A core tenet of basic economic theory is the principle of diminishing marginal returns. 

Here’s the basic gist of it. Let’s say Jim owns a yardstick company and wants to sell as many yardsticks as possible while also minimizing his costs. At first, he has one worker, Hassan, who operates one yardstick-making machine that Jim has affectionately named Carrie (this analogy is incredibly on the nose). Jim decides he wants to increase his output, so he gives Hassan more Carries, but each one costs money for Jim to purchase. At first, Hassan makes many more yardsticks out of each Carrie, so the cost is worth it, but as Jim buys more and more, they become difficult for Hassan to manage. He gets tired trying to run all these Carries on his own, so with each new Carrie, the company produces fewer additional yardsticks and thus less additional revenue. 

Jim’s company is exhibiting diminishing marginal returns to capital; for each new Carrie Jim gives him, Hassan produces fewer and fewer additional yardsticks. In an ideal, fully rational world, Jim would continue to purchase Carries until the additional revenue from each one is equal to the cost of the machine.* For example, if each Carrie costs $20 and the company can sell each yardstick for $4, Jim will give Hassan more Carries until each additional machine results in five yardsticks per Carrie. 

What this horrible, way-out-of-hand analogy aims to do is explain the reasoning behind splitting carries between running backs. With each consecutive carry you give a back, his production will drop on average, because of fatigue, defensive adjustments, and the added risk of injury. Even if your top running back is significantly better than the others, you’ll have to share the workload to some extent. The question is, how much? 

The Wolverines haven’t had a true workhorse back under Josh Gattis. Based on the eye test alone, it feels like those offenses have split carries far too much. But especially with an emotional fanbase like Michigan’s, the eye test can be deceiving. Let’s put some hard numbers to it. 

*In the real world, no firm actually behaves this way. In recent years, behavioral economists have found that most firms just set a sales target and produce until they hit it. Economics, it turns out, is great at telling people how they should behave, but terrible at modelling how they actually behave. 

jump for data

The Data

Unfortunately, there’s no readily available stat out there about how much a team splits its carries, so I’ve created two rough estimates of it: the percent of carries by the starting running back vs. all other running backs (“RB1 pct. carries” in the spreadsheet below) and the percent of rushing yards gained by that running back (“RB1 pct. yards”). Note that the difference between those two stats is effectively a measure of relative yards per carry. From our economic analogy, we would expect a coach to give the top back the ball until his percentage of yards gained tends toward his share of carries, as that would mean the starter is getting the ball in all situations where the expected yardage is greater than the other backs’, but never when it’s less. Of course, in situations where one back is truly better than the others, this rarely happens, as the coach (rightfully) wants to mitigate the risk of injury, and it’s impossible for that coach to evaluate exactly when a back’s returns start diminishing. The real world is annoying.

Still, too great a gap can indicate that a back is being under-utilized. As an extreme example, let’s say Hassan Haskins gained 70% of rushing yards but received just 52% of carries among Michigan’s running backs. That would mean Haskins should have gotten more carries, because he had far more payoff per attempt than other rushers, and the risk of injury probably wasn’t great enough to justify keeping him off the field that much.  

I’ve also excluded quarterbacks, fullbacks, and wide receivers from this measurement because I’m only interested in how much coaches rotate their running backs; whether they run too many jet sweeps or too few QB keepers are questions for someone far smarter than me. 

Have I lost you yet? Good. Here are the numbers: 

Of course, there are limitations to this data. Number one, because I’m calculating these numbers myself and like to sleep occasionally, I can only include a handful of teams in my analysis. As such, I’ve tried to pick the teams that are most relevant to fans: Ohio State and Michigan State for the rivalries; Alabama and Clemson because they’re perennial contenders; Oklahoma because they’re a more QB-focused offense; and Wyoming because LFG pokes. A second limitation is that it’s impossible to measure an “ideal” gap between percent yards and percent carries, so it’s hard to make suggestions for what Michigan should shoot for. My initial instinct is to point to Alabama and Clemson and say “do that,” but the existence of Najee Harris and Travis Etienne complicates that. Basically, even with all the data, any recommendations I make are going to be heavily subjective. Third, I’m not taking injuries into account because, again, I like sleeping, and reconfiguring who the starter is every time someone gets hurt would prevent me from doing so. 

Still, even if limited, it’s data worth looking at. Sure, it’s a rudimentary, unscientific analysis, but football is a rudimentary, unscientific sport. I’m not trying to solve the Wolverines’ rushing offense, nor am I evaluating the development gap to Ohio State. I just want to answer two simple questions: how much has Michigan split carries under Josh Gattis, and how does that compare with the teams it competes (or wants to compete) with? 

Michigan

Let’s get this part out of the way: Michigan’s rushing offense is not very good, and its problems run deeper than mismanagement from the coaching staff. Somewhat predictably, Michigan State was the only team both seasons to have fewer rushing yards from running backs — something especially problematic considering the Wolverines’ QB run game wasn’t particularly potent either. I already wrote about Michigan’s longtime struggles to develop elite running back recruits last week, but in the short term, the problems are more localized in the offensive line. If run blocking doesn’t improve, the Wolverines will continue to struggle on the ground, regardless of how it divvies up the carries. 

Relative to competition in 2020, though, Michigan did not split its carries all that much. Again, it’s hard to draw strong conclusions based on this limited data, but I wouldn’t be surprised if teams across the country spread out reps more evenly, just by virtue of the shorter fall camp and already thinned-out rosters from COVID protocols. That eight percent gap in carries and yards, though, still indicates that Haskins may have been under-utilized in 2020, though I think the timing of substitutions was a greater problem than how frequent they were on average. 

Consider last season’s Michigan State game. Haskins was, unsurprisingly, the Wolverines’ most effective back, notching 58 yards on eight carries, but he struggled for consistency, as a good amount of those yards came from a few chunk plays. Much of that struggle, in my mind, falls on the coaches’ shoulders. In the first quarter, he tallied one run for two yards, and that was it. Then, in the second quarter, after disappearing for three drives, Haskins picked up a pair of 15+ yard runs, but was pulled out of anything resembling a rhythm by a pair of wildcat plays. In the third quarter, he ripped off an 18-yard run, then saw the ball just twice more for the rest of the game. He was never given any real chance to find a rhythm, and as a result, he didn’t. 

In fairness, Michigan’s rep-splitting in 2019 more closely fit each player’s production, but the timing was still off a lot of the time. It prevented any of the Wolverines’ backs from finding any rhythm, and it probably played into Charbonnet’s decision to transfer. Lots of people talk about how Michigan’s offense doesn’t play to its strengths, and I think this is a place where that’s pretty visible. 

The Rest

Moving beyond Michigan, I think the most intriguing data point on this chart comes from Ohio State. In 2020, Trey Sermon was, to put it lightly, a beast in the backfield. He put together a conference-leading 7.5 yards per carry, yet split reps almost exactly with Master Teague, who averaged just 4.9 yards. In contrast, J.K. Dobbins received over 60% of the Buckeyes’ carries in 2019, despite being about as effective and competing with a Master Teague that averaged 5.8 yards per carry. Since 2020 was a short season, part of that number is skewed by Sermon’s early injury in the national championship, and I also wouldn’t be surprised if defenses keyed more on Sermon on read options, but that’s still a pretty significant gap between usage and production. It’s not often that anyone not named Nick Saban gets the chance to say they’d make better coaching decisions than Ohio State’s staff, so everyone should take advantage of this rare opportunity and laugh at Ryan Day for not running Trey Sermon more. 

Michigan State’s numbers are also interesting, for two reasons. First is that they illustrate just how catastrophic Mark Dantonio’s last offense was. Effectively, it was made up of Elijah Collins, Cody White, and a pile of brightly colored rocks. Even with Collins receiving 68.7% of carries — by far the largest share of any running back in either year — he still theoretically should have gotten more if not for fear of injuries. Second, you can actually see the shift in priorities between coaching staffs right there on the chart; sharing the load is something that Mel Tucker himself has emphasized as one of his priorities. 

The rest of the numbers are fairly predictable. Alabama and Clemson gave the ball more to their starters because, well, they were Najee Harris and Travis Etienne. Interestingly, Oklahoma seemed to split its carries too little in 2019, when Rhamondre Stevenson was the backup, then did it too much in 2020, when Stevenson was the starter. Wyoming, apparently run by economists, tended toward a perfect proportion of carries to yards. 

Conclusion

So, how much should a team split carries? After all this, I don’t know. It’s always going to depend on the team’s talent, its depth, and the coach’s own aversion to injuries. The difference between a rusher’s share of carries and his share of yards can give us clues in hindsight, but that data isn’t really useful without a reasonably large sample, so a coach can’t use that on the field. 

Really, it comes down to feel. Part of coaching is being able to recognize when a player is finding a rhythm and helping to foster that. Yes, there are more significant issues impeding Michigan’s run game, but the way that the coaches split up the carries simply isn’t working.