Beyond 60 tables, the formula for first place in a one-session sectional is 10 * log(t) - 6.02. This log formula is used for all tournaments. What happens when there are 588 tables?

With increasing field size, a bad formula eventually becomes too painfully bad, so it is usually patched. But there is no patch for this formula, and it is used even for the 588-table field. I am guessing that this large of field only occurs for STaCs, but it does occur.

So let's look at this formula for 1175 pairs (588 tables), comparing it to 123 pairs (62 tables).

First place still grows faster than it should, but the increase is reasonable. It is difficult to make intuitive judgments about this, but the facts are that first place for 123 pairs is 11.90 and first place for 1175 pairs is 21.67.

The log portion of the tournament formula punishes the lower awards. For 1175 pairs, they become ridiculous.

For example, in terms of percentiles, 2nd out of 123 is about the same as 15th out of 1175. So they should probably receive about the same award. Second out of 123 awards 8.93 masterpoints; 15th out of 1175 awards .51 masterpoints. (Of course, the section award will be higher, so the 15th-place award is never given out.)

In the field of 123 pairs (62 tables), 7 pairs win overalls. That is 5.7% of the field. In the field of 1175, there apparently are only 25 overall awards. That's only 2.1% of the field. But the true difference worse than that. The 25th overall award, if it was actually given, would be for .03 masterpoints. The award for 12th place was a meager 1.22, suggesting that at most 12 overall awards are functional. That corresponds to only 1% of the field.

I have been considering just the A overall awards. If only A overall awards were given, the field of 123 pairs would award .335 masterpoints per person in overalls, and the field of 1175 would award .078 masterpoints per person in overalls. That's a discrepancy of 332%. Of course, section awards would ameliorate this difference considerably. On the other hand, it is fair to say that in the large field, people are paying extra for both increased section awards and the possibility of an overall. In the very large field, the expected gain from the overall is essentially irrelevant.

Bottome line, the tournament formula punishes the lower awards in larger fields, to the point of being ridiculous for the 1175-pair field.

If meaningful overall awards were always given to 5.7% of the field, there would have been 67 meaningful overall awards in the field of 1175 pairs. That seems unimaginably large. But a field of 1175 pairs is unimaginably large. If you were playing in it, you would find 67th overall to be just as difficult to obtain as 7th in the field of 123 pairs.

This just illustrates the same point that can be made with smaller fields -- the formulas aren't good. I suspect that no one even considered the possibility of 1175 pairs in a one-session sectional. But a good formula would work for any size of field.