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    The Likelihood of Two Ties in One NFL Season (10/30/16)

    By Frank Brank @realfbra
    After the Redskins-Bengals tie in this week's London game at Wembley Stadium, ESPN's Darren Rovell reached out to Johnny Avello of Wynn Sports Book to find the probability of two NFL ties in a single NFL season.

    At first glance, this looked wildly incorrect to us, so we decided to use mathematics to determine if Avello's determination of true odds holds any weight.

    Since 1978, the NFL season has featured 16 games per team. There have now been a total of 20 ties over the course of 39 seasons. For the purpose of this exercise, we will assume there will be no more ties for the remainder of this season (even though we almost got another tie in Tampa Bay on Sunday afternoon).

    Given 20 ties over 39 seasons, there's a 51.2% chance of a tie in an NFL season. Using 51.2% as the mean and using the Poisson distribution, we can quickly figure out that there's a 90.6% chance of one tie or fewer in a single NFL season. Thus, the odds of two or more ties in an NFL season is 9.4%. We can also use Poisson to determine that the odds of exactly two ties in an NFL season is 7.9%.

    Additionally, we can use the binomial distribution on a game level (instead of a season level) to find the probability of two ties in a 256-game span (one 16-game NFL season). Again, let's be generous and assume there will not be any more ties this season. The binomial distribution will tell us the probability of n successes, or ties, in N trials, or games.

    Since the 256-game season began, there have been 20 ties in 9984 games, or 0.2% of games resulting in ties. Using the binomial distribution, it's easy to find that the probability of exactly two successes (ties) in 256 trials (games) is 7.8%; a similar number to the Poisson approach above.

    We can determine that the probability of zero ties in a 256-game span is 59.8%. The probability of one tie in a 256-game season is 30.7%. Adding those together, there's a 90.5% chance of one tie or fewer in a 256-game season. Hence, according to the binomial distribution on a game level, there's a 9.5% of two or more ties in an NFL season, which again, is similar to the Poisson approach above.

    These probabilites are quite different than Avello's proposed number of 0.0013% (converting 75,000-to-1 odds to probability). According to the Poisson and binomial distribution, one would expect at least two ties in a season roughly once every 10.5 years; not once every 75,000 years!

    To top it off, the NFL overtime rules changed just a few seasons ago. Teams are actually more likely to tie now due to rule changes. The team that kicks off in overtime is guaranteed an offensive possession if the receiving team kicks a field goal to start overtime. In the previous 35 years or so, the first score would have ended the game. This means that the numbers we are suggesting above are actually fairly conservative. For the purposes of this exercise, we opted to use a larger sample size of data since there would have been a lot of variance in using a smaller set of data over the past couple of seasons.

    Since the 1978 expansion of 16-game seasons, there have now been three NFL seasons where two games have ended in ties. Conveniently, this amounts to once every 13 years, which is a little longer than our projection of once every 10.5 years, but also accounts for old rules. According to our calculations, the true odds of two or more ties in one NFL season would be 181-to-19 (best represented in American odds as +953). If any sportsbook on the planet is offering 75,000-to-1, sign us up!

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    UPDATE: Could the Browns Go Winless? (12/07/16)
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