Federer As Probabilist
What am I saying exactly? Am I implying that you need a PhD to shine on the grass (clay would be more appropriate here in Spain)? Is tennis, a la derivatives, about to be overtaken by quants? No, not really. What I am saying (what my coach tells me) is that real players (read Roger Federer and his peers) are constantly calculating probabilities in their heads prior to hitting the ball. Clearly, these calculations are done at record speed, in an almost intuitive manner. Tennis pros choose each particular stroke to the ball depending on the assumed probability of hitting a successful return. As a rule (so am told) you should never try a selection where odds are worse than 70% (seven out of ten times the ball should get in). Of course, many times you may be forced by your opponent to hit something that usually only works 30-40% of the time. But provided that you are free to choose, only go for the highly probable stroke.
This probability-driven approach bothers me slightly, because I have a tendency to go for the glory-seeking point-achieving applause-arousing difficulty-filled shot, which I only manage to conquer 10-20% of the time. It is a great pleasure when you score, but it is a strategy that in the long run would make you lose a game. Clearly, you can´t win a game of tennis when you are missing 80% of your tries.
The key here is that points obtained through boring, conservative, yawn-causing shots are worth exactly the same as those obtained via gloriously-challenging, beautiful complex ones. Thus the importance of probability distributions. To win, your shots must get in at least 60-70% of the time. Thus, you must select strokes that are assigned by your distribution a probability of at least 60-70%. Here and there you may try the odd low probability sensational shot (especially if you lead 6-0, 5-0), but please make it the exception not the norm.
This probabilistic reality has several implications. First, it deprives fans of the best possible shots. Clearly, few professional players would gamble when there is a trophy at stake. I see it even at the amateur and veterans levels here. Guys who take wild chances during friendly harmless exchanges (resulting in highly exciting play full of extraordinary moments) choose a much more prudent route when it comes to "official" matches.
Second, it makes glory attainable through conservatism, not daring. The best route to winning is for a player to restrain, not encourage, his most creative instincts. Take less of those 40% shots, more of those 80% shots. Of course, by definition the better players are those whose 80% shots are equivalent to others' 40%-shots, but the point is that the point-equivalency reality of tennis heavily discourages everyone from deviating from the path most travelled.
Third, in tennis there is no Black Swan. The rare highly unlike event will NOT have a destabilizing shocking highly-altering impact. The unimaginably impossible return backhand will count no more than one point. Its practial relevance will be absolutely minimal. It won´t be remembered five minutes after it happened. It won´t belong to history (except in the odd chance that it became the match's winning point, at which level its relevance would have been complexity-neutral).
In finance, unlike tennis, the presence of black swans is guaranteed by the fact that the unlikely event counts more than the normal event. A market crash and a 0,1% drop do not count the same. The amounts of money lost are not equal. The payout is not digital, as it is in tennis.
For Federer et al, black swan-searching strategies make no practical sense (apart from the good feeling inside and the round of enthusiastic applause). They would be a certain route to the poorhouse. Looking for the low probability, rare event would get these players nowhere in the grand scheme of things. Those wishing for Wimbledon silver (unlike option traders) have zero incentive to venture into Extremistan.
ptriana@profesor.ie.edu
