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Teams Versus Pairs

Changing the massive discrepancy between team and pair events

The Formula

Criteria for a good formula, problems with the current formulas, and a better formula.

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OKBridge has the following formula (except for one presumed patch). The first place award is the number of pairs in the tournament times .10. The second place is 3/4 of this. The remaining awards follow a pattern: 3rd is 1/2 of first, 4th is 1/3 of first, 5th is 1/4 of first, etc.

Of course, it is "illogical" that the second place award doesn't follow the pattern -- if the pattern was "right", it would be used for all of the places. The problem of course is that the pattern isn't perfect and the awards better fit what they should be because of this "illogical" assignment of the second place award.

The top 20% receive awards. This is more than receive overall awards in ACBL tournaments (except for very small field sizes), and more than the 10% I suggested. However, an ACBL tournament will also award section awards, so that ultimately about 40% of the participants win awards. So 20% turns out to be a little stricter than the ACBL awards.

The OKBridge formula is very much like the club formula used by the ACBL. As for that formula, larger fields receive more points per person. When there are 50 pairs, .358 points per person are awarded; when there are 100 pairs, .430 points per person are awarded. That's an increase of 20%. 20% isn't bad, but I would still rate it as undesirable, especially since this is only doubling the size of the field. However, the current OKBridge fields rarely are larger than 100 pairs.

As discussed elsewhere, a formula can also be tested for it's performance at the top and bottom of the masterpoint awards. At the bottom, this formula is nearly perfect. For example, 10th out of 50 should equal the average of 19th and 20th out of 100. Ignoring the rounding error, 10th of 50 is .556 points and 19th/20th out of 100 is .541 points, a discrepancy of 3%. That's very good.

However, because the masterpoints per person is increasing as field size increases, the fact that it is staying about the same at the bottom just means that the increase is occuring all at the top. And that's not good. The first place award for a field of 50 is 5.00. That same pair's expected award in a field of 100 is 7.81, an increase of 56%.

If this formula was followed for smaller fields, the consequences would be disasterous (relatively speaking). A game with 18 pairs (the smallest size I observed) would award .258 points per person, creating 66% increase from 18 pairs to 100.

Fortunately, the formula was patched. The smallest first place award is 5.00. The smallest second place award hence is 3.75, and so on, with again 20% of the field receiving awards.

Unfortunately, this overcompensates. The 18-pair field awards .718 points per person. That's a 100% increase over the 50-pair field.

Fortunately, this error tends to be self-correcting. When a small field does not award enough points per person, it tends to be shunned, making it smaller and exacerbating the problem. That doesn't happen here. OKBridge has the small field awarding too many points, which would tend to attact competitors, at least partially correcting the problem. Of course, I did see one field of 18 pairs.

Self-correcting or not, OKBridge should use a formula that keeps masterpoints per person constant over differing field sizes. Players should be able to choose the events they want and be assured that their choice does not influence their expected point winnings.