The come-from-behind victory by Oracle Team USA over Emirates Team New Zealand in the picturesque San Francisco Bay is being rightly hailed as one of the greatest in sailing history.
Team USA was down 8-1 on 11th September. But in the following two weeks, culminating in the spectacular and decisive victory on 25th September, Team USA had run off 8 straight wins to claim victory in the first-to-nine regatta.
How improbable was 8 straight victories?
A student taking an elementary course on statistics may calculate the probability this way: Probability that either Team USA or Team New Zealand will win in any given race is 1/2, or fifty-fifty, similar to when you toss a coin and ask for the probability of getting a head or a tail.
The probability of getting 8 heads (or tails) in a row, using the law of multiplication for independent events, is (1/2)8 = 0.0039, or 0.39%, less than one-half of one percent.
That’s highly improbable. In other words, the likelihood of getting 8 heads in a row, or running off 8 straight victories in a regatta is extremely low.
The student can shrug off the victory by saying, “well, the improbable happens all the time in life, even if statistics says otherwise.”
That’s true, but the logic of (1/2)8 is faulty in this case.
The probability of winning was higher than ½ for Team USA. As the Team began to win and gained psychological momentum, meshing technology and sailing skills in ways that eluded members of Team New Zealand, its probability of winning increased dramatically from 0.5.
In addition, the races were not independent events. Each win increased the probability of subsequent wins, so that the probability of running off straight wins was much higher than what one would expect from a series of independent, binary events.
Statistics comes to life not only when its basic laws are proven true in real-life events but also when simplistic applications of these laws reach their limits and one has to consider other factors, some of which are within the reach of statistics and some not.
In the case of the 34th America’s Cup and the amazing win by Team USA, conditional probability, along with all its associated quirkiness, had to be considered before estimating a probability of running off 8 consecutive victories. That would be an amazing feat by itself!