What Are the Odds That a Given Cow Will Make It to the Super Bowl?

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We blogged last fall about the Book of Odds, an interesting site that generates “odds statements” of all sorts. Now, David Gassko and Ian Stanczyk of the Book of Odds have written a guest post which answers just the kind of question we like to ask around here: What are the odds that a given cow will make it to the Super Bowl?

Super Bowl Cows
By David Gassko and Ian Stanczyk

A football is often referred to as a “pigskin,” though it’s been a long time since that term was accurate. Modern-day footballs are made from cow leather, made from the hides of slaughtered cattle. That got us wondering: What are the odds a given cow will make it to the Super Bowl?

There are roughly 66.2 million adult cattle in the U.S.; of those, 1-in-1.99 are slaughtered every year. Wilson Sporting Goods, the official supplier of footballs to the NFL, makes about 2 million footballs per year. Of those, about 700,000 are regulation NFL balls.

According to the Wilson website, one hide can produce 15 to 25 footballs. Taking the midpoint of 20, that means that roughly 35,000 cow hides are used to manufacture regulation NFL footballs. How many of those are actually used by the NFL?

NFL rules require the home team to provide 36 new balls for each outdoor game and 24 for each indoor game, as well as 12 balls used solely for kicking, regardless of venue. There are eight NFL teams that play in domed stadiums; since each team plays eight home games per year, that’s a total of 64 games requiring 36 new balls. The other 24 teams play outdoors; they play a total of 192 home games, each requiring 48 new balls. Multiplying through, we find that NFL teams must use 11,520 footballs every regular season. (And that’s not even counting the too-long preseason.)

But we also need to account for the playoffs. There are 10 playoff games every postseason, not counting the Super Bowl. If we assume that the average playoff game requires the same number of balls as a regular season game, we can simply divide 11,520 by 256 (the total number of games played every season), and multiply by 10. We find that NFL teams use another 450 balls during the playoffs.

The Super Bowl is its own entity. To be on the safe side, the NFL orders 76 balls specifically for the big game. In total, then, we’re looking at 12,046 game balls used per year. That seems about right; in a phone interview, a Wilson representative told us that the company distributes about 12,800 footballs to the NFL every year, leaving around 750 extras for various uses.

Let us get back to our cows. We noted earlier that the hide of one cow can make about 20 footballs, which translates to 35,000 hides a year going into the manufacture of regulation NFL footballs. With 1-in-1.99 adult cattle being slaughtered every year, 1-in-952.4 cows that are slaughtered will see their hides turn into an NFL football. Of those, 1-in-58.11 will be used in an NFL game. And of those, about 1-in-158.5 will make it to the Super Bowl. Multiplying all those numbers through, what are the odds a randomly chosen cow will see its hide made into a football used in the Super Bowl?

Right around 1-in-17,420,000.

Which is roughly the same as the odds that a person will be diagnosed with the plague in a given year.


sygyzy

I love these types of "facts." especially how they are derived. Very interesting!

wx27

Your estimation actually answers the question "What are the odds a randomly chosen cow will see its hide made into a football used in _this_ Super Bowl".

If the question is any future Super Bowl, then you have to take into account that the cow you have chosen may not get slaughtered this year, but does get slaughtered next year. Or not selected for the first two years and gets slaughtered the third... You end up with roughly twice the odds of the single-year question.

Ben

Only 750 balls left over for various NFL purposes seems small... seeing as how many balls would be used during training camps, practices, etc... unless they recycle the balls that are used elsewhere.

Joshua Ozer

That is an uncannily accurate estimate about the number of balls the NFL uses every year.

Jack

include the chances that a cow, in beef form, will be eaten at the superbowl.

YX

With 1-in-1.99 adult cattle being slaughtered every year, 1-in-952.4 cows that are slaughtered will see their hides turn into an NFL football.

Your mail fail

66200000 / 1.99 / 35000 = 950, so it's 1-in-950 cows will see heir hides turn into an NFL football, not those slaughtered.

YX

And my English fail, so let's call it even.

Mike

Assuming that every single supplied ball is used at each game is erroneous. 36 non-kicking balls per outdoor game would mean a ball switch in less than each 2 minutes of game time, which I'm certain doesn't occur. The unused balls will sit in storage until whenever they're needed.

Pete Krawczyk

I believe the analysis assumes that only two cows will wind up producing all of the balls required for the Super Bowl. This may be accurate, as the balls are produced with special branding at the same time; thus, it might make sense that only two cow hides are needed.

However, what if we assume that each ball comes from a different hide? Given the assumption of 45 balls per playoff game, the odds reduce to roughly 1 in 740,000 - or roughly the same odds as being injured in a tornado: http://www.bookofodds.com/Accidents-Death/Natural-Disasters-Hazards/Odds/The-odds-a-person-will-be-injured-by-a-tornado-in-a-year-are-1-in-739-600-US-2004

Dr. Mom

You are assuming the NFL footballs are made with cows from the US.

Tonya

A great, light-hearted read to end my day =) Thanks guys!

#10 - unfortunately, a very good point!

mh

Mike,

Given that the estimate of the number of balls used matches the number of balls sold, it would make sense to assume that each ball designated for that game is "consumed" in that game. Whether or not that ball is actually used in play is up in the air however.

Basically, if the NFL is buying that many balls every year and is not using them/giving them away as "game balls," that would imply that the NFL is stockpiling footballs, which to me doesn't make any sense.

joe

@ YX your math is wrong. Look at it again.

@ Dr. Mom - From Wilson FAQ section: "Wilson uses the hide from Light Native Steer to manufacture the best game footballs in the world."

Native means US, no?

Cool post.

Ben

There's also the assumption that all hides from slaughtered cows are collected for use as leather and not say, stripped for their collagen to make sausage skins.

Christophe

Also under the assumption that the hides that are used are picked at random out of all available cows? I suppose some areas are more/less likely to get the hides turned into a ball, just like some areas are more/less likely to have you end up with the plague.

Anyway, I get the idea, don't worry :)

science minded

I assume that not all the slaughtered cows are the same age and that the number of breeders is relatively small in the US. So how many cows are the children or chidren's children of the same cow. Seems to me that the odds of a given cow making it to the Super Bowl are much higher genetically speaking?

Mike

Like a learned economist, I will assume that a specialty cow -- her name's Betty -- was bred specifically for the purpose of becoming an NFL Super Bowl football in 2010.

With all of the assumptions made above (in the article and in the comments) it is futile to come to an answer that's any better than mine: 1.00 chance that Betty will be in the Super Bowl.

Much like the can opener assumption -- there's really no problem so long as the proper assumptions are made.

Paul

Why do you think that regressing any variable on any other variable is economics? So the world's full of data and you're moderately good at OLS in SAS. Jees. If this was biology or chemistry or physics, and you were randomly associating any observable variable with any other observable variable and calling that science, you'd be laughed out of grad school, let alone academia.

M

Umm.... if 76 balls are ordered, and each of them is made from a different cow, and there are 66 million cows to choose from, doesn't that mean that the chances are roughly 1 in a million? Which is to say, I agree with Pete and not the author. And the calculation is so much simpler.

Though I'm not even convinced each football is made from a single cow, since it's stitched together from four different pieces of leather.

John Martin

I would rather have the plague than be a cow. At least that way I would have a chance of surviving. Maybe there is a vaccine for plague?