## Thursday, February 13, 2014

### Oh Slate, you're being igorant again

I didn't stay up last night to finish watching the women's downhill final, but that's OK. It's not a sports movie, it's sports; I'm watching for the thrill of the game, not on the edge of my seat to see if the American someone in particular won.

Anyway, I wake up this morning and find this nonsense on my Facebook feed:
But it’s still weird that the race had to end like this, because the timekeepers know who really won. The official timing for all Olympic events is supervised by the Swatch Group, through its divisions Omega Watches and Swiss Timing... and today Swiss Timing can measure every race in every event with such precision that there should never be any question about who won. The International Luge Federation, for example, times its races down to 1/1000th of a second. So does speedskating. Why can’t the FIS do the same?
Well, it can, and it does. That’s the weird thing. The official FIS rule book for international ski competitions says competitors’ times “must be immediately and automatically sequentially recorded on printed strips to at least the 1/1000th (0.001) precision.” As Bill Pennington reported today in the New York Times, the clock in the official timing booth on the downhill ski slope actually exceeds that standard, measuring skiers’ times to 1/10000th of a second. So even though the women’s downhill was scored as a tie, “in the timing control booth, three people—the head timer, a backup timer and a computer operator—saw who won the race according to the timing data.”
Incorrect, Justin. At least three people saw the raw numbers assigned by the timing mechanism to the two skiers. But that's not the same thing as seeing who won. And why is that? Because even though the timing booth may record a number with 4 decimal places, does not mean that this number is correct to all those places.

This is something we were all supposed to learn in middle-school or high-school science: that any measuring device in any experiment is reliable within a certain tolerance, but is useless for distinguishing variations smaller than that tolerance. This is known as the "precision" of the instrument. If the instrument reports numbers in decimal notation, one normally distinguishes between those digits which are known to be correct, and those which are uncertain. (If the tolerance within which the equipment can measure is $$\varepsilon$$, and $10^{-e} > \varepsilon \geq 10^{-e-1}$then the digit corresponding to $$10^{-e}$$ is the first uncertain digit.)

Note that the same piece of equipment may have different reliable precision in different experiments. Think about luge: the timing gate is extremely small and the profile of the athlete is very uniform (they're coming in toes-first), so an additional order of magnitude might be warranted. Or maybe, the true tolerance is only half of the true tolerance for skiing, but that's still enough to warrant one fewer digit in the official time.

Think about it this way: the FIS' decision to truncate to two decimal places means that, in their judgement, it is possible for the timing mechanism to report skier A's time as X.035 and skier B's time as X.037, while skier B actually made it down the course in less time. This is not an absurd judgement, and awarding these skiers a tie is actually more scientifically literate than pushing for the ghost in the Swatch machine.