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Forgot I had this site bookmarked: http://www.advancednflstats.com
Here's an article about running back "overuse". I see that term thrown around by the mediots of the 4-letter and in general football conversations. It's a good read and interesting how a stats-proud website doctored things to create a buzz about something that doesn't really exist, The 370 Carries Per Season Barrier.
http://www.advancednflstats.com/2008/07/drunkards-light-posts-and-myth-of-370.html
ul 27, 2008
Drunkards, Light Posts, and the Myth of 370
.fullpost{display:inline;}
Running back overuse has been a hot topic in the NFL lately, partly because of Football Outsiders' promotion of their "Curse of 370" theory. In several articles in several outlets, including their annual Prospectus tome, they make the case that there is statistical proof that running backs suffer significant setbacks in the year following a season of very high carries. But a close examination reveals a different story. Is there really a curse of 370? Do running backs really suffer from overuse?
Football Outsiders says:
"A running back with 370 or more carries during the regular season will usually suffer either a major injury or a loss of effectiveness the following year, unless he is named Eric Dickerson.
Terrell Davis, Jamal Anderson, and Edgerrin James all blew out their knees. Earl Campbell, Jamal Lewis, and Eddie George went from legendary powerhouses to plodding, replacement-level players. Shaun Alexander struggled with foot injuries, and Curtis Martin had to retire. This is what happens when a running back is overworked to the point of having at least 370 carries during the regular season."While it's true that RBs with over 370 carries will probably suffer either an injury or a significant decline in performance the following year, the reason is not connected to overuse. What Football Outsiders calls the 'Curse of 370' is really due to:
In the 25 RB seasons consisting of 370 or more carries between the years of 1980 and 2005, several of the RBs suffered injuries the following year. Only 14 of the 25 returned to start 14 or more games the following season. In their high carry year (which I'll call "year Y") the RBs averaged 15.8 game appearances, and 15.8 games started. But in the following year ("year Y+1"), they averaged only 13.0 appearances and 12.2 starts. That must be significant, right?
The question is, significant compared to what? What if that's the normal expected injury rate for all starting RBs? If you think about it, to reach 370+ carries, a RB must be healthy all season. Even without any overuse effect, we would naturally expect to see an increase in injury rates in the following year.
In retrospect, comparing starts or appearances in such a year to any other would distort any evaluation. This is what's known in statistics as a selection bias, and in this case it could be very significant.
We can still perform a valid statistical analysis however. We just need to compare the 370+ carry RBs with a control group. The comparison group was all 31 RBs who had a season of 344-369 carries between 1980 and 2005. (The lower limit of 344 carries was chosen because it produced the same number of cases as the 370+ group as of 2004. Since then there have been several more which were included in this analysis.)
Fortunately there is a statistical test perfectly suited to comparing the observed differences between the two groups of RBs. Based on sample sizes, differences between means, and standard deviation within each sample, the t-test calculates the probability that any apparent differences between two samples are due to random chance. (A t-test results in a p-value which is the probability that the observed difference is just due to chance. A p-value below 0.05 is considered statistically significant while a high p-value indicates the difference is not meaningful.) The table below lists each group's average games, games started, and the resulting p-values in their high-carry year and subsequent year.
.nobrtable br {display: none} table {border-collapse: collapse; border-width: 1px 1px 1px 1px; border-style: solid; } th {padding: 3px} td {text-align: center; padding: 3px;} #logocell {padding: 0px 3px 0px 3px; } #colorcol {background-color:#ffffe0}
G Year YG Year Y+1GS Year YGS Year Y+1370+ Group15.813.015.812.2344-369 Group15.814.015.412.6P-Value0.620.68
The differences are neither statistically significant nor practically significant. In other words, even if the sample sizes were enlarged and the differences became significant, the difference in games started between the two groups of RBs is only 0.4 starts and 1.0 appearances. RBs with 370 or more carries do not suffer any significant increase in injuries in the following year when compared to other starting RBs.
Regression to the Mean
The 370+ carry group of RBs declined in yards per carry (YPC) by an average of 0.5 YPC compared to a decline of 0.2 YPC by the 344-369 group. This is an apparently statistically significant difference, but is it due to overuse?
Consider why a RB is asked to carry the ball over 370 times. It's fairly uncommon, so several factors are probably contributing simultaneously. First, the RB himself was having a career year. He was probably performing at his athletic peak, and coaches were wisely calling his number often. His offensive line was very healthy and stacked with top blockers. Next, his team as a whole, including the defense, was likely having a very good year. Being ahead at the end of games means that running is a very attractive option because there is no risk of interception and it burns time off the clock. Additionally, his team's passing game might not have been one of the best, making running that much more appealing. And lastly, opposing run defenses were likely weaker than average. Many, if not all of these factors may contribute to peak carries and peak yardage by a RB.
What are the chances that those factors would all conspire in consecutive years? Linemen come and go, or get injured. Opponents change. Defenses change. Circumstances change. Why would we expect a RB to sustain two consecutive years of outlier performance? The answer is we shouldn't. Running backs with very high YPC will get lots of carries, but the factors that helped produce his high YPC stats are not permanent, and are far more likely to decline than improve.
If I'm right, we should see a regression to the mean in YPC for all RBs with peak seasons, not just very-high-carry RBs. The higher the peak, the larger the decline the following year. And that's exactly what we see in the data.
The graph above plots RB YPC in the high-carry year against the subsequent change in YPC. The blue points are the high-carry group, and the yellow points are the very-high-carry group. Note that there is in fact a very strong tendency for high YPC RBs to decline the following year, regardless of whether a RB exceeded 370 carries.
Very-high-carry RBs tend to have very high YPC stats, and they naturally suffer bigger declines the following season. 370+ carry RBs decline so much the following year simply because they peaked so high. This phenomenon is purely expected and not caused by overuse.
Statistical Trickery
Why did Football Outsiders pick 370 as the cutoff? I'll show you why in a moment, but for now I'm going to illustrate a common statistical trick sometimes known as multiple endpoints by proving a statistically significant relationship between two completely unrelated things. I picked an NFL stat as obscure and random as I could think of--% of punts out of bounds (%OOB).
Let's say I want to show how alphabetical order is directly related to this stat. I'll call my theory the "Curse of A through C" because punters whose first names start with an A, B, or C tend to kick the ball out of bounds far more often than other punters. In 2007 the A - C punters averaged 15% of their kicks out of bounds compared to only 10% for D - Z punters. In fact, the relationship is statistically significant (at p=0.02) despite the small sample size. So alphabetical order is clearly related to punting out of bounds!
Actually, what I did was sort the list of punters in alphabetical order, and then scanned down the column of %OOB. I picked the spot on the list that was most favorable to my argument, then divided the sample there. This trick is called multiple endpoints because there are any number of places where I could draw the dividing line (endpoints), but chose the most favorable one after looking at the data. Football Outsiders used this very same trick, and I'll show exactly how and why.
The graph below plots the change in yards per carry (YPC) against the number of carries in each RB's high-carry year. You can read it to say, a RB who had X carries improved or declined by Y yards per carry the following year. The vertical line is at the 370 carry mark.
Note the cluster of RBs highlighted in the top ellipse with 368 or 369 carries. They improved the following year. Now note the cluster of RBs highlighted in the bottom ellipse. They had 370-373 carries and declined the next year.
If we moved the dividing line leftward to 368 then the very-high-carry group would improve significantly. And if we moved line rightward to 373, then the non-high carry group would decline. Either way, the relationship between high carries and decline in YPC disappears. There is one and only place to draw the dividing line and have the "Curse" appear to hold water.
To be fair to Football Outsiders, they have recently admitted there is nothing magical about 370. A RB isn't just fine at 369 carries, and then on his 370th his legs will fall off. But unfortunately, that's the only interpretation of the data that supports the overuse hypothesis. If you make it 371 or 369, the relationship between carries and decline crumbles. It's circular to say that 370 proves overuse is real, then claim that 370 is only shorthand for the proven effect of overuse. It's pretty clear from the graph above that they assumed overuse was real, then sought an analysis to support their claim.
As Mark Twain (reportedly) once said, "Beware of those who use statistics like a drunkard uses a light post, for support rather than illumination."
Here's an article about running back "overuse". I see that term thrown around by the mediots of the 4-letter and in general football conversations. It's a good read and interesting how a stats-proud website doctored things to create a buzz about something that doesn't really exist, The 370 Carries Per Season Barrier.
http://www.advancednflstats.com/2008/07/drunkards-light-posts-and-myth-of-370.html
ul 27, 2008
Drunkards, Light Posts, and the Myth of 370
.fullpost{display:inline;}
Running back overuse has been a hot topic in the NFL lately, partly because of Football Outsiders' promotion of their "Curse of 370" theory. In several articles in several outlets, including their annual Prospectus tome, they make the case that there is statistical proof that running backs suffer significant setbacks in the year following a season of very high carries. But a close examination reveals a different story. Is there really a curse of 370? Do running backs really suffer from overuse?Football Outsiders says:
"A running back with 370 or more carries during the regular season will usually suffer either a major injury or a loss of effectiveness the following year, unless he is named Eric Dickerson.
Terrell Davis, Jamal Anderson, and Edgerrin James all blew out their knees. Earl Campbell, Jamal Lewis, and Eddie George went from legendary powerhouses to plodding, replacement-level players. Shaun Alexander struggled with foot injuries, and Curtis Martin had to retire. This is what happens when a running back is overworked to the point of having at least 370 carries during the regular season."While it's true that RBs with over 370 carries will probably suffer either an injury or a significant decline in performance the following year, the reason is not connected to overuse. What Football Outsiders calls the 'Curse of 370' is really due to:
- Normal RB injury rates
- Natural regression to the mean
- A statistical trick known as multiple endpoints
- (And this should go without saying, but the "unless he is named Eric Dickerson" constraint is silliness.)
In the 25 RB seasons consisting of 370 or more carries between the years of 1980 and 2005, several of the RBs suffered injuries the following year. Only 14 of the 25 returned to start 14 or more games the following season. In their high carry year (which I'll call "year Y") the RBs averaged 15.8 game appearances, and 15.8 games started. But in the following year ("year Y+1"), they averaged only 13.0 appearances and 12.2 starts. That must be significant, right?
The question is, significant compared to what? What if that's the normal expected injury rate for all starting RBs? If you think about it, to reach 370+ carries, a RB must be healthy all season. Even without any overuse effect, we would naturally expect to see an increase in injury rates in the following year.
In retrospect, comparing starts or appearances in such a year to any other would distort any evaluation. This is what's known in statistics as a selection bias, and in this case it could be very significant.
We can still perform a valid statistical analysis however. We just need to compare the 370+ carry RBs with a control group. The comparison group was all 31 RBs who had a season of 344-369 carries between 1980 and 2005. (The lower limit of 344 carries was chosen because it produced the same number of cases as the 370+ group as of 2004. Since then there have been several more which were included in this analysis.)
Fortunately there is a statistical test perfectly suited to comparing the observed differences between the two groups of RBs. Based on sample sizes, differences between means, and standard deviation within each sample, the t-test calculates the probability that any apparent differences between two samples are due to random chance. (A t-test results in a p-value which is the probability that the observed difference is just due to chance. A p-value below 0.05 is considered statistically significant while a high p-value indicates the difference is not meaningful.) The table below lists each group's average games, games started, and the resulting p-values in their high-carry year and subsequent year.
.nobrtable br {display: none} table {border-collapse: collapse; border-width: 1px 1px 1px 1px; border-style: solid; } th {padding: 3px} td {text-align: center; padding: 3px;} #logocell {padding: 0px 3px 0px 3px; } #colorcol {background-color:#ffffe0}
Comparison of Games Played and Started for High-Carry RBs
G Year YG Year Y+1GS Year YGS Year Y+1370+ Group15.813.015.812.2344-369 Group15.814.015.412.6P-Value0.620.68
The differences are neither statistically significant nor practically significant. In other words, even if the sample sizes were enlarged and the differences became significant, the difference in games started between the two groups of RBs is only 0.4 starts and 1.0 appearances. RBs with 370 or more carries do not suffer any significant increase in injuries in the following year when compared to other starting RBs.
Regression to the Mean
The 370+ carry group of RBs declined in yards per carry (YPC) by an average of 0.5 YPC compared to a decline of 0.2 YPC by the 344-369 group. This is an apparently statistically significant difference, but is it due to overuse?
Consider why a RB is asked to carry the ball over 370 times. It's fairly uncommon, so several factors are probably contributing simultaneously. First, the RB himself was having a career year. He was probably performing at his athletic peak, and coaches were wisely calling his number often. His offensive line was very healthy and stacked with top blockers. Next, his team as a whole, including the defense, was likely having a very good year. Being ahead at the end of games means that running is a very attractive option because there is no risk of interception and it burns time off the clock. Additionally, his team's passing game might not have been one of the best, making running that much more appealing. And lastly, opposing run defenses were likely weaker than average. Many, if not all of these factors may contribute to peak carries and peak yardage by a RB.
What are the chances that those factors would all conspire in consecutive years? Linemen come and go, or get injured. Opponents change. Defenses change. Circumstances change. Why would we expect a RB to sustain two consecutive years of outlier performance? The answer is we shouldn't. Running backs with very high YPC will get lots of carries, but the factors that helped produce his high YPC stats are not permanent, and are far more likely to decline than improve.
If I'm right, we should see a regression to the mean in YPC for all RBs with peak seasons, not just very-high-carry RBs. The higher the peak, the larger the decline the following year. And that's exactly what we see in the data.
The graph above plots RB YPC in the high-carry year against the subsequent change in YPC. The blue points are the high-carry group, and the yellow points are the very-high-carry group. Note that there is in fact a very strong tendency for high YPC RBs to decline the following year, regardless of whether a RB exceeded 370 carries.
Very-high-carry RBs tend to have very high YPC stats, and they naturally suffer bigger declines the following season. 370+ carry RBs decline so much the following year simply because they peaked so high. This phenomenon is purely expected and not caused by overuse.
Statistical Trickery
Why did Football Outsiders pick 370 as the cutoff? I'll show you why in a moment, but for now I'm going to illustrate a common statistical trick sometimes known as multiple endpoints by proving a statistically significant relationship between two completely unrelated things. I picked an NFL stat as obscure and random as I could think of--% of punts out of bounds (%OOB).
Let's say I want to show how alphabetical order is directly related to this stat. I'll call my theory the "Curse of A through C" because punters whose first names start with an A, B, or C tend to kick the ball out of bounds far more often than other punters. In 2007 the A - C punters averaged 15% of their kicks out of bounds compared to only 10% for D - Z punters. In fact, the relationship is statistically significant (at p=0.02) despite the small sample size. So alphabetical order is clearly related to punting out of bounds!
Actually, what I did was sort the list of punters in alphabetical order, and then scanned down the column of %OOB. I picked the spot on the list that was most favorable to my argument, then divided the sample there. This trick is called multiple endpoints because there are any number of places where I could draw the dividing line (endpoints), but chose the most favorable one after looking at the data. Football Outsiders used this very same trick, and I'll show exactly how and why.
The graph below plots the change in yards per carry (YPC) against the number of carries in each RB's high-carry year. You can read it to say, a RB who had X carries improved or declined by Y yards per carry the following year. The vertical line is at the 370 carry mark.
Note the cluster of RBs highlighted in the top ellipse with 368 or 369 carries. They improved the following year. Now note the cluster of RBs highlighted in the bottom ellipse. They had 370-373 carries and declined the next year.
If we moved the dividing line leftward to 368 then the very-high-carry group would improve significantly. And if we moved line rightward to 373, then the non-high carry group would decline. Either way, the relationship between high carries and decline in YPC disappears. There is one and only place to draw the dividing line and have the "Curse" appear to hold water.
To be fair to Football Outsiders, they have recently admitted there is nothing magical about 370. A RB isn't just fine at 369 carries, and then on his 370th his legs will fall off. But unfortunately, that's the only interpretation of the data that supports the overuse hypothesis. If you make it 371 or 369, the relationship between carries and decline crumbles. It's circular to say that 370 proves overuse is real, then claim that 370 is only shorthand for the proven effect of overuse. It's pretty clear from the graph above that they assumed overuse was real, then sought an analysis to support their claim.
As Mark Twain (reportedly) once said, "Beware of those who use statistics like a drunkard uses a light post, for support rather than illumination."
