Usain Bolt was disqualified in the final of the 100 meters at the World Championships due to a false start.  Under current rules, in place since January 2010, a single false start results in disqualification.  By contrast, prior to 2003 each racer who jumped the gun would be given a warning and then disqualified after a second false start.  In 2003 the rules were changed so that the entire field would receive a warning after a false start by any racer and all subsequent false starts would lead to disqualification.

Let’s start with the premise that an indispensible requirement of sprint competition is that all racers must start simultaneously.  That is, a sprint is not a time trial but a head-to-head competition in which each competitor can assess his standing at any instant by comparing his and his competitors’ distance to a fixed finished line.

Then there must be penalty for a false start.   The question is how to design that penalty.  Our presumed edict rules out marginally penalizing the pre-empter by adding to his time, so there’s not much else to consider other than disqualification. An implicit presumption in the pre-2010 rules was that accidental false starts are inevitable and there is a trade-off between the incentive effects of disqualification and the social loss of disqualifying a racer who made an error despite competing in good faith.

(Indeed this trade-off is especially acute in high-level competitions where the definition of a false start is any racer who leaves less than 0.10 seconds after the report of the gun.  It is assumed to be impossible to react that fast. But now we have a continuous variable to play with.  How much more impossible is it to react within .10 seconds than to react within .11 seconds? When you admit that there is a probability p>0, increasing in the threshold, that a racer is gifted enough to reach within that threshold, the optimal incentive mechanisn picks the threshold that balances type I and type II errors.  The maximum penalty is exacted when the threshold is violated.)

Any system involving warnings invites racers to try and anticipate the gun, increasing the number of false starts. But the pre- and post-2003 rules play out differently when you think strategically.  Think of the costs and benefits of trying to get a slightly faster start.  The warning means that the costs of a potential false start are reduced. Instead of being disqualified you are given a second chance but are placed in the dangerous position of being disqualified if you false start again.  In that sense, your private incentives to time the gun are identical whether the warning applies only to you or to the entire field.  But the difference lies in your treatment relative to the rest of the field.  In the post-2003 system that penalty will be applied to all racers so your false start does not place you at a disadvantage.

Thus, both systems encourage quick starts but the post 2003 system encouraged them even more. Indeed there is an equilibrium in which false starts occur with probability close to 1, and after that all racers are warned. (Everyone expects everyone else to be going early, so there’s little loss from going early yourself. You’ll be subject to the warning either way.) After that ceremonial false start the race becomes identical to the current, post 2010, rule in which a single false start leads to disqualification.  My reading is that equilibrium did indeed obtain and this was the reason for the rule change.  You could argue that the pre 2003 system was even worse because it led to a random number of false starts and so racers had to train for two types of competition:  one in which quick starts were a relevant strategy and one in which they were not.

Is there any better system?  Here’s a suggestion.  Go back to the 2003-2009 system with a single warning for the entire field.  The problem with that system was that the penalty for being the first to false start was so low that when you expected everyone else to be timing the gun your best response was to time the gun as well.  So my proposal is to modify that system slightly to mitigate this problem. Now, if racer B is the first to false start then in the restart if there is a second false start by, say racer C, then racer C and racer B are disqualified.  (In subsequent restarts you can either clear the warning and start from scratch or keep the warning in place for all racers.)

Here’s a second suggestion.  The racers start by pushing off the blocks.  Engineer the blocks so that they slide freely along their tracks and only become fixed in place at the precise moment that the gun is fired.

(For the vapor mill,  here are empirical predictions about the effect of previous rule-regimes on race outcomes:

  1. Comparing pre-2003, under the 2003-2009 you should see more races with at least one false start but far fewer total false starts per race.  The current rules should have the least false starts.
  2. Controlling for trend (people get faster over time) if you consider races where there was no false start, race times should be faster 2003-2009 than pre-2003.   That ranking reverses when you consider races in which there was at least one false start. Controlling for Usain Bolt, times should be unambiguously slower under current rules.)