Running the numbers on Le’Veon Bell’s decision not to play in 2018

I wonder what Richard Thaler thinks of the Le’Veon Bell saga. Thaler is known as the founder of Behavioral Economics, which is essentially the study of why human beings don’t make rational financial decisions. Cognitive limits, bias and emotion all cloud our ability to behave as mathematics tell us we should. The multi-year Le’Veon Bell drama would be a great case study for the academically curious.

Ever since Bell decided not to attend training camp before the 2017 season, he started a new game that mixes together emotion, bias and financial projections - and now he’s going to play it out until the very end. He took the world of the known and entered into a world where probabilities rule the day, and that narrative has been lost in the debate.

There are pundits, like Mike Florio, who have been vocal that Bell has definitely made the right choice. Plenty of others suggest this is the dumbest holdout of all-time. Of course pundits are paid to be bold, but the reality is that we simply don’t yet know if Bell’s bold move will pay off for him.

The other reality is, and Thaler will back this up, we will never know if Bell made the right decision.

That shouldn’t stop us from trying to have a more nuanced conversation. Rather than being bold, how about getting what is known out on the table and do some of the math that Le’Veon and his agent and the Steelers have been doing for the last two seasons?

There are two rational reasons why Bell chose to not play in 2018. The first is that a serious injury would reduce the value of his next contract. The second is that additional touches would reduce that same contract. This second bet is counter to what has been the history of contract year performance theory across all sports for decades. Normally soon-to-be free agents seek to have a peak year as they head into free agency. Bell opted to use the opposite strategy and not play at all. It’s counter to traditional wisdom but it’s not without its reason. Let’s explore these two rationals.

Injury Risk

Before delving too far into the numbers some assumptions need to be made about what constitutes a bad outcome for Bell. Obviously any injury wouldn’t be great but he’s mostly worried about a significant injury, the kind that would dramatically reduce his next contract. For our purposes let’s keep things simple and assume an injury of 8 weeks or longer would have a disastrous effect on Bell’s future contract and reduce to guaranteed money to zero. That’s certainly dramatic, but it gives Bell the benefit of the doubt.

Publicly available NFL injury data is scarce but fortunately there was excellent work on the topic done by Football Outsiders a few years back. They collect injury data and published a review of the trends over 15 seasons. According to the Football Outsiders database an NFL player has a 9% chance of collecting an injury that runs 8 games or longer over the course of a season. Running Backs surprisingly are no more susceptible to such injuries compared to other positions but let’s skew things a tad for Bell, who was set to be used more than the average player. Let’s up the ante by 50% for Bell and assume, had he played the 2018 season, he’d have a 13.3% chance of picking up an injury that would ruin his next contract.

We haven’t spoken about Bell’s contract potential for next season, but assume for this argument that he’ll receive “Todd Gurley” guaranteed money in his next deal. Bell seems to think he will. Given Bell’s age this seems highly unlikely. Gurley is over two years younger and the $45 million he received was guaranteed was across four years, while Bell’s is likely to be three. If Bell played 2018 and was uninjured he’d accumulate $59.5 million over the next two contracts in terms of guaranteed money. But in the injury case let’s say he only gets that one franchise tag year guaranteed at $14.5 million. The expected value of his status going into the season, with a 13.3% chance of being seriously injured, was $53.5 million. That’s $8.5 million more than he would make sitting out the season and receiving the $45 million.

To spell that example out there is a 13.3% chance that Bell walks away with just his $14.5 million and an 86.7% chance that he gets the full $59.5 million. Add those outcomes together and Bell has $53.5 million of guaranteed value. The non-guaranteed part of the deal makes the bet less clear but Bell has made it clear that the guaranteed money was the sticking point and that assumption is not a big factor. In a dream scenario where Bell gets the full value of Gurley’s $57.5 million dollar deal the financial loss shrinks only modestly to $7.4 million.

Some argue that by not playing this year Bell extended the back end of his career, but after this next presumably three year deal Bell will be a 30 year old back with 2,000+ carries, and it’s hard to imagine he’d get an incremental guarantee on his deal of $8.5 million because he sat out this season. It’d be hard to imagine he gets $8.5 million guaranteed at all. For comparison, at age 32 Frank Gore got $6.5 million guaranteed over three seasons. By that time Bell will be judged by what he has left in the tank, not the fact that he didn’t play in 2018.

What level of injury risk would make Bell’s decision a good one? Bell would have needed a 33% chance of disastrous injury to make this a breakeven financial decision, even using these numbers that give him the benefit of the doubt. That is much higher than the historical data reveals. If you assume Bell’s next contract won’t have that kind of guaranteed money the bet only gets crazier. If the guaranteed money in the next contract was even with the Steeler’s reported $30 million deal then Bell would have needed a 49% risk of serious injury to breakeven.

But what about showing up at the last possible minute, as Bell recently declined to do? The math is still not in his favor but it’s less of an egregious financial decision. If he had showed up to play the final seven games and taken the prorated salary and likelihood of season ending injury (which according to Football Outsiders data is a fair assumption) his expected guaranteed contract value would be $48.7 million, only $3.7 million more than the guaranteed $45 million he’s expecting.

At this point it all comes down to the risk someone is willing to take. If there was a 13% chance you’d get zero, would you pay $8.5 million to lock in $45 million? Or even $30 million? It depends on how much money you have to begin with.

Workload risk

But these high level numbers leave out important nuance related to Bell’s future contract potential, and that is his workload. Next season Bell will be 27 and, more importantly, he’ll have 1,229 carries under his belt. According to this analysis by NumberFire running back productivity starts to decline after 1,500 carries and falls precipitously after 1,800 carries. Assuming that NFL analytics is even more aware of these trends than public analysis suggests, that information places specific emphasis on Bell’s decision to avoid the 2018 season. This season with the Steelers would have put him past that 1,500 carry mark and would leave him with just one elite season remaining, according to this model. That means it could very well be that by taking his $14.5 million, Bell would have likely reduced his guaranteed money by some amount. This is a point not often discussed in the narrative but likely front and center in the mind of Bell and his agent.

But the workload factor also suggests more clearly that Bell should have played the latter half of the season. He could have minimized his loss with reduced injury risk and proven that he “still has it”, while not picking up enough carries to take one of his elite seasons off the table. Given his holdout that would have been, it appears, the optimal strategy for Bell.

Taking into account historical injury risk it’s clear that Bell sacrificed some amount of financial value by sitting out 2018. However, when considering a person’s tolerance to take risk, a key factor in Behavioral Economic circles, the decision becomes more difficult to criticize. This is why no expert can ever be certain Bell was right or wrong. When you factor in emotion and the personal relationships behind the scenes the situation gets even murkier, exactly where it stands right now. Only time will tell if Bell will get his guaranteed money and be able to say “I told you” to all of the fans. Based on the math above he’ll actually need $52 million guaranteed for him to justify that claim. Given his mileage it would be irrational for a team to pay him that much, but as Richard Thaler and Le’Veon Bell know all too well, NFL franchises don’t behave rationally either.