra yards tacked on at the end of long runs are the least significant rushing yards. The fact that a team broke a 70-yard run instead of a 40-yard run may be important in the particular game in which it occurred, but it shouldn't carry that much weight when evaluating the rushing attack as a whole.

I think this is why the Outsiders folks tried to talk about median carry length. However, they've gone too far in the other direction now. They're throwing the baby out with the bath water, so to speak. In my opinion, the correct approach is to use some sort of modified YPC system that compensates for the effect of long runs. As an extremely simple example, you could just say that on each run, every yard gained after 10 only counts as half a yard. (Obviously there would be much more sophisticated ways to go about this, but you get the idea.)

Anonymous said...


Just posted a "breakaway potential" idea on another board yesterday. Using what I had available from, I came up with the idea of

BP = (20+ carries)/(10+ carries)

It is a measure of "What percent of your 10 yard+ carries went at least 20+ yards"? Or, how often when you made it to the secondary, did you break a really big gain.

The results were interesting. Dwyer from GT was #1 (61%), Best from Cal was very high (they tied for national lead in total 20+ carries).

What was interesting was that scheme may have a big effect of that. Navy, GT, and Fresno St had 2 players each in the top 20, Florida had 3. And neither Harvin nor Tebow was one of them.

I think the only QB in the top 20 was the guy from Baylor.

Anonymous said...

Anon @ 10:09:

An interesting idea, but you would also have to somehow factor in the number of breakaways.

For example, let's say I had a runner who averaged 1.9 yards a carry. But he had one run for 21 yards and no other run that exceeded 10 yards. If I understand the BP correctly, his BP would max out at 1.0. But obviously no one would consider the guy a breakaway threat!

Anonymous said...

Anon @11:09,

Well yeah, like anything else, you need a minimum number of cases to make it realistic. Like the backup QB who plays 1/2 a game and leads the league in passer rating.

I used the top 100 rushers (total yards) in the nation. All had at least 5 20+ runs.

Caradoc said...

Didn't you have a writeup a while back about the different situations that offenses face and the performance needed in each? It seems to me the best measure of a running back's effectiveness is how often he gets the job done. Extra yards are great, but what matters is making the first down (or the score).

Anonymous said...

The right variable depends on what kind of offense you want to run. I want my high risk/reward plays to come from the pass game, not the run game. From the run game, I want low-risk, reliable success.

Since I want both a successful gain and reliability, I'd try to find the player with the lowest percentage of carries that go for between 0-4 yards. I use those numbers because I assume that (1) any time a RB gets negative yardage it's either a problem with the OL or the RB will be benched; and (2) 4 yards is a success.

4 yards is not always a success. Consider third and long. But if you want your high risk/reward plays to come from the pass game, you're probably not running on third and long unless you see something funky out there or you are making a long-term strategic decision ("long-term" by intra-game standards). And in both of those situations, your expectations for running success are different than baseline, so they are appropriately excluded from the analysis.

Similarly, I would want to exclude situations in which which the defense is aligned (almost) exclusively to stop the run, as that would change my expecations for running success. You frequently see this on third/fourth down with 3 or fewer yards to go. You also see this by default inside your opponent's 10 yard line (where the end line condenses the field). So I would exclude all of those plays from my analysis here as a proxy for excluding "defensive alignments that change my expectations."

And I know that I'm valuing a 4 yard gain the same as an 84 yard gain. But I'll take the guy who gives me 4 yards on each of 20 carries over the guy who gives me 19 carries for no yards and then an 80 yard gain. And, besides, no variable can reasonably be viewed in a vacuum.

Andy said...

The balancing act here seems to be how to appropriately take into account the relative contributions of long gains, and short/no gain plays.

What I would look at is the outcome for each down and distance. Each outcome likely has a different impact on the probability of winning the game. (A 0 gain play reduces the probability of a first down and therefore reduces the team's likely winning percentage, a 4 yard gain has a more positive effect, a long run for a touchdown has a more positive effect). If these impacts are linear (a running back that runs for 0, 0 and then 12 yards on first down is the same as one who runs for 4 on all three downs, or that if the same runner ran for 15 instead of 12 that has the same value as the other runner running for 5 on each play) then a measure like the football outsider measure DYAR probably is the best measure.

My intuition is that there is some significant non-linearity (The big play is nice but if it comes coupled with a lot of negative or 0 plays I need to count this against). I think you would want to apply a transform to each of yard/down/game situational outcomes (each run is one outcome). The transform would be derived from the change in win percentage generated by each outcome compared to the typical outcome (or if you really wanted to get complex, the range of typical outcomes) (Advanced NFL Stats has an in game win percentage calculator which essentially does this). You would want the transform to sufficiently complex/accurate to take into account the value of the different outcomes over the replacement play (although it may not need to fully take into account every variable.)

This might be excessively complicated, but I think it would be the best statistical way of going about it.

Charlestowne said...

You need Bloxplots to campare an individual to an aggregate total of all starting backs in the league. This won't only tell you where he stands on average, but would give you an indication on where he is most effective. (By the way, currently studying for a decision analysis test for business school, for what that's worth) ;)