Sunday, February 1, 2015

2015.2: Did the New England Patriots experience a decrease in fumbles starting in 2007?

Here's a timely guest entry from Jeffrey Witmer (Oberlin College).

As the “Deflate Gate” saga was unfolding, Warren Sharp analyzed “touches per fumble” for NFL teams before and after 2006, when a rule was changed so that teams playing on the road could provide their own footballs ( Sharp noted that, for whatever reason, the Patriots went from being a typical team, as regards fumbling, to a team with a very low fumble rate. Rather than rely on the data the Sharp provides at his website, I choose to collect and analyze some data on my own. I took a random sample of 30 games played by New England and 30 other games. For each game, I recorded all rushing and passing plays (except for QB kneels), but excluded kicking plays (the NFL, rather than the teams, provides special footballs for those plays). (Data source: I also recorded the weather for the game. (Data source: Once I had the data (in a file that I called AllBig, which can be downloaded from, I noted whether or not there was a fumble on each play, aided by the grep() command:
grep("Fumb", AllBig$Detail,
I labeled each play as Late or not according to whether it happened after the rule change:
AllBig$Late <- ifelse(AllBig$Year > 2006, 1, 0)
Now for the analysis. My data set has 7558 plays including 145 fumbles (1.9%). I used the mosaic package and the tally() command to see how often teams other than the Patriots fumble:
tally(~Fumble+Late, data=filter(AllBig,Pats==0))  
Fumble     0    1      
 0      2588 2919      
 1        54   65
Then I asked for the data in proportion terms:
tally(Fumble~Late, data=filter(AllBig,Pats==0))
and got
Fumble       0      1      
 0      0.9796 0.9782      
 1      0.0204 0.0218
For non-Pats there is a tiny increase in fumbles. This can be displayed graphically using a mosaiplot (though it's not a particularly compelling figure). mosaicplot(Fumble~Late, data=filter(AllBig,Pats==0)) Repeating this for the Patriots shows a different picture:
tally(~Fumble+Late, data=filter(AllBig,Pats==1))       
Fumble   0   1      
 0     996 910      
 1      19   7

tally(Fumble~Late, data=filter(AllBig,Pats==1))       
Fumble       0       1      
 0     0.98128 0.99237      
 1     0.01872 0.00763
I fit a logistic regression model with the glm() command: glm(Fumble~Late*Pats, family=binomial, data=AllBig)
  Estimate Std. Error z value Pr(>|z|)     
(Intercept)  -3.8697     0.1375  -28.14   <2e-16 *** 
Late          0.0650     0.1861    0.35    0.727     
Pats         -0.0897     0.2693   -0.33    0.739     
Late:Pats    -0.9733     0.4819   -2.02    0.043 *  
I wanted to control for any weather effect, so I coded the weather as Bad if it was raining or snowing and good if not. This led to a model that includes BadWeather and Temperature – which turn out not to make much of a difference:
AllBig$BadWeather <- ifelse(AllBig$Weather %in% c("drizzle","rain","snow"), 1, 0)

glm(formula = Fumble ~ BadWeather + Temp + Late * Pats, 
  family = binomial, data = AllBig)

               Estimate Std. Error z value Pr(>|z|)     
(Intercept) -4.23344    0.43164   -9.81   <2e-16 *** 
BadWeather   0.33259    0.29483    1.13     0.26     
Temp         0.00512    0.00612    0.84     0.40     
Late         0.08871    0.18750    0.47     0.64     
Pats        -0.14183    0.27536   -0.52     0.61     
Late:Pats   -0.91062    0.48481   -1.88     0.06 .  
Because there was suspicion that something changed starting in 2007 I added a three-way interaction:
glm(formula = Fumble ~ BadWeather + Temp + IsAway * Late * Pats,
  family = binomial, data = AllBig)

                    Estimate Std. Error z value Pr(>|z|)     
(Intercept)      -4.51110    0.47707   -9.46   <2e-16 *** 
BadWeather        0.34207    0.30013    1.14    0.254     
Temp              0.00831    0.00653    1.27    0.203     
IsAway            0.14791    0.27549    0.54    0.591     
Late              0.13111    0.26411    0.50    0.620     
Pats             -0.80019    0.54360   -1.47    0.141     
IsAway:Late      -0.07348    0.37463   -0.20    0.845     
IsAway:Pats       0.94335    0.63180    1.49    0.135     
Late:Pats         0.51536    0.71379    0.72    0.470     
IsAway:Late:Pats -3.14345    1.29480   -2.43    0.015 *  
There is some evidence here that the Patriots fumble less than the rest of the NFL and that things changed in 2007. The p-values above are based on asymptotic normality, but there is a cleaner and easier way to think about the Patriots’ fumble rate. I wrote a short simulation that mimics something I do in my statistics classes, where I use a physical deck of cards to show what each step in the R simulation is doing.
#Simulation of deflategate data null hypothesis
Late = rep(1,72)  #creates 72 late fumbles
Early = rep(0,73)   #creates 73 early fumbles
alldata = append(Late,Early)   #puts the two groups together
table(alldata)  #check to see that we have what we want

cards =1:length(alldata)  # creates 145 cards, one "ID number" per fumble

FumbleLate = NULL  # initializes a vector to hold the results
for (i in 1:10000){# starts a loop that will be executed 10,000 times
  cardsgroup1 = sample(cards,119, replace=FALSE) # takes a sample of 119 cards
  cardsgroup2 = cards[-cardsgroup1]  # puts the remaining cards in group 2
  NEPats = (alldata[cardsgroup2])  #reads the values of the cards in group 2
  FumbleLate[i] = sum(NEPats)  # counts NEPats late fumbles (the only stat we need)

table(FumbleLate) #look at the results
hist(FumbleLate, breaks=seq(2.5,23.5)) #graph the results

sum(FumbleLate <= 7)/10000 # How rare is 7 (or fewer)? Answer: around 0.0086
Additional note: kudos to Steve Taylor for the following graphical depiction of the interaction.

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