A tale of tie-breaks and rugby

Posted by David Smerdon on Mar 30, 2015 in Chess, Non-chess |

A while ago, I wrote a post about tie-breaks in chess. It  was inspired by a research proposal I submitted on social network formation as applied to round-robin chess, which basically consisted of a lot of mathematics.

One point to come out of it was that no matter which tie-break system one chooses in chess, there are always going to be situations in which the resulting rankings would be considered unfair by any human definition. There are many notable examples, with the 2011 Commonwealth Championships being a personal case. The huge open tournament had over 700 players, and because the final places were decided by Buchholz (‘sum of opponents’  scores’, the standard method) tie-break, the medals for gold, silver and bronze were ultimately came down to the results of a couple of games played between rank amateurs hundreds of boards from the top. Well, with one exception: my swindle in the final round not only contributed to Gawain Jones edging Nigel Short on tie-breaks for the gold medal, but also handed me the bronze (on account of one of my earlier opponents winning his final game on board 250 or so).

I had always just assumed that this was an organic problem to chess that wouldn’t occur in other professional sports. And generally this is indeed the case; many sports have structures where either there is a natural mechanism to break ties (e.g. goals for/against) that doesn’t rely on the results of lesser teams, or else ties are simply impossible (e.g. tennis, or knock-out tournaments). However, there was an interesting exception recently in the world of rugby. In the esteemed Six-Nations Cup in Europe, half the teams ended up in a tie for first place. Ireland, England and Wales all finished with four wins each in the knockout competition. The tie-break was decided on points difference, which was also incredibly close, with Ireland eventually declared the winner.

The final day’s competition was incredibly exciting, with the three superior teams each winning their games. Bizarrely, the final round’s matches were played sequentially rather than simultaneously (as is the case in chess, football’s Champion’s League, etc), which, while somewhat unfair, added to the excitement of the day. First up, Wales, the worst placed of the three contenders in terms of points difference, thumped Italy 61-20. This temporarily put them in first place, but then Ireland comprehensively beat Scotland 40-10 to reclaim the lead. Finally, England beat France in an incredibly high-scoring encounter (55-35), falling just shy of the 26-point margin it needed to claim first.  With a superior For/Against score by just six points over England, an incredibly slim margin for rugby, Ireland was declared the winner. So far so good; a fair decision, if a close one, one might say. But this is not the whole story.

In the final moments of the Ireland-Scotland match, there was an apparently innocuous incident. The Scottish team, having had a dreadful Cup campaign, had resigned themselves to defeat. Suddenly, a break was on, and the Scotsman Stuart Hogg seemed certain to score a late consolation try. However, either through laziness or the sheer dejection of defeat, Hogg committed a tiny, uncharacteristic knock-on (a sort of foul). The referee, who also could have been forgiven for overlooking a seemingly meaningless and minute indiscretion at this stage of the dead rubber, referred the incident to the video referee. The try was disallowed, with no fuss made by either party; after all, the margin of victory was still thirty points.

A try in rugby is worth five points. It is coupled with a conversion attempt, usually successful in the modern game, which is worth a further two points. Overall, this anonymous moment, attributable to the morose inertia of a player from the team that finished dead last in the competition, boosted Ireland’s final tie-break score by (most likely) seven points. Two hours later, Ireland lifted the cup on the basis of a superior points difference of six points.

Of course, I can’t really directly compare this incident to chess, and certainly not to what happened to Gawain, Nigel and me in Johannesburg. But the principle of a lower, outside party playing a very relevant role in the top standings is quirkily similar. It’s perhaps too much to say that Stuart Hogg decided the Six Nations Cup with his final-moment ‘fingerfehler’…but it makes a much better story.

1 Comment

Jonathan Sarfati
Apr 24, 2015 at 12:05 am

Is it really possible to find a “mathematical” tie breaking system that is any more valuable than a coin toss?

In a round robin, the winners have played the same opponents apart from each other. Sonneborn-Berger basically says that it’s better to beat high-scorers and lose to low-scorers, but why could it not be argued that it’s a more serious defect to lose to low-scorers and break the tie in the opposite direction?

Swiss tournaments are accurate for the top places only; lower places are not so accurate because the players face different opposition. But sum-of-opponents’-scores has the absurd method of using less accurate places to calibrate the more accurate places; no scientist would use low-precision instruments to calibrate high-precision instruments. So the absurd results that occur from time to time are not anomalies but should be expected.

One example that sticks in my mind is the 24th Chess Olympiad (Malta 1980): the Soviet Union and Hungary tied for first, then they waited with baited breath for one low board result to finish, Scotland vs. Greece IIRC.

Another crazy result involves you from a long time ago: tying with Craig Duxbury on the Gold Coast with 10.5/11; drawing with each other and winning the rest. Obviously it was impossible to improve on 10/10 against the rest, so it was moot how “strong” the rest of the field was. Even more reprehensible, IIRC the tie-break was used for something it should never be used for: dividing prize money.


 

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