Last weekend, Steelers running back Le’Veon Bell sat out the first game of the regular season rather than play under the NFL franchise tag. Slated to earn $14.5 million in guaranteed money in 2018, Bell loses out on $855,529 each week he fails to report. The franchise tag would make Bell the third highest paid running back in the NFL this season — but only if he actually plays. Around the league, there is a wide range of speculation on how long Bell’s holdout will last. ESPN’s Adam Schefter reports that his sources believe Bell could be back by the end of September, while others note his holdout could conceivably last through Week 10.

Bell’s agent, Adisa Bakari, has hinted that Bell is holding out at least partially because of concerns that the Steelers will overuse him in what is likely his final year with the team. Bakari and Bell appear to have decided to hold out as long as possible to avoid that potential workload and the injury risk it brings. This is a legitimate concern: If Bell suffered a major injury without already obtaining significant guaranteed money, it could end up costing the star running back tens of millions of dollars.

So for now, Bell and Bakari’s plan seems to be to maximize his future earnings by forgoing a guaranteed weekly paycheck. But if profit maximization is the aim, is this actually the correct approach? Should Bell hold out through Week 10 if his goal is to earn the most money?

To answer those questions, Bell’s camp must balance the amount of guaranteed money he is likely to earn in the open market with the risk of injury if he plays this season. The market for elite running backs in the NFL is difficult to gauge, but we have two recent comps to help us land on an approximate value. I asked NFL salary cap expert Jason Fitzgerald of Over the Cap for his opinion, and he believes Bell will likely command a contract that will land somewhere between what Todd Gurley and David Johnson were able to negotiate.

“Realistically, I can’t see a path to exceed $45 million in guarantees to top Gurley,” Fitzgerald told me. “In light of the Johnson deal, I’d probably say a fair number to use is something between $35 [million] and $38 million in injury guarantees and probably looking at a three-year deal.”

Bell and his agent surely have a salary target in mind, and it may well be different from what Fitzgerald estimates Bell is worth. For now, we’ll use the high end of Fitzgerald’s range and assume that Bell lands a contract with $38 million in guarantees. Next we need to calculate the injury risk of playing running back in the NFL. Moreover, we need to adjust the injury rate to account for players who see a large volume of touches. Over his career, since 2013, Bell has averaged 24.9 touches per game, the most in the league. Each of those touches is an opportunity for a serious injury that could rob Bell of his future earnings.

According to Football Outsiders, the running back position has the second highest rate of serious injuries in the league at less than 20 percent. Serious injuries are defined as those that cause a player to miss four or more games, which is the outcome Bell surely wants to avoid. This injury rate estimate is probably too low, however. Football Outsiders includes all running backs on each 53-man roster in its rate calculation, regardless of whether they actually take the field. Being tackled in the NFL is a major driver of injury, so we need to account for touches on the field of play.

One way to do this is to leverage fantasy drafts as a proxy for running back usage in the upcoming season. Fantasy players use the early part of their drafts to take running backs who they anticipate will see high volume. To estimate the injury rate for these players, I reached out to epidemiologist Zach Binney, a sports performance and injury consultant and a writer for Football Outsiders. Binney took average draft position (ADP) data from 2007 to 2015 and used Football Outsider’s proprietary injury database to calculate the serious injury rate for running backs with a preseason positional ADP of 24 or greater. He estimates that the true likelihood of serious injury is between 20.9 and 32.8 percent for NFL running backs over a season.

Armed with these findings, we can create payoff curves based on a range of possible per-game injury probabilities.

The teal curve assumes that Bell reports for Week 2 and begins collecting his $855,529 paychecks, and then signs a contract with $38 million in guaranteed money at the end of the season. This would make Bell’s total compensation close to $52 million, representing a probable best-case scenario for Bell. The orange curve assumes that he holds out until Week 11, and thus loses out on $855,529 for the next nine weeks, but then signs the same contract with $38 million guaranteed in free agency. In this scenario, Bell would earn $44 million in total.

Crucially, both models assume that Bell receives no future contract if he is injured. Should he go down after signing with Pittsburgh for this season, Bell would collect only the salary guaranteed him under the franchise tag, a very pessimistic scenario. Yet in our chart, we see that the point at which a holdout is expected to become more profitable is outside the range accounting for our best guess at the true injury rate. So reporting and playing is the best option if Bell is seeking to maximize his earnings.

Is this the end of the story? Perhaps not — if Bell is actually worth more in free agency than Fitzgerald estimates. If Bell is able to land a contract worth more than Todd Gurley’s, for a total guaranteed contract value of $55 million, holding out becomes a profitable decision.

In this scenario, the point at which a holdout is expected to become more profitable falls within our true injury range estimate. Bell’s decision to hold out here makes sense because it balances future earnings with the risk of injury.

In both scenarios, there is a possibility that the injury rate we’ve calculated is underestimating the true danger to Bell’s health and future earnings. After all, Bell’s workload is extreme: He led the NFL with 406 touches last season. There may also be motivations at play in Bell’s holdout that are not related to compensation, and not all costs can be captured in a simple model.

That said, the chances of Bell getting a contract north of $38 million seem very low. The last best offer from the Steelers reportedly included just $10 million guaranteed. James Conner, Bell’s replacement, recorded 192 yards from scrimmage along with two touchdowns against the Browns in Week 1. If Bell’s overriding goal is to get paid and maximize his earnings, his best course of action is to report immediately to team headquarters and start cashing his checks.

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CORRECTION (Sept. 13, 2018, 6 p.m.): A description of the first chart in a previous version of this article transposed the colors of the curves.