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Boxing Maths and Aftermaths: Why Similar Scores Are A Mean System

Aug 10, 2012

Four years ago, Irish boxer Paddy Barnes lost to China's Zou Shiming by a score of 15-0 in Beijing. Today in London, Barnes fought his way back into their match to tie Zou at 15-15 — but he still lost. Barnes accepted the decision, but the result might confuse anyone who isn't familiar with boxing's scoring system.

Olympic boxing is like the Ukrainian Parliament, combined with the Illinois governorship, mixed with a Real Housewives show on Bravo: It's chaotic, it's corrupt, and everyone knows it's going to descend into chaos.

These games have seen an Azerbaijani referee and an Azerbaijani official dismissed for negligence and violation of the rules. This after the BBC program Newsnight documented an Azerbaijani plot to influence Olympic boxing results.

AIBA, the body that controls boxing, thought it had rooted out the Azerbaijanis on the take, but perhaps a few others were slipped some Manat.

Thus far there have been several overturned decisions in this tournmanet, mostly because referees simply failed to apply the rules. But equally disturbing is the fact that that the rules themselves, even when fairly applied, seem bizarre.

Put plainly, the actions that earn an Olympic boxer points are only tangentially related to the actions that correlate to success in boxing.

Against this backdrop, it seems almost pointless to note that there is a math problem undermining boxing. When glaring injustices abound, when deserving fighters are robbed of victories thanks to the vagaries of perception and definition, who really cares that the formula for computing points is flawed?

I do. And I, and my calculator, seem to be alone in this regard.

The scoring of Olympic boxing depends solely on five referees' perceptions of how many punches a boxer lands. The quality of the punches is irrelevant, only the number matters. There used to be a very stupid way of defining a landed punch; now there is a smarter way. A judge simply notes that punch has landed. Five judges watch each match, and during each round, every judge notes, via computer, the punches he or she sees as connecting.

The question becomes: How do the perception of these five judges effect the boxers' scores? One simple system is to take the five different numbers generated by the judges, throw out the highest number, throw out the lowest number, and average the remaining three. This is known as the "trimmed mean" — it has its strengths and weaknesses, but it is a familiar and more or less equitable system.

Boxing relies on a trimmed mean as a backup option, once another score tabulation process is applied. AIBA, boxing's governing body, has decided to use something called a "similar score." A formula is applied to the five judges' scoring that determines which ones are similar to each other.

The official AIBA documents describe "similar score" this way:

  • "Similar score means that the individual scores of those Judges which are closest to each other are taken into account.
  • "The difference in points of all possible combinations of 3 Judges ie. (J1, J2, J3)/(J1, J3, J4)/(J1, J3, J5) etc is calculated.
  • "Those 3 individual scores which are closest together (showing the lowest maximum deviation to their joint average are counted).
  • "The score given is the average of those 3 individual Judges combination."

It's confusing, I know — and apparently so did they, because a helpful document the Olympic News Service circulated provided this examples:

"Similar score — the individual scores of the three judges which are closest to each other are taken into account. So, if the five individual scores are 2, 2, 2, 5, 6, the three scores closest to each other are 2, 2, 2. An average of these scores is then taken (2+2+2 divided by three), meaning this particular boxer would be awarded two points for the round."

Which is a terrible example, because of course 2, 2, and 2 are similar to each other. How about these scores: 4, 8, 4, 6, 7.

That's from an actual match I saw. The similar score among them was deemed to be 7. The reason this was a problem is multifold, and I'll get back to it in a second.

As I documented on the air, the "similar score" is deeply, deeply flawed. There are certain situations where an individual judge granting a boxer a higher score would actually result in a lower overall score. Here's my example:

Let's say the five judges give scores of 6, 6, 3, 3, 0.

Under the rules, there is no similar score. So the judges would revert to the trimmed mean, and the boxer would get a 4. But let's say that one of the judges who gave the boxer a 0 changed his mind and gave him a 3. The boxer would then have a similar score and would be awarded a 3 for the round. In other words, if a judge INCREASED his score, the boxer's score would DECREASE.

When I reported this flaw before the games began, it was simply theoretical. Now I know it is affecting decisions in real life. The cluster of scores I presented before — 4, 8, 4, 6, 7 — came in a match between Freddie Evans of Great Britain and Custio Clayton of Canada.

Those were Evans' first-round scores. The similar score was a 7. But imagine, for a moment, that the judge who saw the most number of punches land, 8, actually thought he had seen 10 punches land. In that instance, Evans would have earned a total score of 6 for the round.

So, if a judge had seen more punches land, the boxer would have received a lower score. As it happens, the fight ended in a tie. In a "count back" system, Evans won. Had the bizarre similar scoring method not been used, the Canadian would have advanced to the medal rounds.

The AIBA does not release each judge's scores after every round. It only makes public the final three scores used in its calculation. This makes it impossible to accurately evaluate their process. But the scores after rounds 1 and 2 are displayed inside the boxing arena, and it was from these displayed scores, in person, that I compiled my notes.

To its credit, the AIBA seems to know that its sport is hurting, its scoring is weird, its fan base eroding, and its status as an Olympic sport coming into question. To that end, it is totally revamping the scoring system for the next Olympics. Here's to hoping what they come up with isn't at all similar to the similar score.

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