overtime madness

The most talked about matchup so far has been the Boston/Chicago series. Four out of six of their games have gone to overtime, one of those went to double overtime, and the game last night went to triple overtime. To put it another way, out of 13 times that the buzzer has sounded at the end of an overtime period or at the end of a 4th quarter, 7 times the score has been tied.

To emphasize just how unlikely a series is to have 4 overtime games out of the first 6 played, I estimated the probability of any one game going to overtime using this year's regular season data. Since I couldn't easily find the total number of games that went to overtime, I estimated it by using team data and looking at total minutes, subtracting at the total number of minutes in regulation, then dividing by 5 to see how many overtime periods were played in total. The minute statistic is subject to rounding error and I ended up getting 81.76 overtime periods played in the regular season. I use this exact number because without additional information there's no way to know if the true number is really 82, 81, or some other number close to that. Our estimate for the probability of a game going to overtime is then the number of overtime periods divided by the total number of games played, or 81.76/1230 = 0.06647. This is most likely a high estimate since it's assuming that every overtime game had one overtime period, which is almost certainly false but is still a very close estimate. So if any one game has a 6.647% chance of going to overtime, the chances of 4 out of 6 games in a row going to overtime can be calculated using this equation:

(n!/((k!)*(n-k)!))*(p^k)*(1-p)^(n-k)

where:

n=the number of games (6)

k=the number of games that go into overtime (4)

p=the probability any one game goes into overtime (0.06647)

After plugging in the values we get the result of 0.00025518 or 0.025518%. Basically 2.5 times out of every 10,000 series that go at least 6 games will have 4 overtime games in the first 6 games played. If you add in the possibility of having 5 or 6 overtime games the result is only slightly higher at 0.00026254. Also, we can calculate the chances of out of 13 possible times to close out a game that 7 of those times end up tied. The value for p will change slightly since we are including overtime periods, so instead of 81.76/1230 we use 81.76/(1230+81.76) = 0.06233. The value for n changes to 13 and the value for k changes to 7. In this scenario the probability ends up being 0.00000426282 or 0.000426282%. Essentially, just over 4 times out of every 10 million. Again, if we add in the possibility of having more than 7 ties out of 13 attempts, the probability increases slightly to 0.00000448341.

As a result, I don't think we're going to see a series like this ever again.