Kicking Off Could Become Flipping Off in NFL

April 17, 2012 at 8:03 pm 3 comments

One of the most exciting plays in the history of professional (American) football was the opening play of the second half of Super Bowl XLIV, when the New Orleans Saints recovered an onside kick. They then scored to take a 13–10 lead, and eventually won the game 31–17.

But onside kicks could be a thing of the past. Yesterday, New York Giants’ co-owner John Mara suggested that kickoffs might someday be eliminated from the NFL. This caused a lot of sports pundits to react, saying that it would inherently change the game. On the Mike and Mike Show, analyst Mark Schlereth responded with these rhetorical questions:

What’re you gonna do, flip a coin three times in a row? You gotta get heads three times in a row to get an onside kick?

Once again, probability was placed front-and-center in recent football discussions. While I like Schlereth’s new, less violent, and more mathematical approach to onside kicks, I just wish he had gotten the math right.

If you flip three coins, the probability of getting three heads is 12.5%. That’s not enough. Data shows that onside kicks in the NFL are successful 26% of the time. So the following would be a reasonable modification to Schlereth’s proposal:

Flip two coins. Two heads results in a successful onside kick.

Then the probability would be 25%, closer to the current reality.

Unfortunately, that’s not exactly right, either — it’s based on a misleading statistic. The success rate of onside kicks is highly dependent on whether the team receiving the kickoff is expecting it or not. When teams are expecting it, the success rate hovers around 20%; when teams aren’t expecting it, however, the success rate jumps to 60%. Considering that data, the process might be modified as follows:

  1. Kicking team indicates to referee that they will try an onside kick.
    • Of course, this must be done secretly, so as not to arouse the suspision of the receiving team. I propose that one referee be assigned to each team; the team would encode the message using RSA encryption, and the assigned referee would be given the corresponding RSA numbers. A message can then be passed without fear of interception by the receiving team. To ensure that this procedure does not signficantly delay the game, messages stating “we WILL try an onside kick” and “we WILL NOT try an onside kick” could be prepared in advance, and unemployed math PhD’s could be hired as NFL referees to decode the messages.
  2. The receiving team must similarly indicate whether or not they suspect an onside kick.
    • Again, use RSA encryption.
  3. If the kicking team chooses an onside kick, and the receiving team suspects an onside kick, then:
    • Flip 9 coins. If 9, 8, 3, or 1 of them land heads, the onside kick is successful.
    • P(9, 8, 3, or 1 head with 9 coins) = 20.1%
  4. If the kicking team chooses an onside kick, but the receiving team does not suspect it, then:
    • Flip 9 coins. If 9, 8, 5, 4, or 2 of them land heads, the onside kick is successful.
    • P(9, 8, 5, 4, or 2 heads with 9 coins) = 60.0%
  5. If the kicking team does not choose an onside kick, then:
    • Flip 9 coins, just so the receiving team is unaware of what the kicking team decided to do, which will allow for the element of surprise with future kicks.

If the NFL decides to accept Mark Schlereth’s suggestion for using coins to determine onside kicks, I am hopeful that they will give my proposal serious consideration. If necessary, I have an Excel spreadsheet that I would be willing to share with them.

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Questions to Which I’ll Never Answer, “No” A Busy Week — Fun at NCTM and USASEF

3 Comments Add your own

  • 1. xhenderson  |  April 17, 2012 at 9:11 pm

    And where does the ball end up after the kick? We can’t really assume a fair catch, so starting on the 20 doesn’t make sense. Would it be possible to flip enough coins to determine whether or not the receiving team runs the ball back for a touchdown? Do they get the extra point? In fact, why don’t we just abandon the game, and determine the outcome using coins.

    A Baseball Fan 😛

    • 2. venneblock  |  April 18, 2012 at 9:37 am

      It’s no doubt a flawed system. But I had the same thought as you, let’s use coins to determine the entire outcome. The NFL always talks about how they try to shorten the time to complete a game… this could get it under 15 seconds!

  • 3. JimsMaher  |  April 22, 2012 at 9:53 pm

    What about incorporating how often, out of the total number of kick-offs, a team attempts an onside kick. Then use that to determine the percentage of total kick-offs are onside kicks recovered by the kicking team.

    Supposing 25% of onside attempts are recovered by the kicking team, for the total 1 in 8 odds given on TV to hold true, approximately 50% of all kicks would need to be onsides attempts. It seems unlikely that any team wouldn’t expect the attempt at that frequency.

    2 to the third power = 8
    Three heads occurs once out of eight possible outcomes.
    100% / 8 = 12.5%
    For n = percentage of total attempts being onsides kicks
    n * 25% = 12.5%
    n = 12.5% / 25% … or .125 / .5
    n = 50% … or .5

    If they do find some more realistic percentage, I would suggest starting on the 25 normally, and based on some trigger have the would-be “kicking” team start on the 50 yard line some small percentage of the time.

    But that’s not going to happen anytime soon, if ever.

    I’ve heard speculation for having kick-offs that go through the goal posts count as an extra-point. This later remark stemmed from the fact that last season they started kicking from the 35, in an effort to shorten the distance and thereby hopefully reduce injuries on the only play that has both teams in a full-on charge at each other … the kick-off.


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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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