## Club Games: Effect of Field Size

### The Club Formula

The current formula for club games is that the first place award is the number of tables multiplied by .10 masterpoints. Second place receives 70% of first place award. (Everything is rounded up if needed.) Third place receives 50% of the first place award. That is very close to being 70% of the second place award. Fourth place is 50% of the second place award and 70% of the third place award. The first 40% of the finishers (rounded to the nearest integer) receive awards.

There are patches to this formula for large club games. First of all, when there is a fifth place award, it is 57% of the fourth-place award, and the sixth place award is approximately 83% of the fifth place award. This patch is good -- dropping awards by 70% is inappropriately large, especially at these lower awards.

Second, 1.50 is the ceiling for first place -- no matter how many tables are playing, the largest award for a regular game is 1.50. The subsequent awards however are proportional to what the first-place award would have been, but for 17-tables the second and third-place awards are also capped.

This too is appropriate in its way, because the awards for club games inappropriately increase too much with larger fields. So, essentially, the madness stops at 15 tables. But it still isn't good. The reality is, winning a 20-table field is better than winning a 15-table field, so it should receive a higher award. And one perhaps unfortunate consequence is directors dividing a large field into two sections. If they want to do that, fine, but they shouldn't have to be doing it just to increase masterpoints awards (per person).

### Masterpoints per Person

Table 1 lists masterpoints per person for club games. It is compared to my formula for clubs games, which is .8 * log(t/(r-.5)).

Number of Tables | 5 | 10 | 15 |

Club Formula | .170 | .255 | .292 |

Log Formula | .244 | .255 | .259 |

The club formula shows considerable variation across the normal range of a club game -- there is a 72% increase from 5 tables to 15 tables. There is no need for this variation. My log formula has a 6% increase from 5 to 15 tables. (With my formula, a 100-table game would award .265 masterpoints per person, so there is only a 9% increase from 5 to 100 tables.)

Without the patches, the 15-table game would have awarded .298 masterpoints per person. Without the patches, a 20-table game would offer .310 masterpoints per person; with the patches, it offers .281 masterpoints per person. (In practice, 20-table fields are divided in two.)

### First Place

The first place pair in a 5-table game receives .50 masterpoints. It is possible to calculate how many masterpoints this pair would be expected to win if it had been a 10-table game or a 15-table game. This value should be about .50 -- we are assigning no more or less merit to this pair, we are just putting them in a larger game. The actual values, for the club formula and for the log formula:

| 5 tables | 10 tables | 15 tables |

Club Formula | .50 | .78 | .97 |

Log Formula | .80 | .79 | .78 |

Thus, the first-place pair in the 5-table game would be expected to win 94% more masterpoints in the 15-table game. Of course, masterpoints per person is increasing, but it is increasing only 75%. This shows that the increase in masterpoints per person, as the number of tables increases, is going moreso to the elite players than the regular players.

### Regular Players

Imagine a regular player with little chance of winning but some chance of receiving an award. In the 5-table game, that player has a good day and comes in 2nd. What if the player had been in a 15-table game?
If they have the same good day and finish in the same percentile, they will be either 4th, 5th, or 6th in the 15-table game. So, ideally, the second place award in the 5-table game should equal the average of the 4th, 5th, and 6th place awards in the 15-table game.

| 5 tables | 10 tables | 15 tables |

Club Formula | .35 | .425 | .36 |

Log Formula | .42 | .425 | .427 |

As can be seen, increasing table size has little effect on the smaller awards. In fact, it even decreases from 10 to 15 tables. So most of the increase in masterpoints per person is going to the elite players.

The patch has exacerbated this problem. With the normal formula, where each award is 70% of the higher award, the expected award for 15-tables would have been .39.

### The "Half-Table" Error

In a 13 1/2 table game, both sections receive the awards for a 14-table game, even though one section has only 13 competitors. This is because awards are based on tables, not competitors. This is a small effect, to be sure. But it is still obviously wrong. (As noted in the discussion of pair versus team events, the formula should be based on number of competitors, not number of tables. This is a serious bug for team versus pair events; the half-table error is minor.)

As a consequence, the most masterpoints per person is awarded in the 13 1/2 table game, .302 per person, and the "short section" in that game actually receives .314 masterpoints per person. That's 85% more than the 5-table game.

### Stratification

The above calculations are just for the awards for the A players in a stratified game. The awards for the B and C players will follow the same pattern -- more masterpoints per person because the sections are larger.

See Stratification for a discussion of some details.