Scoring in small entry pairs events
I had the opportunity to play twice at my local club this week; once in an “improvers session” of 14 tables, then at the normal club night, beset by those sick and on holiday, of just 3.5 tables.
The results were more disparate than I could have imagined, then I considered the facts
The first session played 7 x 3 boards in one of two 7-table sections utilising a standard Mitchell movement.
The second session played a four table Howell movement of 7 x 4 boards with each pair sitting out one round.
In the first session, the results of any other table affected our result by 0.2%. (Roughly, 5% per board with 14 results on it equates to 0.2% for a drawn board or 0.4% for a win against each other pair).
In the second session, the results of another table affected our result by 1%. (Roughly, 4% per board with two other results on it equates to 1% for a drawn board or 2% for a win against each other pair).
One “freak” result in the smaller movement affected our result enormously, (and there were many!) resulting in scores of 77% (1st) in the first event, and 43% (5th=) in the second event. Was this fair?
I considered IMP’ing each players score against the par (we had duplimated hands) and we would have come 2nd, and indeed other than the 1st place which would have remained unchanged, other places change dramatically.
This method of IMP’ing in a pairs game is probably not entirely fair either, and cross IMP’ing would fail on this point and the lack of comparison, but I do wonder whether there are fairer methods of scoring pairs events when table numbers are low.
Comments
IMPing in pairs tends to increase the chance of extreme results, rather than reducing it. The reason is that with matchpoints, each board has the same number of matchpoints on offer, so you have roughly equal opportunities to balance out the rounds you spend against good opponents and the rounds you spend against bad opponents; but if you're using any form of IMPs, then players will get a huge advantage if they happen to be paired against bad opponents on the boards which have the potential for large swings.
I think this is an inevitabale result of the difference in the number of masterpoints being awarded for each hand. On the first event, the board is played 14 times resulting in a top of 26, in the second event the board is played 3 times, resulting in a 'top' of just 4. So you either get 100%, 75%, 50%, 25% or 0%. (You can see this if you look at the scores on the bridgemates after round 3 of a larger event). If you x-IMP then making a slam gets you 26 imps and the opponents each get -13, which is a very large swing (and the boards that you miss out may be swingy, depriving you of the chance for large gains. Not only that, but your bridge technique varies between masterpoints (frequency of gain) and imps (amount of gain).
As for a solution - I don't think there is one. This is a common problem in statistics where any large sample tends towards a Normal Distribution Curve, but a small (quantisised!) sample can be handled by a binomial or poisson distribution. Equally it applies to opinion polls, which can have quite a large variance.
I just accept that there is an element of luck in Bridge and any scoring system introduces random noise to the results.
With movements where boards are not played so many times the random luck element becomes more significant.
Alan
Sadly, the amount of times a board can be played is constrained by the number of players, and as others have pointed out this does increase variance.
I sometimes think playing X-IMP pairs might be a better option, you'd still have some problems with wierd pars, but there's less results you'd just look at and think you couldn't do anything with, there's always the chance to save some IMPs. Could even VP the rounds. I sometimes think with 4 tables a simple teams movement would be sensible.
The problem with both these options really is arranging them in advance, you need to know pair number may be low, and really players should know what to expect when they turn up. Also, teams simply doesn't work with a half pair.
Improvers sessions and sessions with small numbers of tables can each be highly variable.