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.


Dan

I think you're making this calculation more complicated than it needs to be, and getting the wrong answer. The first question is how many cows the 76 Super Bowl balls come from. It could be 76 different cows, or it could be as few as 4 cows. If it's 76 cows (as I would guess), then that means that, of the 33.1 million cows slaughtered this year, 76 will be in the Super Bowl, so each slaughtered cow has a 76/33,100,000 chance, which is 1 in 438,000. And cows that are not slaughtered this year have a 1 in 438,00 chance of going to the Super Bowl in the year that they are slaughtered, so any randomly selected cow has a 1 in 438,000 chance of making it to a Super Bowl. That's the answer I'd give (though the chance of making it to a particular Super Bowl is half that, 1 in 876,000).

If the football manufacturing process is such that the 76 balls come from only 4 cows, then a randomly selected cow has a 4/33,100,000 chance of making it to a Super Bowl, or 1 in 8.3 million. Or, for a particular Super Bowl, 1 in 16.6 million. If you used 3.8 cows instead of 4 (3.8 = 76 balls divided by 20 balls per cow), then you'd get the answer in the post, a 1 in 17.4 million chance of making it to a particular Super Bowl, but fractional cows don't make sense here.

Given that footballs are pieced together, it's also possible that more than 76 cows contribute to those balls.

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horsttesten

Funny but unfortunatly wrong.
Gassko and Stancyk computed the probability of a cattle in a given year making the superbowl under the assumption that the 76 superbowl footballs are made from the least number of cattle hides possible. You can sum up the article in two sentences:
One needs 3.8 cattle to make 76 footballs (76/20). The odds a cattle makes it into the supberbowl this year are 66.2 million divided by 3,8 which gives you a 1 in 17.42 million chance.
A better analysis is:
All cattle are eventually killed and their hides are used. So for the probability a cattle makes it into the superbowl, you just need to consider the year the cattle dies. Thus you start with the 66.2/1,99 million cattle that die every year.
Then you need to ask yourself: How many cows make it into the superbowl every year. At least 4, since you need 3,8 hides to make the 76 footballs. But how likely is it that out of the 700,000 NFL regulation footballs you select the 76 footballs from just 4 cattle hides? It is much more likely that the footballs come all from different hides. Thus 76 cattle make it into the superbowl every year. 66.2 million divided by 1.99 divided by 76 equals about 1 in 438,000 cattle make it into the superbowl. This probability is about 7 times less likely than that for a highschool male (chance 1 in 64,000 from an earlier post on the book of odds site) but still much higher than the original estimate of 1 in 17.42 million.

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noel

But what about all the burgers that will be consumed in the stadium that sunday ... have those cows not also made it to the super bowl?

Ian Kemmish

What happens to the 33 million-odd cattle whom you don't count? Do they emigrate? Are they immortal?

Even if you kill 33 million one year olds and 33 million two year olds each year, the total still has to be 66 million, doesn't it? Either that or you've got a population explosion on your hands.

Or to put it yet a third way, the odds that a cow is going to be slaughtered are not the same as the odds that it is going to be slaughtered in a given year (let alone "every year" which opens a whole new surreal can of worms).

Christopher Strom

The later comments (15, 19, 21, 22) make valid arguments concerning the number of unique hides might be used in making the 76 Super Bowl footballs. However, when one considers the football manufacturing process, Gassko's and Stanczyk's approach can be simplified:

The 76 Super Bowl footballs are clearly marked as such, and are thus not interchangeable with other NFL footballs. As a result, the discussion of how many footballs are made for the NFL (and thus how many cows' hides would be required for all NFL footballs) is irrelevant.

When the 76 Super Bowl footballs are manufactured, they will all be made at one time. The manufacturing process for NFL footballs is as follows (from the video on the Wilson site):

1. Die cut prepped hide
2. Emboss base pattern on all cut parts
3. Emboss printing pattern (flat areas) on parts to be printed
4. Print parts to be printed
5. Assembly (details unimportant for this discussion).

Once the parts are cut, they are placed in a pile. Parts are drawn from this pile for step 2, then placed in another pile. Parts are drawn from the second pile for step 3. Once a part goes through step 3, it is committed to being a particular football (Super Bowl or other).

Although 76 footballs may be made from as few as 4 hides (or as many as 304 [76*4]), given the manufacturing process, it is likely that there will be some mixing (as far ah hides are concerned) of the die cut parts. But given the desire to minimize the quantity of WIP (work-in-progress), it is likely that the extent of this mixing is low - perhaps 5 or 6 hides max.

So (if my math is correct), the probability of a cow making it to the Super Bowl (as a football - ty Jack and noel) should be [# hides used in SuperBowl footballs] / [#hides available]

No lower than:

( (76/20)[rounded up] / (66200000/1.99) ) = 1:8.3MM

No greater than:

( (76*4)[rounded up] / (66200000/1.99) ) = 1:109K

But more likely in the neighborhood of:

( 6 / (66200000/1.99) ) = 1:5.5MM

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Cory

Ironically, it's also the odds that the Vikings will make it to the Super Bown in any given year (and forget even thinking about winning one).

-- Disgruntled Minnesota Vikings Fan

keith

There's an assumed independence in the population of cows that I do not think is warranted. Is the "given cow" a dairy breed or a beef breed? Or is the given cow a random draw from all cows?

Josh M

I was diagnosed with the plague in 1984. So if I died and donated my hide to the NFL, are my chances greater that I will be used in the Super Bowl?

James Curran

@John Martin:
Yes, The plauge is one of many things medical research has found a cure for in the past 700 years -- in this case, good old penicillin. (*)

Also, this calculation reminded me of one I did a while back:

Odds that a randomly chosen American has walked on the Moon: 1 in 28 million (similar to your chances of winning the lottery) (rationale: 308M Americans, and (AFAIK) 11 living Moon-walkers)

(*) Actually, those days it's a course of streptomycin, and I' count reducing mortality from 90% to 30% as a "cure"

Zach

It doesn't smell right to me. The sniff test I'm using is if you apply these odds to the starting population, appoximately 4 cows will win this lottery. As Dan pointed out, the minimum number of cows needed to complete the task of making the number of balls needed is 3.8. It only works out if care is taken to make sure that the materials used in the end come from the minimum number of donators. I think the problem here comes from all the elimination rounds.

To me, the only elimination round that matters is whether or not a given cow's hide ends up in the stock that is chosen from when the balls are made. This one matters because there is a very good chance that a cow that makes it this far will be used in multiple superbowl balls. If you win one slot, you will probably win other slots. But the four that win with the proposed odds will probably not get all the slots.

Well, there is one way. I've heard talk of ball manufacturers keeping cow DNA on record to detect counterfeits on the sports memorobilia market. They may then have a incentive to fulfill the order with the fewest possible cows.

Final thought: I heard the Colts planted real grass in their dome so the cheerleaders would have a place to graze. Do they get credit for appearing in the superbowl if a cow that donated its hide gets credit?

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Brad

How about shoe leather and gloves? Won't some cows be used to catch and kick other cows?

Peter

Although I enjoy the detailed calculations that go into it, the calculation of odds can be done a lot easier. The only necessary questions to answer are:
1) How many cows (cattle) are there in the population that we're looking at?
2) How many cows are used to make game balls?

The second can be broken down further to:
2a) How many balls are used?
2b) What are the chances that more than one of the balls used are from the same animal?

Questions 1 and 2a are covered directly in the post above (66.2 million cattle and 76 balls). Question 2b is much more difficult to answer: each animal that contributes makes between 1 and 25 balls to the big game. So the footballs are made from between 4 and 76 cows (assuming the segments on a given football don't come from different cows).

It's reasonable to think that the NFL might select the balls from the same cows to minimize that number. In that case, the odds that a given cow makes it to a game ball is 4 in 66.2 million or 1-in-16.55 million.

If there's no such effort made, there are a lot of balls made, so we are unlikely to get much overlap. The odds are about 76 in 66.2 million (as mentioned in an earlier post), meaning about 1-in-870,000.

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jackcb

Quibbles ad nauseum:

Why not include the cows that get there as hamburger, hot dogs, etc.?
Is the Parking Lot included as "making it", rendering the tailgating participants eligible? (If not, shouldn't partially digested cows be counted.?)

What about imported Hides, on or off the cow? (One would presume Wilson Sporting Goods uses only domestic raw materials, esp. for Super Bowl equipment, but hey, you never know.)

Gloves, Hats, underwear and apparel in general (thanks to #31)

Cows that are already there, by virtue of contributing to the Stadium itself, like lux.box seat upholstery, bar tops, etc.

Are we using the restrictive definition of 'cow' - a female - or 'cow' as a generic bovine?

How do specifications on the hides used affect the population size? (Ever seen a black & white football?)

Are adjustments for causes of death prohibiting harvest of the hide included in the population estimate, such as road kills, predation, cow-tipping fatalities or victims of alien mutilations?

I could go on, but it's obvious the question is insufficiently defined.

btw, do they still use leather laces.....

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Thomas

This analysis only takes into account cows who will make it to the Super Bowl as footballs ... and that doesn't answer the original question, "What are the odds that a given cow will make it to the Super Bowl?"

Other cows may make it to the Super Bowl if their hides were used to manufacture shoes or belts worn by those present for the game (fans, players, stadium employees, etc.), other cows contributed to food products served at the game (hamburgers, ice cream), cow hides may have been used to construct leather seats in the stadium's private suites, and it's even possible that a cow would make a live appearance during pre-game or halftime ceremonies.

I have no solid data to provide a specific answer to the question, but I'm going to *guess* that the correct answer to the original question is 5000 times greater than the number of cows whose hides are turned into Super Bowl footballs.

So by my reckoning, the "Book of Odds" folks missed 99.98% of the lucky Super Bowl cows!

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science minded

Dear jackcb;

I think that you have a good point. But it does leave open a question re any experiment with human beings. Can result be predicted in advance?

Station

The balls are cut from few hides (I'm paraphrasing a comment made on the original Book of Odds page): see the 2nd slide of 17 from the Houston Chronicle photo essay (3 Feb 2010) on Wilson's hand-made Super Bowl XLIV balls:

http://www.chron.com/sports/photogallery/The_making_of_Super_Bowl_footballs.html#20272776

So, Christopher Strom (#25) is right to hazard that few hides are used (and it is obvious from the photo that Wilson doesn't utlize a full 76 separate hides for them).

SpyOne

Ian, I can explain what happens to the remaining cows

A population explosion is out of the question. In a species that bears a single young at a time and takes a year to mature, if you kill half the adult population every year that species is on the express train to extinction: this year there were 66 million, 33 million of which survived to have 16.5 million kids. This time next year there will be 49.5 million, 24.25 million of which survive to have kids.

The reason cows aren't going extinct is that most of the slaughtered cattle are male, and the species' ability to restore population is based not on the number of surviving [i]individuals[/i], but on the number of surviving [i]females[/i]: 33 million female cows + 1 bull = 33 million calves in the next generation (roughly). Add those to the 33 million adults surviving this year, and you'll see we have 66 million again next year, of which we will kill 33 million again and the cycle repeats indefinitely.

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buck

The question was: What Are the Odds That a Given Cow Will Make It to the Super Bowl?

1) so some cows were slaughtered and some were not. Obviously those were not slaughtered were not chosen, but that does not matter, because a cow is a cow no matter moo(who) are. in other words, the conditional prob that a cow was slaughtered is not relevant.

a) # of balls. 76
b) avg # of footballs that can be made from a cowl? according to the article, one hide can make about 15 to 25 footballs. For my estimate, I will use 22 footballs, because when i was in grade school there was a projector film that discussed (from the 1980s) this exact issue. It showed the process of making a football and that an average hide made about 22 official NFL ball. (yes, public grade school and it was a math class)
c) # of cows, living or dead. 66.2 million

Answer = 1 in a/(c/b), where it is not necessary to truncate (a*b) to the nearest integer because part of Molly the Cow may be in ball #1, part may be in ball #19 and part may be in ball #76.
a = 66.2, b = 22, and c = 76
66.2/(76/22) = 19.16 million.

on the other hand, what is the CONDITIONAl prob of a cow that was slaughtered making it to the SB?

a. 76 balls
b. 22 balls per moo moo
c. 66.2 moo moos
d. prob of cow being slaughtered in given year. (1/1.99)

Answer = 1 in (a*d)/(c/b) = one in 9.6 million

Of course conditionally speaking, may I refer readers to this NYT article about the production of NFL footballs
http://www.nytimes.com/2008/02/02/sports/football/02footballs.html
"The footballs get their start on the backs of cows taken from feedlots in Iowa, Kansas and Nebraska. Riegle said he preferred young, lean steers over fat dairy cows because their leather did not stretch as much. "

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