By Anthony Zonfrelli

Every week, NFL coaches list their players with injuries as either “Doubtful,” “Questionable,” or “Probable” to play that weekend. What many people don’t know is that these statuses are supposed to indicate a specific probability of playing. Under NFL rules, these labels mean that the designated player has a 25 percent, 50 percent, and 75 percent chance, respectively, of playing that Sunday, which raises the question: are NFL Coaches assigning their injured players these statuses with any accuracy?

Using every injury status update for each team through the 17 weeks of the 2012 season, I went back to chapter one of the statistics textbook and used one-sample t-tests to examine the coaches’ accuracies. I only used data from the one season to (essentially) hold coaching staffs constant.

The status breakdown for the league went like this:

Injury Status Assignment Number of Players Listed Expected Fraction of Players to Play Fraction of Players that Played Doubtful 167 0.25 0.27 Questionable 3146 0.50 0.62 Probable 1986 0.75 0.89

With a p-value of 0.63, there isn’t evidence to suggest that the true mean of “Doubtful” play rates is not 25 percent. However, the play rates for “Questionable” and “Probable” are both substantially and significantly higher than their implied values. This means that coaches tend to overestimate the severity of week-to-week injuries when they are not serious. Therefore, players labeled as either “Questionable” or “Probable” have a higher chance of playing than their statuses indicate.

This trend may exist because of the subjectivity of the terms “Questionable” and “Probable.” In everyday speech, these terms mean different things to different people in different situations. If somebody says that something will “probably” happen, then they more than likely assign the event nearly a 100 percent chance of occurring, but that’s not what it is supposed to mean in the NFL Injury Report.

If we use the sample means as our best estimates of the true means for “Questionable” and “Probable” listed players, then they really have a 62 percent and 89 percent chance of playing, respectively. Keep that in mind when you are setting your fantasy lineup.

Some of the more interesting findings, though, happen just from eyeing the differences between teams in the sample. For example, while Bill Belichick is often criticized for abusing the injury report, the Patriots only ranked 8th and 6th in the league in terms of highest “Questionable” and “Probable” play rates last year. Actually, Buffalo was first in both categories (T-1st in “Questionable” play rate). In fact, 98 percent of the 81 Bills listed as “Probable” last year saw playing time that week. The Bills might not even be aware of this rule.

The Green Bay Packers, though, nearly hit all three categories on the money – they had marks of 25 percent, 49 percent, and 75 percent. They would have been perfectly accurate if just one more wimp listed as “Questionable” had played. Also, with a perfectly legal and accurate 75 percent play rate, Green Bay had the lowest play rate for “Probable”-listed players, which is to say that players listed as “Probable” really have at least a 75 percent chance of playing. Similarly, at 49 percent, the Packers were tied for the second lowest “Questionable” play rate; New Orleans curiously only played 36 percent of their “Questionable” players.

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