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

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.