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Would a little extra pay make the Coyboys’ Demarco Murray more likely to take risks (like plowing headfirst into another player)? Would the threat of a fine deter him? Reuters

Does a running back’s pay affect his willingness to take risks?

How much risk are you willing to take as part of your job?

This may be a question that has never crossed your mind. However, it is very clear that certain professions involve greater degrees of risk than others. For example, being a Bering Sea crab fisherman is inherently more dangerous than being an accountant. This raises the question, would an increase in pay entice you to accept a position with a much greater risk of injury, or even death?

Labor market research has well documented the effect of pay on individuals’ willingness to accept jobs with different degrees of risk. Generally, people expect a higher salary to accept a more dangerous position, other factors remaining constant.

But how would changes in pay affect a person’s willingness to accept greater risk within his or her current job? That is, would our Bering Sea crab fishermen be willing to take riskier actions for additional compensation? And conversely, when an employer or government seeks to deter risk-taking, do monetary fines make an individual less likely to engage in dangerous behavior?

The answer has implications for many stakeholders, including government agencies hoping to make workplaces safer and insurers who have to cover the costs when risky behavior leads to harm.

In a recent research study with fellow economist Thomas Kniesner, of Claremont Graduate University, we attempted to answer that very question: How does money affect employees’ willingness to accept risk at their jobs?

Whose job is more risky, crab fisherman or an accountant? Crab accountant from

How to define risk

One difficulty in answering the question is how can we measure risky actions. Furthermore, if we can define actions that increase an employee’s injury risk, we must be able to quantify them. We also need to have individual injury information, as opposed to the number of injuries for a given job.

In other words, we need a well-defined job setting where individual actions are quantifiable, risky actions can be identified, and employee injury and compensation information are known.

Enter professional sports.

Football, hockey and other professional sports offer economists and other social science researchers an excellent setting to conduct studies on the labor market. There is an abundance of data, covering both employees and employers. Furthermore, the data is consistently and continuously recorded. The data provide information on personal characteristics, job characteristics, employer characteristics, employee and employer actions, employee and employer productivity and pay.

Economic analysis of professional sports has proven fruitful with respect to other important topics such as discrimination in labor markets. Recent research on the National Football League, for example, shows that wage discrimination may exist for several positions, including quarterbacks and linebackers.

Yards after contact

Since we are interested in individual risk-taking, we examined a professional sport where players face a significant risk of injury: football. The subject of worker safety is especially relevant in the NFL, in light of medical evidence linking football to poor health later in life. The league has also recently taken steps to make the game safer for its players.

Since different positions face different risks and take different actions, we decided to focus on one: running backs. They have a well-defined job setting that allows us to identify actions that increase a player’s risk of injury.

For example, “yards after contact” is a measure of the number of yards gained by a running back after an opposing player first contacts him during a play. It is a relatively new measure but is recorded by several sources, including ESPN and Pro Football Focus. We hypothesized that the more yards a player gains after he has already been hit, the greater his injury risk because he is exposed to more contact.

Using injury data from Fox Sports on the 2013 NFL regular season, we learned that the yards after contact metric has a significant effect on injury. Increasing the number of yards after contact (per rushing attempt) increases both the probability a player could get injured and also the total number of injuries he has in a given season. Specifically, one additional yard after contact per rushing attempt increases the odds of being injured by 150%.

Thus, the market for NFL running backs provides an ideal setting to analyze risk-taking within a job.

Mining for models

We then analyzed whether or not compensation affects the number of yards after contact. Using previous labor market research as our guide, we hypothesized that compensation should have a significant effect on a player’s willingness to accept risk.

We mined the data extensively to find a model that would show the greatest impact of pay on yards after contact, trying linear regression, instrumental variables estimation, quantile regression and other statistical models aimed at trying to show a relationship, all estimated with a variety of specifications.

However, regardless of which model we used, we found no relationship between pay and yards after contact. And the results were the same no matter how we measured pay, whether using total salary or salary cap value (how much a player’s pay counts against a team’s overall salary cap). In all, we tried more than 100 models to find an impact. But at most, a change in compensation of $100,000 only affects the number of yards after contact per rush by 0.82%.

That is, if you were to increase an average running back’s compensation by $100,000, his number of yards after contact per rush would rise just 0.74 inch, which is completely meaningless. Over the course of an entire season, with an average of 106 rushing attempts, the player would have 2.2 additional yards after contact, again statistically insignificant.

Our research showed that the level of compensation does not change the amount of risk running backs are willing to take. Higher pay did not cause players to assume more or less risk, and neither did less of it. That means the amount of risk players are willing to accept is determined by factors other than their pay.

One possible factor is the opportunity cost of playing in the NFL. The compensation from any outside employment option is far less than an NFL salary. Therefore, players are willing to take risk regardless of their pay because it is far greater than their next best option. Another possibility is the culture of the NFL. Players may be highly rewarded, not monetarily, but perhaps socially, for taking risk.

What does it mean

Broadly, our research shows that acceptance of risk in the workplace may be governed by factors other than compensation. For example, risk-taking may be more affected by the wage of an employee’s next best option than by his or her actual wage. Therefore, employers, or other entities, may not be able to affect risk-taking behavior through changes in compensation.

And what does this mean for the NFL? The league has recently enacted several rules changes to increase player safety. One of these pertains specifically to running backs, who are no longer allowed to lower the crown of their helmet when taking on an opposing tackler. Doing so is one very risky way to increase the number of yards after contact.

One method of enforcement of the new rules is to fine players. For example, Demarco Murray of the Dallas Cowboys was fined $21,000 week 17 of the 2013 regular season for a crown of the helmet violation.

However, our research shows that reducing the compensation of running backs does not change their risk-taking behavior. If the NFL wants to protect its players, fines may not be an effective method. The recent push by the NFL to increase player safety may prove even more difficult than first thought.

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