Wednesday 29 August 2012

Luck In Sport.

I've never tried my hand at archery except on the Wii and I strongly suspect that competence on the video version doesn't adequately equip you for the real thing. Therefore, should I be lucky enough to be allowed to challenge an Olympic archer it would become rapidly obvious where the talent lay in the one sided competition.

Let's imagine I scored zero bulls from ten attempts and my opponents scored a perfect 10. Our  knowledge of the task being undertaken is enough for us to decide that hitting the bull is a talent and the respective scores should give us a strong indication that the gulf in talent between myself and my opponent is huge. From this limited information we could probably conclude that the Olympian could hit around 99% of such shots because they are yet to miss, although we have only seen 10 trials. I could be generously given a likely future success rate of say 1% purely on the basis that I have a bow in my hand and am competing.

If we repeat the process and the returns are 9 from 10 for the archer and 1 from 10 for me. We can begin to make another informed opinion. The archer is still clearly better than me, but no longer perfect and I have shown enough ability to hit one bull from ten attempts. A reasonable new assessment of the gulf in talent would put the archer at just below his actual 90% strike rate and me just above my figure of 10%. Natural random variation has perhaps favoured the professional and deserted me and I'm actually a little bit better than I've shown and my opponent is really slightly worse than their fine return implies.

We can continue this balancing of random variation and true ability as our respective scores converge, but at some point, say 6 out of 10 and 4 out of 10, we cease to become sure that the discrepancy in scores is still down to a combination of the two factors. It may now be just down to the same forces that allow a fair coin to yield 6 heads from 10 tosses. In short I may now be the equal of my opponent based on talent, but one of us has had a lucky day and the other hasn't.

And if two "coins" can demonstrate variation in "talent" where none exists in limited trials, then so can sports players. It's a point worth remembering the next time you look at raw conversion rates for both teams and individuals and try to pick out "the best".

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