# Probabilities of Streaks – NFL® Playoffs Edition

Probabilities of Streaks – NFL® Playoffs Edition

The NFL® playoffs are one of the more exciting postseasons in major sports, with a single elimination format and a win or go home reality. There are 32 teams in the league and 12 of those teams earn the privilege of reaching the postseason each year. If each of the teams were evenly matched then they would all start with a theoretical 37.5% chance of reaching the postseason. With that said, we know that no team is equal and some teams start the season with a better ensemble of players and coaches giving them a far greater or worse chance of reaching the playoffs.

Let’s take a look at how extraordinary the recent Buffalo Bills playoff drought was in terms of statistical significance. The Bills just made the playoffs for the first time since 1999, putting an end to the longest active stretch in North American Sports. To put that in perspective, the last time the Bills made the playoffs, Tom Brady had yet to be drafted (2000), the iPod had yet to be released (2001), and Facebook had yet to be created (2004). Buffalo went 17 consecutive seasons from 2000 to 2016 missing the postseason, in a league where 12 of the 32 teams advance each year.

If Buffalo were to start each of those 17 seasons with a theoretical even chance of making the playoffs as one of the 12 teams to advance, then they would start each year with a 37.50% (12/32 = 0.3750) chance of reaching the postseason. You could also say they would have a 62.50% chance of not advancing in any year, all other things being equal. The odds of 17 consecutive misses at that probability is equal to a 00.03% chance, which works out to about a 1/2950 occurrence. Inversely, that would mean that over the course of a 17-year span they would have a 99.97% chance of reaching the playoffs in at least one of those years if all teams were evenly matched.

0.6250^17 = 0.00033881317= 00.03%

1 – 0.00033881317 = 0.99966118683 = 99.97%

Even if you consider that Buffalo had some less than stellar years, where they were probably not on equal footing with their opponents, the streak is still statistically remarkable. If you assume they cut their chances in half each year and only had an average probability of 18.75% chance of reaching the postseason, they still would have greater than a 97% chance of reaching the playoffs at least once over that period.

1 – (0.8125^17) = 0.97069125083 = 97.07%

Cut the probability in half one more time and give them a 9.375% chance of making the playoffs and they’d still have a greater than an 81% chance of making the playoffs in at least one of those years.

1 – (0.90625^17) = 0.8124071278 = 81.24%

No matter how you look at it, the Buffalo Bills and their loyal fan base endured quite a dry patch in a league where 37.5% of the teams reach the playoffs each year. NFL teams that play during the Wild Card week have to win 4 consecutive games to be crowned Super Bowl champions, while any of the 4 teams that start off with byes only need to win 3 consecutive games to end the season as champions.

What if I told you that last year’s Super Bowl Champion New England Patriots started the postseason this year with an 80% chance to win each playoff game they played. What would you say their chances would be of repeating as Super Bowl champions with an 80% chance of winning each game? Well, surprisingly, even if New England had an 80% chance of winning each game they would barely be a favorite to repeat vs. the field with a 51.2% chance of winning 3 consecutive games.

(0.80*0.80*0.80 = 51.20%)

If the Patriots did not have a bye and were forced to play a Wild Card game then they would actually be an underdog vs. the field with a 40.96% chance of 4 consecutive wins.

(0.80*0.80*0.80*0.80 = 40.96%)

In trading, it is more of the same with probability analysis. A trader is accessing the market risk to the potential profit of each trade opportunity.  When trading binary options, you have a trading instrument which is priced as a probability to finishing in the money.

In this example below, here is a Gold chart at about 9:37 a.m. ET on January 12th, which is based off the February NYMEX Gold Futures® price. Along the right axis are some of the daily binary option strikes available on the NADEX exchange, which expires at 1:30 p.m. ET the same day, leaving almost 4 hours until expiration.

If you bought the Gold >1,324.60 binary option strike for 80 then you would be risking that \$80 per contract for a maximum profit of \$20 if the contract expired in-the-money for full settlement value of \$100. However if at expiration the 1324.60 binary strike finished out of the money, the binary position would be worthless and the \$80 initial cost would be forgone per contract.  At the time of the trade, Gold was currently trading more than \$3 above the \$1,324.60 strike price, which is why you would be risking \$4 for every potential \$1 in profit for this trade. What if you planned on making 4 trades every day and holding the positon until expiration, with each trade having an 80% chance of success? What would the probability be on any given day that you are profitable on all 4 trades if they each had an 80% chance of success? The answer is 40.96%. (0.80*0.80*0.80*0.80* = 40.96%). This applies to longs and shorts, regardless of your market expectation. It might be surprising to learn that even making such high probability trades, and only making 4 of them a day, that you are more than likely to lose at least once a day.

If you would prefer to risk less capital vs. a potential profit then you could always use a mental stop to exit the position early if the underlying instrument traded against your position. Looking again at the previous Gold binary option example, if you planned on exiting your position if Gold traded back to your strike price of \$1,324.60 you could plan on selling the binary option at around \$45. This could cut your planned risk down from \$80 to only \$35. Of course, this will decrease the probability that your trade will result in a profit, but you would now only be planning to risk \$35 to profit \$20, or risking \$1.75 for every \$1 of potential profit.

If you’re a trader that plans on making high probability trades where you’re risking \$4 for every \$1 of potential profit then you should be aware of the very real possibility that losses will be incurred on a regular basis, just as upsets can happen very regularly in the NFL playoffs. And like in the Bill’s case, sometimes streaks can defy logic and you should make sure your money management is in place to weather that storm should it ever appear on the horizon.

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