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Changing the massive discrepancy between team and pair events


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Masterpoints per Person: The Tournament Formula


The Tournament Formula

For less than 61 tables, the one-session sectional tournament formula for first place overall is 1/6 * (t + 10), where t is the number of tables. All tournament formulas, even the section awards, apparently follow this formula, changing only the factor by which t + 10 is multiplied by.

This is a linear function.

For more than 61 tables in the one-session sectional, the formula changes to 10 * log(t) - 6.02. This is not a linear function.

There is also a lower bound -- 5-tables is enough to use this formula, but a 3-table game is not. (61 tables can use either formula -- the two formulas are designed to produced the same answer for 61 tables.)

Each award after the first-place award is 75% of the previous award. Thus, the second-place award is 75% of the first-place award, the third-place award is 75% of the second place award, etc.

Masterpoints Per Person

The first place award for a 10-pair tournament is 2.50, four pairs (40%) win overalls, and .684 masterpoints per person are awarded. (The same awards are given for a 10-team tournament, with masterpoints per person being twice as high.) For 122 pairs, the first place award is 11.83. There are 7 overall awards (6%), and .336 masterpoints are awarded per person.

So, across the range of this formula, there is a 104% discrepancy.

The log portion of the tournament formula also rewards smaller fields. A field of 124 pairs awards .394 masterpoints person, and a field of 216 pairs awards .254 masterpoints per person. This is a discrepancy of 55%. The overall discrepancy, from 10 to 216 pairs, is 269%. The following table gives masterpoints per person for the tournament formula and also my log formula for tournaments.
Number of Pairs1050122216
MPP: Tourn. Formula.684.368.336.254
MPP: Log Formula.340.375.377.387

Who Benefits?

Linear formulas increase the first-place award much faster than it should increase (as field-size increases). The first place finisher in the 50-pair field receives 5.83. Their expected award in the 100-pair field is 8.00, an increase of 37%. Note that this increase occurs despite the fact that masterpoints per person is decreasing.

The lesser players must be suffering, and this is indeed the case. Consider the award for 5th in the 50-pair field, which is 1.85. If the 100-pair field gave awards to 10% of the finishers, the average award for 9th and 10th would be .875. This is a 111% discrepancy favoring the smaller field.

Of course, the percentage of overalls is not held constant, it actually decreases. The 100-pair field gives out only 6 or 7 overalls, so the actual value for 9th and 10th is zero. Meanwhile, even the 6th place finisher receives an overall in the 50-pair field.

At the extreme. the 10-pair field, with 4 overall awards, hugely favors the regular player.

Now consider the log formula. The expected winnings for first place is only 9% higher for the 248-pair field than for a 124-pair field. This is probably tolerable. However, this same range has a 36% reduction in masterpoints per person, and this decrease is taken out on the lower scores. The 6th place award in the 124-pair field is 2.82, and the average award for 11th and 12th in the 248-pair field is .735, a discrepancy of 284%.

The Ratio Between Awards

In the tournament formula, each award is 75% of the higher award.

Holding this ratio the same, without correcting for field size, is incorrect. It yields absurd results. For example, who could argue that 5th out of 124 pairs is as good as 6th out of 248 pairs? Yet the first outcome receives 3.77 masterpoints and the second outcome the slightly smaller value of 3.54 masterpoints. It is responsible for the fact that larger fields punish regular players.

In defense of the people who constructed the current formulas, they were using a linear function for calculating the first place award. A linear formula, combined with a constant ratio for calculating the lower awards, increase masterpoints per person with increasing field size. If the ratio decreased with increasing field size, the increase in masterpoints per person would have been untolerable.

And with a linear formula, which increases the first-place reward much more than it should be increased (for increasing field size), the reduction in the lower awards is not as obvious.

However, with a proper calculation of the first-place awards, this ratio can be reduced for larger fields, which is appropriate.

Additional reading:

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