Statistics and Injuries

Those of you who know me know that I am interested in mathematics and statistics and will occasionally look at them in order to prove a point or guide a discussion. In the e-world, many Giants fans have been pointing to the strength and conditioning program and how the many injuries that the Giants have had are entirely the fault of the S&C program not keeping up with modern training techniques. The flip side is the Coughlin perspective who said over and over again that the piling up of injuries is just bad luck. The truth probably lies somewhere in between - you certainly cannot blame every injury that occurred on a flawed S&C program. Football is a violent sport, with heavy collisions that put a medical and orthopedic strain on the body. No doubt injuries will occur no matter how well conditioned the athletes are. Having said that, there are certainly training programs that can limit or contain some of the injuries, especially those that are not direct result of collisions and are more muscular and soft tissue injuries. Last year, after Beatty tore his pectoral muscle while working in the weight room, Coughlin instituted some changes in the program. There were "spa days" or recovery days, they used GPS devices to track the number of hits and the force of the collisions that each player experienced during practice, but still the injuries continued. (Note: later Beatty tore the rotator cuff in his shoulder while rehabbing from his pectoral injury.) The changes that Coughlin instituted after the Beatty injury, I believe were effective in reducing injuries. But they didn't address the core problem - a strength and conditioning program that was mostly focused on the "strength" part of the program and not enough on the "conditioning" part. Core strength, balance, flexibility, long lean muscles, efficiency of movement and pure conditioning are more important than how much weight the player can lift. Strength is important, but not at the expense of conditioning. Better conditioning contributes not only to reduced injuries but also to more effective play on the field.

Now to my statistical analysis of why this injury bug just can't be luck. Football Outsiders tracks a statistic called adjusted games lost (AGL) for each team. The reason it is adjusted games lost and not just total games lost is that they adjust the number on basis of which player was lost. They value loss of a starter or regular rotation player more than a bench player, rendering the statistic a little more meaningful. The Giants finished last of all 32 teams in the league in this AGL statistic for the last 3 years, something that's very hard to do. But it's too easy to simply say, it's unlikely and that this could happen by chance without putting some hard measurements around it. Here goes.

I looked at the AGL statistics for the last two years, 2015 and 2014. I made the fairly safe assumption that the  AGL sample for each year was normally distributed. I then calculated the average and standard deviation for each year. The standard deviation is a measure for how widely spread the measurements are around the mean. For example, if a student's average score on two tests that he took is 80, he may have gotten 75 and 85 on his two tests or may have gotten scores of 100 and 60. In both cases the average is 80, but in the second case the standard deviation is greater because the scores are more widely spread around the mean. For a "normal distribution" 99.7% of all the possible measurements are within 3 standard deviations of the mean. In 2015 the Giants' AGL was more than 3 standard deviations away from the mean and in 2014 it was slightly less than that, about 2.59 standard deviations away. Using these statistics and the normal distribution, you can calculate the probability that a team will get a sample score less than (or greater than) a particular number.

OK ---- for those of you whose eyes are glazed over with these boring statistics, let me turn this into English. The probability that by pure chance a number would be less than or equal to the Giants AGL for year 2015 is 99.88%. The same probability for year 2014 is 99.5%.
Looking at it another way, the probability that a random score would be greater than the Giants for 2015 and 2014 are respectively: .119% and .482%

Putting these together - the probability that any team could do as badly as the Giants in both years together is .000574%

Understanding this better - that is 5.7 chances out of a million.
(With apologies to D&D, quoting Lloyd Christmas... " so you're saying there's a chance")

Looking at the second worst team in the two year period, the Washington Redskins were .38%

In other words, Giants were roughly 1,000 times worse than the second worst team in the league over the 2 year period.

Here's hoping the new S&C coach does a little better than the last one.