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!
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