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.
Richard Mayhew
And yes, I spend a good fifteen minutes trying to come up with a title that combined Balls on the Ground and Sacks… no luck there
OzarkHillbilly
@Richard Mayhew: I’ll give you an “A” for effort.
Baud
One thing has become clear over the last few days: Testicles and their euphemistic synonyms make any subject understandable and interesting.
MomSense
@Baud:
My 11 year old has loved this. He was giggling like crazy when we saw a clip of Belichick talking about rubbing balls.
rikyrah
I love seeing your name in posts. Learn something always.
JPL
@MomSense: One can wonders about The Gronk but that sounds painful.
Mike E
@Richard Mayhew: Robert Kraft will be demanding an apology in 5, 4, 3…
Robert
Hmmm…It seems the older I get, the closer my ball sack gets to the ground…TMI?
Ecks
@Richard Mayhew: “Does the firmness of your balls matter, or is it how they sit in the sack?”
dmsilev
(from nytimes.com/2015/01/28/sports/football/nfl-investigator-seeks-to-consult-columbia-physicist-over-pat… )
OzarkHillbilly
@Robert: That’s nothing. I’m a caver*** and my balls are regularly in the ground.
***or used to be, age and decrepitude have accomplished what good sense never could.
Xboxershorts
@dmsilev:
And lets morph into fart jokes next!
Amir Khalid
@OzarkHillbilly:
I suppose if you were a climber, you’d regularly have your balls to the wall.
cervantes
Actually the butt fumble was not exactly as you describe it. Patriots nose guard Vince Wilfork forklifted the Jets guard and used his derriere as a battering ram with which to dislodge the ball.
And it’s high school physics that if you measure the air pressure of footballs in a 75 degree locker room and then again at halftime outside where it’s 38 degrees, the pressure will be lower on the second measurement. It happens, obviously, in every cold weather game, they just never bothered to check before. The colts balls were within the range of the rules because they started near the top. The patriots started near the bottom. The whole thing is idiotic.
dmsilev
@Xboxershorts: That’s really more the purview of the chemistry department.
Francis
@cervantes: But the weight won’t change. Which is why the league uses scales, not pressure gauges.
maybe not everyone’s an idiot after all.
marduk
@dmsilev: Unreal. The week + of leaks smearing the Patriots and they’re just now wondering if maybe there wasn’t anyone cheating after all. Maybe you should have considered that first?
What a clown show Goodell is running. It’s amazing he still has a job.
dmsilev
@cervantes: Yeah, this. You’re talking about a ~8 percent change in absolute pressure when going from a nice warm room to freezing outside. Say the nominal pressure is about 14 psi gage (relative to atmospheric pressure), or about 29 psi absolute (relative to a hard vacuum). So, an 8 percent drop in absolute pressure is about 2 psi, yielding a gage pressure of a cold ball of 12 psi.
marduk
@Francis: This is just false. The league uses a pressure gauge to measure the pressure (duh). The weight of the air involved in 2psi of pressure is negligible. The humidity of the outside air will change the weight of the ball more.
OzarkHillbilly
@Amir Khalid: And if I were a fireman I’d have GREAT BALLS ON FIRE!!!!
SRW1
@Xboxershorts:
NE fires ball boy because he passed gas.
YOU ASKED FOR IT!
JPL
Ball, ball, ball. This ball talk is going to spoil the fun at every super bowl party.
lol
Amir Khalid
@OzarkHillbilly:
Goodness gracious!
cervantes
@Francis: They calibrate the weight for the ambient temperature? Where did you hear that? In any case, that means the pressure will vary depending on the temperature. If they wanted a constant pressure, they should check the pressure on the field just before the kickoff. But they don’t.
Also, is the weight of the balls (without air) always exactly the same? Since they are made of leather, which is a variable material, that would seem to be impossible.
JPL
@SRW1: haha
low-tech cyclist
@OzarkHillbilly:
Yeah, I guess I’m a used-to-be caver too. When I was cleaning out the shed this past fall, I was looking at my helmets and (carbide!) lamps stored there and thinking, “when the heck did I last use any of these?”
What happened to me was that my caving buddies gradually moved out of the area, and I’ve never been enough of a fool to go caving solo. I’m sure my body could still handle caving, but I expect I’d need more time to recover afterwards.
OzarkHillbilly
Marshawn Lynch only showed up at the SB Media day “so I won’t get fined.” and you can quote him on that!
MomSense
@JPL:
Stop rubbing your balls or you’ll get the Gronk!
cervantes
@marduk: You’re right and Francis is wrong. They use a pressure gauge. (You have to suffer through a double check commercial to see the video.)
Also, game time temp was 50 degrees but it was much colder by halftime.
Ecks
@cervantes: The pressure will drop with temperature, sure. But that’s only half the question. The part you assumed away is HOW MUCh the pressure will drop.
OzarkHillbilly
@low-tech cyclist: If you are interested look for a Grotto near you. I belong to 2, MVG in STL and the MOLES in Arkansas. Both groups do a lot more than just caving.
SRW1
@Ecks:
pV=nRT
marduk
@Ecks: It’s about 1.9 PSI.
dmsilev
@Ecks: See calculation above. It’s a couple of psi.
MattR
The biggest things that jumps out at me about his whole thing are that the NFL not only gives teams so much flexibility with regards to the balls they use (when they are so anal about every other little thing down to sock color) but that they test the balls “legality” under conditions that vary significantly from those expected at game time. (Obviously, the temperature will change during a game, but you would think the testing would be done after the balls were left in a similar temperature, or perhaps a bit cooler to account for a projected drop during the game, for a decent amount of time to let them adjust)
Ian
There’s a selection bias problem, too, that I haven’t heard anyone mention yet. We’re hearing about Ballghazi, in large part anyway, because the Patriots have won a lot of football games. (One imagines there’d be very little discussion if they’d lost that last one.) If you select for scrutiny a team that has won a lot, they’re likely to be statistical outliers on many points, due to both skill and luck; to put it a different way, SOME team on luck alone could have the lowest fumble rate, and it would be surprising if that wasn’t a team that won a lot, seeing as fumbles are fairly central to football outcomes.
Or to go back to health care, it’s like (and here I exaggerate the effect) “we found this one guy who ran up twice as much in insurance payouts as anyone else – and it turns out he has three separate cancers! now what are the odds of this one random person getting three kinds of cancer? it’s a total statistical outlier!”
Of course, that doesn’t account for a stat that’s actually entirely outside the realm of reasonable chance, but as noted, it’s far from clear that we have that here.
Lurking Canadian
@MattR: This. What an absolute clown show.
MattR
@dmsilev: It should be less than 1 psi. The difference in pressure between a 75 degree room and a 38 degree room is roughly 7% (276.5 Kelvin / 297 Kelvin = .931 with all other things being equal) and the Pats say that their balls started at the minimum 12.5 PSI. (7% of 12.5 = .875 PSI, 8% of 12.5 would be 1)
However, since the temperature never dipped below 47, that leads to a 5.25% (281.5/297) drop in PSI which would be about .65 PSI (which would leave the balls at 11.85). Given that the league has not release any official numbers about the PSI’s they found in each of the 12 footballs they checked at halftime, it is hard to say if the deflation was normal or not.
Francis
well shit. im absolutely wrong. apologies
marduk
@MattR: You’re making the same mistake Neil Degrasse Tyson made. You’re using gauge pressure. You need to use absolute pressure, which is about 27.2 PSI (14.7 atmospheric and 12.5 gauge). So the contribution from temperature alone by the ideal gas law, all else being equal, would be 1.428 PSI. That would leave the balls close to 11 PSI. Add in the effect of water on the ball (and on atmospheric pressure for that matter) and the amount of abuse the balls were getting from the Pats offense (run it again!) and 2 full PSI would be well within expected deflation.
MattR
@marduk: Thanks. That is what happens when I try and dust 15 year old knowledge off the shelf.
marduk
@MattR: Hey, no worries. You’re in good company- NDT made the exact same error.
Just Some Fuckhead
@marduk: Does that mean the ballboy can unconfess?