Injury Mod Theory

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Drizzt_13
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Injury Mod Theory

Postby Drizzt_13 » Mon Feb 25, 2013 4:10 am

Just doing some quick research on the odds of a player being injured and found a frankly awesome study by the NFLPA on a lot of different aspects of injury which makes the theory fairly easy. With that data it seems fairly doable to calculate the probability of injury per player per game by each position, modify it by playing time and injury rating.

League wide players have a 5.1% chance of getting injured per game and a 1%. Only 38.4% of injuries cause a player to miss time and 9.9% of injuries cause placement on the IR. 63.3% of injuries take place during games (both preseason and practice), 16.1% of injuries take place during training camp and 19.2% take place during practice. We have positional rates for total injuries but obviously in game total injuries will be effected by the number of players on the field, this means we have to come up with numbers for how often teams use certain defensive and offensive sets in the actual NFL. While obviously this will differ for each team Pro Football Focus has data on the total amount of snaps teams spend in each defensive package from 2008-2011.

I crunched some numbers and over the past 4 years (leaving out outliers like the 4-6 defense or psycho packages) on the average NFL snap there were 3.45 DL, 2.95 LB and 4.58 DB on the average NFL defensive snap. On the average offensive play I'm just assuming 1 QB and 5OL but based off of Football outsiders 2012 snap information I find an average of 2.39 WR's 1.38TE's .98 RB's and .22 FB's (wow that position is dead). I then divided the total number of injuries for each position by often they are on the field (e.g. according to the NFLPA LB's account for 13.3% of injuries league wide so I divided that by 2.95). I then averaged all these numbers and compared each individual number to the average. This tells us how many more injuries a position accounts for than we would expect it to account for. I will call the number generated the positional constant and the results are as follows

QB: 67.31%
HB+FB: 184.81%
WR: 102.95%
TE: 96.99%
OL: 62.83%
DL:110.56%
LB: 91.27%
DB: 83.28%
(side note I think there is a fairly small error in the math for this that I haven't caught yet but will try to find later).


Now we have to modify by reserves vs. starters. Fascinatingly according to the NFLPA data reserves actually account for more injuries (in some categories) than starters, those numbers aren't adjusted for the fact that there are more reserve players than starters (50% more actually). I've included the adjusted numbers below.

New Appearances on injury list per team per week per player: Starter.077 Reserve .046
New injuries causing missed games per team per week per player: Starter .027 Reserve .019
New Appearances on the injured reserve list per team per week per player: Starter .0055 Reserve.0061

So this tells us that while starters are more likely to get banged up reserve players are more likely to sustain season ending injuries. Now obviously we can't just label some players starters and some players reserve because then there is no incentive to sit starters to avoid injuries. We need a number that relates playtime to injury probability. I'm going to call this variable simply, playtime. Playtime will be the ratio between how many snaps a player actually played and how many snaps we would expect an average player at that position to play. We can do this either by just assuming based on Depth chart position (e.g. CB3 most likely played 40% of the teams defensive snaps), or deriving based on statistics (CB 3 has 3 tackles and 2 catches allowed we plug that into a formula and find out he played 23 snaps). The average starters playtime should be 1.252 and the average reserve should be .747. While it would seem simpler to just set one as the constant for the average snaps played by a starter, this would cause us to have to introduce an additional constant so it is simpler to do it this way.

In the final overall formula the players odds of coming up injured are: (The league average 6.1%)*(Positional constant)*(Playtime)*((INJ-100)/-X)

X is a value that I would prefer to keep in the calibration files as it determines how strongly injury rating effects the odds of injury. If it is 100 then a player with 0 injury is only twice as likely to be injured as a player with 50 injury. Set it to 4 and they are 25 times more likely to be injured. I'd prefer to leave it open for tweaking.

Feedback would be appreciated though I understand some of this may be unclear. I'm also going to continue working to develop theory for things like what happens after we determine a player has been injured (e.g. how bad of an injury is it, where were they injured, will this make them more likely to injured in the future?) and a more definite equations for the playtime variable.




Information Used
http://www.footballoutsiders.com/stats/snapcounts2012
http://www.esquire.com/cm/esquire/data/ ... squire.pdf

Injury Mod Theory

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DarthViper3k
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Re: Injury Mod Theory

Postby DarthViper3k » Mon Feb 25, 2013 4:23 am

I think I remember reading that the NFLPA also had statistics on how often each injury type appears. It's at least been a year since I've heard mention of it but I think I can dig it up. I can't remember if the data was sorted by position or not (Like QBs more likely to suffer shoulder injuries and HBs more likely to suffer knee injuries and so on).

I might be able to dig it up... not sure.

Drizzt_13
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Re: Injury Mod Theory

Postby Drizzt_13 » Mon Feb 25, 2013 10:06 am

Yeah the "Dangers of the Game" Report lists the body location percentages. It also tells us what percent of injuries are classified as "minor" "major" or "moderate". It does include a fairly detailed breakdown of what specific injuries are what percentage of the leagues total (e.g.Tricep Staris are .04% of total injuries) but unhelpfully classifies a full 45% of injuries as "other". It doesn't have body area information broken down by position but it does tell us what percentage of injures are "major" and what percentage are brain trauma for each position. If you had some other report that had body area broken down by position that would be greatly appreciated.

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DarthViper3k
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Re: Injury Mod Theory

Postby DarthViper3k » Mon Feb 25, 2013 1:55 pm

Hmm... it sounds like we may have the same study.
I remember reading that certain position were more prone to certain injuries but I don't remember how in-depth it was regarding statistics.

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Re: Injury Mod Theory

Postby DrBrownsFan » Mon Feb 25, 2013 7:21 pm

Wow... This is like calculus to understand, but it is really quite brilliant. Drizzt_13, the formula seems like it would do exactly what you want it to do. Personally I would set X pretty low, as I think that the INJ rating should encompass a pretty wide range, so if a player seems to get injured every other snap in real life, he would get injured nearly as often with a 0 INJ rating in the game, but a player who rarely gets injured would still rarely get injured with a 99 INJ rating. I love what you are doing here Drizzt_13, keep up the excellent work!
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Drizzt_13
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Re: Injury Mod Theory

Postby Drizzt_13 » Thu Mar 07, 2013 10:00 pm

So I've been trying to come up with a way to figure out playtime since snaps played is not a stat madden tracks and I've had very little sucess. While this will obviously be very easy for positions like QB and HB as well as #1 WR's this is significantly harder for defensive positions and offensive positions that aren't always on the field. What I did was take a league with my normal sliders and the FFXI roster, tweaked the settings so that injuries and substitutions never occur, and then looked for correlations between snaps played and various stats. Because I knew there were never any injures or substitutions I can know for a fact that any differences occur only because of different formations used. Also because I went through each game log and added up the individual rushing and passing attempts I know exactly how many rushing or passing snaps each defense played. I'm going to lay out my results starting with the defensive side of the ball.

If you take a way players with less than 10 tackles on the season (often times OL and WR's had around 10 tackles which is bizzare) each team has only their starting players plus the backup SS and the nickel (#3) corner. There were some exceptions to this, one team had a third DT, another had a backup FS and not every team sent a backup SS. This is interesting because it suggests that the Simulation engine doesn't use formations that involve #4 and #5 corners and often uses ones that contain a backup SS. It is also possible that backup SS's end up getting a lot of special team tackles for some reason.

So Ideally we want to take a stat and correlate it with snaps, but since all players are not created equal we also want to correlate it with their ratings. I basically took a stat divided it by the relevant number of snaps and then used excel to fit a graph where OVR was the X axis and Stat/snaps was the Y axis. The R^2 Values (a number from 0-1 where 1 means it fits the data perfectly and 0 means it doesn't fit at all) for various stats and positions will be listed below.

Defensive Ends:
ALL 4-3 DE
y=Tackle/Run Snap x=ovr r^2=.276
y=Sack/Pass Snap x=ovr r^2=.193

4-3 LE
y=Tackle/Run Snap x=ovr r^2=.390
y=Sack/Pass Snap x=ovr r^2=.044

4-3 RE
y=Tackle/Run Snap x=ovr r^2=.219
y=Sack/Pass Snap x=ovr r^2=.457
y=Sack x=ovr r^2=.477

3-4 DE
y=Tackle x=ovr r^2=.747
y=Tackle/Run Snap x=ovr r^2=.753
y=Sack/Pass Snap x=ovr r^2=.419

Sacks and tackles are about the only relevant stats to these positions as in the same engine there were so few recorded tackles for loss, forced fumbles, interceptions and deflections that they did not produce an overall trend. As you can see 3-4 DE stats correlate the best with OVR while other positions generally have a weak corellation, though 4-3 RE's have the next strongest with Tackles.


Defensive Tackles
4-3 DT's
y=Tackle/Run Snap x=ovr r^2=.135
y=Tackle/Total Snaps x=ovr r^2=.1.51
y=Sack/Pass Snap x=ovr r^2=.016

3-4 DT's
y=Tackle/Run Snap x=ovr r^2=.242

Neither of these correlate very well. I tried dividing them into #1 and #2 4-3 Dt's but it didn't really make a difference. While I believe the small sample size has something to do with it especiallly for 3-4 DT's I don't believe we would see a strong increase in the r^2 value.

Middle Linebackers

All MLB's
y=Tackle/Run Snap x=ovr r^2=.427
y=Sack/Pass Snap x=ovr r^2=.101

3-4 MLB's
y=Tackle/Run Snap x=ovr r^2=.541
If you remove the worst MLB who had a OVR 10 points lower than any other starter r^2 becomes .733. Just looking at the graph it is evident that the trend works very well from about 75-95 but not so much at the very top and very bottom.
y=Sack/Pass Snap x=ovr r^2=.494
If you remove the two biggest outliers this jumps to .764, meaning it functions pretty well for the guys in the middle.

4-3 MLB's
y=Tackle/Run Snap x=ovr r^2=.344
w/out biggest outlier .499
y=Tackle/Snap x=ovr r^2=.419
w/out biggest outlier .542
y=Catches allowed/Passing Snap x=ovr r^2=.19

Sacks and Pass Deflections barely correlate at all with OVR. So as you can see we have a fairly good correlation for 3-4 MLB and so so correlations for 4-3 MLB's

Outside Line Backers

3-4 OLB
y=Tackle/Run Snap x=ovr r^2=.484
y=Tackle/Snap x=ovr r^2=.444
y=Sack/Snap x=ovr r^2=.161

4-3 OLB
y=Tackle/Run Snap x=ovr r^2=.227
y=Tackle/Snap x=ovr r^2=.220

I tried a lot of other things like deflections or catches allowed but they barely correlated at all. As you can see predicting 4-3 OLB based on anything is going to be pretty hard and even 3-4 isn't all that great.

I've decided to stop at the front 7 for this post and get to the secondary and offense later. What I've concluded from this is that predicting snaps off of player stats for the defensive side of the ball would be very inaccurate. I haven't quite checked how inaccurate yet but seeing as the number of snaps played tends to fall into a pretty small range on a per game level I think it would be a poor way to calculate snaps.

That doesn't mean the time I've pored into turning .txt files into spreadsheets has gone to waste. While the formulas I've produced have all been far too inaccurate for calculating snaps I think they will be effective as part of the stat based evaluation teams use when determining the value of a free agent. I was already planning on using an average of the players actual OVR and an OVR based on the stats they put up to simulate the errors teams make when they judge players. This is giving me a lot of formulas for those stat based OVR's and information about how accurate those formulas are. I'm going to continue writing about it partly to keep momentum up and talk to you guys and also just to think aloud for myself as I keep analyzing this data.

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DarthViper3k
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Re: Injury Mod Theory

Postby DarthViper3k » Fri Mar 08, 2013 3:17 am

While I know you're trying to reproduce the injury data provided by the NFLPA... I think that perhaps there is a more efficient angle to approach these equations.
Simply saying that we can't track snaps... but we can track how many times a player was involved in a play.
I came to this thinking because with the equations you're working on... if you get into the DB's you're going to have a problem with determining if a particular DB was involved in any given play. For example... its zone coverage... CB#1 has WR#1 covered so well that the QB throws to WR#2. CB#1 didn't get physical enough with anybody to even get hurt... no stat for that to even account for if they're on the field or not. Players are more likely to get hurt when they're involved in the play.

Basically what I'm saying instead of trying to reverse engineer Madden NFL stats to write equations that can fit the data provided by the NFLPA... might it be easier to reverse engineer NFL stats against the NFLPA data... find the correlation there to injuries per stat.. or play-involvement.. and try and write equations based off of that that work with how Madden functions?

I'm suggesting that as the NFL tracks far more information than Madden can ever dream of.

So.. find the correlation of NFLPA snap based data with NFL play-involvement stats (ie, tackle, pass deflection, .. stats Madden has available) and I think you'll find a far easier and still accurate means of reproducing the data provided by the NFLPA.

Even better is I think the data you've come up with so far gives you a knowledge base.. and starting point to work off of so you know enough about how madden works that when you're trying to find the correlation of data I'm talking about... you're probably much better prepared to find said correlation than you would have otherwise have been.

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Re: Injury Mod Theory

Postby petroleum » Fri Mar 08, 2013 5:09 pm

Drizzt_13 wrote:If you take a way players with less than 10 tackles on the season (often times OL and WR's had around 10 tackles which is bizzare)
I think this may have to do with turnovers (someone needs to make the tackle after a fumble/interception), but special teams may also play a part, at least with the long snapper being an OL.
Drizzt_13 wrote:each team has only their starting players plus the backup SS and the nickel (#3) corner. There were some exceptions to this, one team had a third DT, another had a backup FS and not every team sent a backup SS. This is interesting because it suggests that the Simulation engine doesn't use formations that involve #4 and #5 corners and often uses ones that contain a backup SS. It is also possible that backup SS's end up getting a lot of special team tackles for some reason.

I've noticed this anecdotally. It brings up an interesting problem for optimizing rosters for Madden use, as opposed to having them reflect actual NFL rosters. Barring injury, #4 CB is basically worthless, while the #2 SS has unexpected value--sometimes it appears to have more valuable than the #3 CB.


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