One of the big challenges when doing policy analysis in the healthcare industry is case mix comparisons. Making sure that one is looking at apples compared to similar apples can be an absolute bitch. We know that young, healthy people, on average are far cheaper to cover than 63 year olds with multiple metabolic conditions. So a program that mainly covers old people with serious chronic conditions that then expands to cover young and reasonably healthy people will have a much lower expenditure per person after expansion. The drop in average cost is not because the insurer suddenly found a great new way to cover people; the insurer just took on a way healthier population.
I was thinking about case mix composition this morning as I was reading through first a great statistical beatdown on Ballghazi from Deadspin, and then looking at Advanced Football Analytics take on the Patriots’ fumble rate:
Here are the offensive plays per fumble for each team in each season since 2010…NE ranks third over that period. Very good, but nothing out of the ordinary. You’d expect teams with good QBs and good offenses to have fewer strip-sacks….if we threw out that game, NE would have a 60 play-per-fumble rate…Hey WAS! What the hell? 37 plays between fumbles?
A commenter at Advanced Football Analytics makes the case mix composition argument:
That “what the hell, Washington” bit? From 2010-2014, Tom Brady fumbled 27 times at quarterback. The Redskins fumbled 68 times at quarterback. *SIXTY-EIGHT*. That’s almost the entire difference between the two teams….it’s not like Brady’s fumbling at some insanely low rate. Manning still fumbles less than he does.
Offensive fumbles can be categorized as three seperate groups. The first is completed pass play fumbles, the second is running play fumbles, and the last is quarterback fumbles during attempted passsing plays. These categories are a little messy as the Brady lateral to Edelman for the touchdown to Amendola would be categorized as a running play fumble, but they are very clear. Running play fumbles are the least probable with roughly one running play fumble per game. Successful passing play fumbles are more common at roughly two fumbles per game. These are low probability events, and yes the Patriots have low but not absurdly low rates of fumbling.
Quarterback fumbles during attempted passing plays are common. Good quarterbacks will fumble on roughly 25% of their sacks and bad quarterbacks will fumble on roughly 40% of their sacks. The Patriots case mix of potential fumbling situations is a function of the number of plays called, types of plays called, the number of sacks taken and the rate of fumbles on sacks taken.
What this all means is a team with an average quarterback that is sacked five fewer times than league average will, on average fumble two less times. And replacing those five sacks with three completions and two incompletions produces .03 successful pass play fumbles. It is an interaction effect of the offensive line giving up few sacks, the quarterback recognizing that a sack is imminent and going protective, and a bit of luck.
This is where there is an outlier. Brady’s sack fumble rate is roughly 20%. Brady is known as a cerebral quarterback, and any Patriots fan who watches the team for four or five games a season will be able to point out at least one if not more instances where Brady knows he is going to be sacked and he starts folding in on himself before the hit to protect himself and the ball. Steelers fans seldom have that experience of seeing Rothlesberger concede the sack. Instead he is looks for a big positive play at a higher risk of conceding a fumble. Jets fans see their quarterback fumble for the hell of it as the quarterback runs into the butt of an offensive lineman. Washington fans have the joy of seeing running quarterbacks and low experience quarterbacks try to play behind a bad offensive line.
The Patriots also just don’t give up a lot of sacks so if the Patriots had a league average offensive line at giving up sacks and a league average quarterback at fumbling on sacks, the Patriots would be slightly below league average on aggregrate fumble rate because their case mix would have changed.
Case mix matters, and it matters a lot when there are very distinct clusters of analysis for health insurance and football.