by Zach Binney

This second part of our four-part series on NFL injuries looks at how those injuries vary by time. We'll look at both calendar time (2000 to 2014) and season time (Week 1 to Week 17).

If you haven't read part I of this series, I highly recommend it. It lays out how we're exploring NFL injury data in this four-part series and gives some important caveats regarding the data.

Injuries by Week of Season

One common perception -- at least common enough that I personally believed it before looking at the data -- is that injuries occur more frequently as the season drags on and the wear and tear builds up on players' bodies. Let's take a look at that in Figure 3.

It's important to remember that Week 1 is an outlier because of the way our regular-season data is structured -- anybody who suffers an injury in the offseason, training camp, or preseason will first appear here. So you can pretty much ignore those numbers when trying to compare Week 1 with other weeks.

Figure 3 lists two things: 1. In orange, the new injury risk in a given regular-season week, adjusted for the number of teams on a bye week (so the numbers along the bottom represent the expected number of injuries if all 32 teams played that week); 2. In blue, the injury prevalence (i.e., percent of players injured) for each week of the regular season. Because epidemiologists love definitions, let's specify exactly what I mean by each of these.

New injury risk: the number of new injuries divided by the number of players at risk for that injury. The denominator (or "risk group") in any week is the number of players still playing without an injury (Figure 3) or without a given type of injury (Figure 4, below). This was calculated as 25,334 players (53 players, 32 teams in 13 years and 31 teams in 2 years), minus the number of injured players who still played each week (since those players are already hurt, they aren't "at risk" to suffer the same injury again). The numerator is the number of new injuries. New injuries are simply new or different mentions of a player on the injury report. For example, a player who strains his hamstring in Week 4 and is on the injury report with it through Week 8 is counted as a new hamstring injury in Week 4, but not Weeks 5 through 8. However, if he strains his hamstring again in Week 15, both Week 4 and Week 15 will count as new injuries. If, in between, he sprains his ankle in Week 10, that would count as a new ankle sprain in Week 10. All three of these would count as "new injuries" in Figure 3. We hypothesized above that injury risk increases over the course of a season. Figure 3, however, shows that the risk of a new injury is roughly flat across all weeks, particularly late in the season. There's a bit of a spike in Weeks 3 and 4, which makes sense as injuries start to manifest after a couple of tough games. Beyond that there's only a small amount of variation week-to-week, especially from about Week 9 onwards. All the variation in this chart is within about a 0.3 percent range (7.7 percent to 8.0 percent), which with 53 players on 32 teams would translate to about ±5 injuries per week. You could easily imagine this amount happening by chance, so I interpret this chart as showing an injury risk that is effectively flat over the course of the season.

the number of new injuries divided by the number of players at risk for that injury. The denominator (or "risk group") in any week is the number of players still playing without an injury (Figure 3) or without a given type of injury (Figure 4, below). This was calculated as 25,334 players (53 players, 32 teams in 13 years and 31 teams in 2 years), the number of injured players who still played each week (since those players are already hurt, they aren't "at risk" to suffer the same injury again). Injury Prevalence: the number of players on the injury report in a given week divided by the number of players at risk for being on the injury report that week. The denominator is 25,334 plus the number of players that needed to be replaced because they were on IR, IR-Designated for Return, PUP, or otherwise were not playing that week. I excluded practice-squad players but did not restrict the analysis to only the 46 players who dress on game day. Figure 3 shows us that injury prevalence -- or the percentage of players out with an injury or playing hurt -- increases substantially over the course of the season, which is exactly what we expected. It rises almost 80 percent from 13.1 percent in Week 1 to 23.4 percent in Week 17. It grows quickly from Week 1 to Week 3 as early-season injuries manifest, then slows a bit until about Week 9 before rising more quickly in the second half of the season. Taken in context with the flat risk of new injuries, this would suggest that injuries occurring later in the season tend to keep a player on the injury report longer than those earlier in the year. However, we have to be careful and remember that the denominators for risk and prevalence are quite different (almost 30 percent different by the end of the season), so we can't draw that conclusion. This, combined with the fact that many injuries (more than 40 percent) appear on injury reports for only one week, also explains why our measure of prevalence only rises 0.5 percent to 1.0 percent per week despite about 8 percent of players getting hurt in any given week.

Survivor Bias

We need to consider the possibility that the flat risk curve late in the season may be due in part to what epidemiologists term survivor bias or the survivor effect. Basically, by late in the season the players prone to any given type of injury will have already gotten hurt. The only players left at risk for a new injury are ironmen with excellent training regimens, good genes, and/or an actual Iron Man suit, and these players are going to have a lower baseline injury risk than those who have already been hurt.

The fact that we have a fixed population size -- all 32 teams need to field 53 players every week -- adds some additional wrinkles. Any time somebody is knocked out with an injury, someone else has to step up. That player could be a younger backup or an aging veteran who did not play a lot or at all earlier in the season. Although older players in particular might have a higher baseline injury risk (to be addressed in Part III of the series), the fact that all these replacements -- young or old -- are going to be fresher with less wear and tear on their bodies might still leave their baseline injury risk lower than that of the full group of starters in Week 1. At least that's my hypothesis, anyway.

All this could lead to an apparently reduced risk of injury in later weeks since the players still "at risk" for a given injury are different from the full cohort of players who began the season -- specifically, they have a lower baseline injury risk. If all the players from the start of the season were at risk for a given injury every week, the injury risk in later weeks would likely be higher than our data shows.

Injury Types by Week of Season

One shortcoming of Figure 3 is that it looks at all injuries together. Are there certain kinds of injuries -- perhaps soft tissue injuries such as hamstrings or groin pulls -- that actually do increase in frequency as the season drags on? I've selected a few candidate injuries to inspect in Figure 4.

Let's break this chart down:

Two of the injuries I would have suspected to have the strongest risk increases as the season drags on -- hamstring and groin injuries -- instead exhibit clear declines in risk as the season drags on. New hamstring and groin injuries drop by around 35 percent from their Week 4 peaks to Week 16 in remarkably similar patterns. This actually provides strong support for the survivor effect theory: the injuries most likely to be influenced by a player's personal susceptibility to injury exhibit some of the clearest declines.

in risk as the season drags on. New hamstring and groin injuries drop by around 35 percent from their Week 4 peaks to Week 16 in remarkably similar patterns. This actually provides strong support for the survivor effect theory: the injuries most likely to be influenced by a player's personal susceptibility to injury exhibit some of the clearest declines. Ankle sprains, which I would have expected to fall somewhere in the middle in terms of risk related to time, look to be about flat over the course of the season.

The same goes for ACL tears. What stands out to me about these, though, is the much higher ratio of Week 1 (i.e., offseason/training camp/preseason) tears to Week 2 tears. For ACLs it's more than 5:1 , while for hamstrings it's just 2:1. This could be due to a couple of things. First, some ACLs might be holdovers from a previous season (e.g., Todd Gurley and Sen'Derrick Marks). Second, ACLs are season-enders, while other injuries like hamstrings might happen in training camp but disappear by the regular season and not get counted in our data. I might try to look at ACLs in more detail later.

, while for hamstrings it's just 2:1. This could be due to a couple of things. First, some ACLs might be holdovers from a previous season (e.g., Todd Gurley and Sen'Derrick Marks). Second, ACLs are season-enders, while other injuries like hamstrings might happen in training camp but disappear by the regular season and not get counted in our data. I might try to look at ACLs in more detail later. I wanted to look at concussions because of their tremendous health importance and the amount of attention they have received in the media, and this is where things get alarming. Concussion risk clearly goes up over the course of the season, with a pretty clear inflection point around week 9.

So the take-home lesson of Figure 4 is that the risk of some injuries falls, while others stay flat or rise over the course of the season. Figure 3 is too simplistic, and answering the question of whether injury risk rises as the season drags on isn't a simple "yes" or "no." The answer is "it depends."

As an aside, the data looks virtually identical if you use the raw number of new injuries rather than injury risk as I've defined it here.

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18-Game Season

Is Figure 3 an endorsement of an 18-game season, then? Has the physical toll of eight more quarters of football been overblown? Not necessarily. Here are some counterpoints:

Probably most importantly, injuries are still occurring in the later weeks. Your cumulative risk of a groin injury is clearly higher if you play 16 games than if you play 10, even though the risk of a new injury in any given week doesn't rise as the season drags on (except, apparently, concussions). Two more games would still clearly result in more players getting hurt (at about the same rate they are getting hurt in Weeks 1-17, or higher for concussions). Taking the injury risk for Weeks 16 and 17 as a baseline, we should expect about 14.8 percent of remaining players to be hurt in two additional games. In Week 19 the prevalence would rise to roughly 24.5 percent of players being hurt, or about 27 more players on the injury report at the end of the year than if we kept a 16-game season.

of a groin injury is clearly higher if you play 16 games than if you play 10, even though the risk of a injury in any given week doesn't rise as the season drags on (except, apparently, concussions). Two more games would still clearly result in more players getting hurt (at about the same rate they are getting hurt in Weeks 1-17, or higher for concussions). Taking the injury risk for Weeks 16 and 17 as a baseline, we should expect about 14.8 percent of remaining players to be hurt in two additional games. In Week 19 the prevalence would rise to roughly 24.5 percent of players being hurt, or about 27 more players on the injury report at the end of the year than if we kept a 16-game season. Also importantly, Figures 3 and 4 only count players who get put on the injury report. They say nothing about the low-grade wear and tear that two additional games would put on players' bodies, potentially shortening careers and/or levying higher health care costs down the road.

Concussion risk increases over the course of a season, and head trauma is kind of important. If we added two more games onto the NFL schedule, the data suggests there will be a major toll to pay in concussions and brain trauma.

These charts also say nothing about how more games might further aggravate ongoing injuries.

I would not want Figures 3 and 4 used to advocate for an 18-game season. But it is interesting to see that our hypothesis about injury risk rising as the season grinds on doesn't hold for all kinds of injuries -- with the important caveat of the survivor effect.

Changes in NFL Injuries Over Calendar Time

You may know from reading FO's pieces on Adjusted Games Lost (AGL) that the number of AGL has been rising in recent years. However, as Scott Kacsmar and others have rightfully pointed out, AGL counts injuries to starters more heavily than those to reserves. Due to changing personnel groupings and game strategies, FO has tended to count more players as starters or important reserves in recent years, possibly driving AGL artificially upward. So let's ask two simpler questions: is the sheer number of injuries increasing? And to get at severity, is the number of weeks players are missing due to injury rising?

One note about Figure 5: you'll notice it begins in 2002 rather than 2000. This is because the last NFL expansion happened in 2002, and we only want to look at 32-team samples.

Let's break this chart down into its three constituent parts. First, the raw number of injuries (orange line) . There's a pretty clear -- and surprisingly steady -- upward trend in the number of reported injuries beginning in about 2007 and plateauing around 2012. The last two years have each shown small decreases in the number of injuries, but 2014 was still above 2011.

The blue line is the total weeks missed due to injury . Here we also see a general increase beginning in about 2007, but it's not as smooth as the raw number of injuries. In 2007 there is a sort of spike to a "new normal" for 2007 to 2009, and then another spike in 2010 followed by a drop for the 2011 and 2012 seasons before another rise in the last two seasons.

The green line is the average number of weeks missed per injury (blue divided by orange), and it tracks with the number of weeks missed pretty well (rising when blue rises, falling when blue falls). We can see a couple of periods where the green line is falling pretty steeply: 2007-2009 and 2010-2012. This could suggest a couple things:

Teams might have been growing more circumspect in reporting borderline or minor injuries. This may have been the case from 2007 to 2009, when the number of reported injuries increased substantially but the weeks missed dropped slightly.

On the other hand, this could also be explained by teams riding players harder and better medical treatments allowing more players to play through or recover faster from reported injuries than in the past, though this seems less likely to explain an acute change like we saw from 2007 to 2009.

Neither of these, however, explains the spike in severity in 2010 or the upswing that began again in 2013. More likely it's random noise or some problem with our data. It's impossible to say from this, unfortunately. This is actually a good example of a problem where coach or trainer intuition is an important complement to "analytics"; analytics can provide the chart, but it takes a knowledgeable football mind to interpret it properly.

Lockout Effects

One influential time point that stands out to me is the 2011 NFL lockout. Recall that this happened in the spring and summer of 2011, or prior to the 2011 season. The potential injury-relevant effects of the lockout are twofold: 1) before the 2011 season players probably got more rest than they would in a typical offseason, allowing for an interesting natural experiment of whether added rest aids players, and 2) from 2011 onward, the new collective bargaining agreement (CBA) installed new rules for fewer and less intense practices and more days off.

I'm going to focus on the number of weeks missed (blue line) in Figure 5 for two reasons: it's what's most relevant for teams and fans, and it controls for trends in injury reporting over time by ignoring minor injuries that don't result in time off the field. Between 2010 and 2011 there was a decline in overall weeks missed. The number of weeks missed in 2012 and 2013 remained lower than in 2010, but still elevated relative to 2009 and earlier. In 2014 we saw a spike to our worst season ever.

Perhaps most importantly, though, we can see clearly that injuries -- in both raw number and population damage -- have been on a long historical upward trend that began well before the new CBA, and there is little evidence to suggest the CBA substantially accelerated that trend.

So unfortunately, Figure 5 doesn't provide a clear answer about the lockout and new CBA's effects. In general the green line suggests that the new CBA's practice limitations might have bent the historical injury curve somewhat, but those effects have evaporated and more players are still missing more games than at any time before 2010. One thing the lockout did not appear to do, contrary to the ramblings of some coaches and analysts, is increase injuries because players "weren't prepared" for the season. It's more likely that the extra rest was helpful than harmful.

Concussions

Because I know someone will ask, here's a look at concussions over time in our data. A ton more work has been done on this by people smarter and more dedicated than me, and I could write a full article or two of this length on just concussion trends. This is merely a surface treatment.

Generally speaking, the number of reported concussions (orange line) rose sharply from 2007 until it peaked in 2012, then it tapered off the last two seasons. The increase from 2007 to 2012 likely reflects a couple of forces: a true increase in the number of concussions as players get bigger/stronger/faster, and diagnostic and reporting biases from better recognition and increasing pressure to report when a player "gets his bell rung."

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In the last three or so seasons, these trends have been countered by new concussion-reduction rules (the banning of spearing with the crown of the helmet, and moving kickoffs up); the increasing prevalence of concussion-resistant helmets and other gear; better and safer player techniques as awareness of the dangers of head trauma grows; and improved treatment through the NFL's concussion protocol. These downward trends seem to be winning, with substantial declines in concussions each of the last two years. Of course there is still lots of room for improvement, and this data says nothing about the repeated sub-concussive blows that have been linked to chronic traumatic encephalopathy (CTE), but the data suggests the NFL actually has turned the tide on increasing concussions. We can just hope this continues in 2015.

The number of weeks missed due to concussions (green line) is noisy, but in general tracks the red line fairly well with the exception of last season. I think the average weeks missed per concussion (blue line) is more instructive. Here there's quite a bit of variation, but since 2009 that number appears to have gone down before rebounding above 2009 levels last season. A drop in severity would be good insofar as it indicates better reporting of less severe concussions (thus dragging down the average), but bad insofar as it suggests players may not be being kept out as long as they need for a safe recovery (i.e., the new concussion protocols aren't working as intended). A rising average, meanwhile, would be good or bad for the opposite reasons. Here we've got dueling forces that call for their own post to tease out.

Next Steps and Comments

In next week's installment we'll look at how injuries have varied by player age and position. As always, comments welcome below!

Zach is a freelance injury analyst and a Ph.D. student in Epidemiology focusing on predictive modeling. He consults for an NFL team and loves Minor League Baseball. He lives in Atlanta.