01 November, 2015

On the unfair rules of tie-breaking

The 2015 World Championships have given the occasion to watch something that does not happen very often in major championships: a jump-off for first place (and in fact, in the case of men's high jump, a jump-off between three athletes). 

Bondarenko, Drouin and Zhang
It would haven't bothered me in the least
if all three had shared the gold medal

That got me thinking on the tie-breaking rules and after perusing them I ended up convinced that the present system is not optimal. In fact the whole tie-breaking scheme articulates around the obsession of a single winner. Somehow in athletics the official rules try to avoid the presence of two athletes at the highest place of the podium. I have discussed, in previous posts, the dire consequences of the millisecond-based decisions in track events. Here I would like to concentrate of the field event ties.

Let us first see what do the rules say. Rule 180 stipulates that

Except for the high jump and pole vault, the second best performance of the athletes having the same best performances shall determine whether there has been a tie. Then, if necessary, the third best, and so on. If the athletes are still equal following the application of this rule, it shall be determined to be a tie. Except in vertical jumps, in the case of a tie for any place, including first place, the tie shall remain.

One can understand this rule as being based on a simple statistical reasoning. The probability that all six performances of two athletes coincide at centimetre precision is admittedly very, very small. Still I can think of one situation where such a thing can happen. Imagine two athletes fouling most of their jumps, say in long jump, and managing to record equal performances in the one or two valid ones. The probability for this, although still small, is now not totally negligible. Were such a situation to arise the rules provide for a tie even in first place.

So why are vertical jumps treated in a different way? The reason for this is that the athletes jump at fixed heights and thus a tie is much more probable in these events. I will not go into the details of how a place is decided in vertical jumps but focus on the case of a tie. Here Rule 181 stipulates that 

If the athletes are still equal, the athletes concerned shall be awarded the same place unless it concerns the first place. If it concerns the first place, a jump-off between these athletes shall be conducted, unless otherwise decided, either in advance according to the technical regulations applying to the competition, or during the competition but before the start of the event by the Technical Delegate or the Referee if no Technical Delegate has been appointed. If no jump-off is carried out, including where the relevant athletes at any stage decide not to jump further, the tie for first place shall remain.

The last sentence is interesting. Reading what is written one may conclude that the athletes may refuse the tie-breaking procedure in which case the tie remains. I hope I am interpreting this correctly and the athletes do indeed have the power to decide. I have seen athletes refusing to jump further but this has always concerned a qualifying competition where the number of athletes remaining in the competition slightly exceeded the number of athletes to be qualified for the final in which case pursuing the competition just in order to eliminate one or two athletes was deemed an unwarranted effort.

And now the jump-off

(a) Athletes concerned must jump at every height until a decision is reached or until all of the athletes concerned decide not to jump further.
(b) Each athlete shall have one jump at each height.
(c) The jump-off shall start at the next height (i.e. the height where the concerned athletes have failed) after the height last cleared by the athletes concerned.
(d) If no decision is reached the bar shall be raised if more than one athlete concerned were successful, or lowered if all of them failed, by 2 cm for the high jump and 5 cm for the pole vault.
(e) If an athlete is not jumping at a height he automatically forfeits any claim to a higher place. If only one other athlete then remains he is declared the winner regardless of whether he attempts that height. 

What is bothering me here is that the jump-off is open-ended: the athletes may continue indefinitely if no decision is reached. I find this unfair. Again a probabilistic argument may be invoked here, based on the fact that most ties are settled after two or three jumps at maximum. But I would be much more confortable if a jump-off comprised a fixed number of jumps. Why not decide that the athletes have three tie-breaking jumps at maximum, the first starting at the height they failed to clear and then, if the tie persists, have two more at bars raised or lowered according to the jump-off rule proviso. In fact I would be even tempted by making things even simpler by proposing that the bar be never lowered. If all athletes fail at the first jump-off height the jump-off ends there and the tie remains. If they succeed then the bar is raised once, and if necessary twice, after which the jump-off ends and if a tie persists the athletes are declared winners ex aequo.  

I find it somewhat unfair to oblige precisely the vertical jumpers who usually make more than 6 attempts in their competition to prolong their efforts through a jump-off while the specialists of the remaining field events do not have to break a tie. Why not decide that where such an improbable situation arise a tie break would be necessary in this case also, allowing the athletes up to three more efforts but stopping the jump- or throw-off after the first or second attempt if the tie is broken. 

Tie breaking in combined events is a nightmare. From Rule 200.12

If two or more athletes achieve an equal number of points for any place in the competition, the procedure to determine whether there has been a tie is the following:
(a) The athlete who, in the greater number of events, has received more points than the other athlete(s) concerned shall be awarded the higher place.
(b) If the athletes are equal following the application of Rule 200.12(a), the athlete who has the highest number of points in any one event shall be awarded the higher place.
(c) If the athletes are still equal following the application of Rule 200.12(b), the athlete who has the highest number of points in a second event, etc. shall be awarded the higher place.
(d) If the athletes are still equal following the application of Rule 200.12(c), it shall be determined to be a tie.

So, two athletes after a herculean effort manage to score the same number of points and they must still be separated by some accountant's argument. The simplest way out would be to apply rule 200.12(a) and if a tie persists stop right there (and don't have me started on the mathematical complications of a three-athlete tie where A beats B, B beats C but C beats A).

For me the simplest thing would be to forget about tie-breaking and accept that from time to time we will have more than one olympic, world or continental champions. If we persist in breaking the tie then let us make our rules somewhat simpler and fairer for the athletes involved.

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