[riverwalk3]

It seems like the masterpoint formula rewards events with more players. A fair formula would have total masterpoints awarded increase linearly with the number of players, but it seems to increase quadratically. The current formula means that if you get each place with equal probability, you gain more masterpoints per tournament on average in larger tournaments. In a fair formula, if you score each place with equal probability, you get the same amount of masterpoints per tournament no matter the tournament size.

This means that you can spend a lot of money on a tournament, but if only a few players show up, you won't get much bang for your buck no matter how well you do. On the other hand, the daylong tournaments give insane amount of points and are relatively cheap due to the number of players that play them.

[Douglas43]

 riverwalk3, on 2022-May-25, 20:34, said:

It seems like the masterpoint formula rewards events with more players. A fair formula would have total masterpoints awarded increase linearly with the number of players, but it seems to increase quadratically. The current formula means that if you get each place with equal probability, you gain more masterpoints per tournament on average in larger tournaments. In a fair formula, if you score each place with equal probability, you get the same amount of masterpoints per tournament no matter the tournament size.

This means that you can spend a lot of money on a tournament, but if only a few players show up, you won't get much bang for your buck no matter how well you do. On the other hand, the daylong tournaments give insane amount of points and are relatively cheap due to the number of players that play them.

If it's BBO points I can't comment because I've not seen the formula. Would you mind posting it please? The EBU does the opposite to what you describe, and masterpoint awards grow more slowly as the numbers of entries get higher.

[riverwalk3]

 Douglas43, on 2022-May-25, 23:11, said:

If it's BBO points I can't comment because I've not seen the formula. Would you mind posting it please? The EBU does the opposite to what you describe, and masterpoint awards grow more slowly as the numbers of entries get higher.

I don't know the exact formula for BBO points, but:

In BBO points the reward for Daylong tournaments is really high due to the number of participants. The winner gets nearly 30 points for example, and the points seems to decrease linearly rather than exponentially. The average number of points rewarded per participant was 1.39 in the last Zenith tournament that I played from a spreadsheet calculation. My best performance on a Zenith daylong tournament was about 30th place, which got me over 14 BBO points. On the other hand, a Robot Rebate tournament might only have 3 participants, in which the winner only gets 0.18 masterpoints (or about 0.06 average). Both cost $1 and the Zenith has a higher percentage of cash-out (generally 1/3 of the players get 55% from my experience, so the Rebate tournament has a payout ratio of 0.5 while the Zenith tournament has a payout ratio of 0.8).

ACBL seems to segment, so your score is only compared against 15 or so other players. Usually the winner doesn't get more than a reasonable number of masterpoints (such as 1.5).

[smerriman]

It's the same as the ACBL formula: https://blog.bridgeb...bo-points-work/

[riverwalk3]

 smerriman, on 2022-May-26, 00:46, said:

It's the same as the ACBL formula: https://blog.bridgeb...bo-points-work/

For daylong tournaments the top reward does not cap out at 15 tables. It seems indefinite.

[barmar]

 riverwalk3, on 2022-May-26, 01:25, said:

For daylong tournaments the top reward does not cap out at 15 tables. It seems indefinite.

That's correct. We felt that defeating thousands of other players should be rewarded far more than beating just a few dozen players.

Here's the formula for BBO daylongs with 12-17 tables.

The award for 1st place is 0.06/table for the first 15 tables + 0.03/table for the next 45 tables + 0.015/table for all the rest. Since most daylongs have far more than 60 tables, it's basically linear. I think the formula for the fist 15 tables was chosen to be the same as the section awards in traditional tourneys, the others just came out of someone's a** were arbitrarily chosen adjustments.

Points are awarded to the top 40% of the field, and the last award is 0.01.

The points in between are calculated using exponential decay.

If there are 18 or more boards, the points for 1st place are increased by 25%. If there are fewer than 12 boards, the top award from the above calculation is multiplied by boards/12. The rest of the calculation remains the same.

ACBL daylongs and the NABC Robot Individual are completely different.

[fhacker]

Riverwalk takes issue with the fact that large events pay many more masterpoints than small ones and that this is unfair financially to people unfortunate enough to find themselves in a small event. The ACBL awards points based on the number of tables in an event and the type of competition (club, sectional, regional national, etc.) The more difficult an event is to win, the more points you get for winning it. Seems fair to me. I believe master points per dollar of player entry fee is an illogical substitute for the traditional parameters.

I do not understand Riverwalks' description of what is fair. I do not understand why he thinks masterpoints increase quadratically instead of linearly. I do not understand what he means by scoring each place with equal probability. He says that the number of masterpoints should be the same regardless of tournament size. I think one consequence of that would be that winners of small tournaments may get more points than winners of large tournaments. That seems a logical consequence of spreading the same number of points among fewer players.

Now for the masterpoint formulas. I usually play in 12 or 18 board games with a single section or a large number of sections. The ACBL requires at least 18 boards to award masterpoints at the full club level. Below that the awards are 60% of club level.

For flight A the 18 board single section formula is .1 times the number of tables up to a maximum of 1.50. For 12 board the formula is .06 up to a max of .9. For multiple section events, there are also overall awards. For 18 board events, these are .1 times the number of tables up to a maximum of 4.00. For 12 boards it's .06 per table up to a maximium of 2.4

This means that the overall award for a 30 table event is 3.00, for a 40 table event, it's 4.00. For 100 tables, it's still 4.00. I'm not sure of the awards for flights B and C. Flight B awards are usually 80% of flight A awards based on the number of tables in flight B and below. Flight B and C partipants are eligible for flight A awards.

None of this seems to be quadratic. It is linear until it levels off.

[riverwalk3]

 fhacker, on 2022-May-27, 17:12, said:

Riverwalk takes issue with the fact that large events pay many more masterpoints than small ones and that this is unfair financially to people unfortunate enough to find themselves in a small event. The ACBL awards points based on the number of tables in an event and the type of competition (club, sectional, regional national, etc.) The more difficult an event is to win, the more points you get for winning it. Seems fair to me. I believe master points per dollar of player entry fee is an illogical substitute for the traditional parameters.

I do not understand Riverwalks' description of what is fair. I do not understand why he thinks masterpoints increase quadratically instead of linearly. I do not understand what he means by scoring each place with equal probability. He says that the number of masterpoints should be the same regardless of tournament size. I think one consequence of that would be that winners of small tournaments may get more points than winners of large tournaments. That seems a logical consequence of spreading the same number of points among fewer players.

Now for the masterpoint formulas. I usually play in 12 or 18 board games with a single section or a large number of sections. The ACBL requires at least 18 boards to award masterpoints at the full club level. Below that the awards are 60% of club level.

For flight A the 18 board single section formula is .1 times the number of tables up to a maximum of 1.50. For 12 board the formula is .06 up to a max of .9. For multiple section events, there are also overall awards. For 18 board events, these are .1 times the number of tables up to a maximum of 4.00. For 12 boards it's .06 per table up to a maximium of 2.4

This means that the overall award for a 30 table event is 3.00, for a 40 table event, it's 4.00. For 100 tables, it's still 4.00. I'm not sure of the awards for flights B and C. Flight B awards are usually 80% of flight A awards based on the number of tables in flight B and below. Flight B and C partipants are eligible for flight A awards.

None of this seems to be quadratic. It is linear until it levels off.

The point is that the total number of masterpoints awarded should scale linearly in the number of players (so the average number of masterpoints awarded per player is the same no matter the event size).

I'm getting a vast majority of my masterpoints from daylongs with the current formula. Scoring 30th place in the Zenith daylong gets you 14 masterpoints, far more than you can in way smaller tournaments even if you get first.

[smerriman]

 riverwalk3, on 2022-May-27, 21:52, said:

The point is that the total number of masterpoints awarded should scale linearly in the number of players (so the average number of masterpoints awarded per player is the same no matter the event size).

This is mathematically nonsensical / impossible.

The basics of awarding points for a single tournament is very straightforward. Coming first is twice as hard as coming second, so second should receive 1/2 the reward of first. Third should receive 1/3 the award, and so on.

Let's consider a basic example - suppose there is a 10-player tournament, we reward the top 40%, and we have 10 "masterpoints" total to give out (obviously way more than real life, just for the sake of nicer numbers).

If the top award is N, then we're giving out N + N/2 + N/3 + N/4 points in total, so want that to add to 10. That makes N = 4.8 - so #1 gets 4.8, #2 gets 2.4, #3 gets 1.6, and #4 gets 1.2.

With me so far?

Now let's say we have a 100 player tournament. By your logic, this tournament should award 100 "masterpoints".

If the top award is N, we're giving out N + N/2 + ... N/40 points total, and want to make that add to 100. That makes N = 23.37. Finishing 5th will give you 4.67 masterpoints, slightly less than winning the 10 player tournament.

But coming 5th out of 100 people is twice as hard as 1st out of 10 people. So a tournament 10 times the size has to give out double the masterpoints to keep the award proportional to the achievement.

Mathematically, the sum 1/1 + 1/2 + 1/x grows proportional to log(x), so the total award for a tournament with N entries should be proportional to N log(N), not linear with regards to N. That extra log factor is what you're seeing with BBO tournaments (as opposed to quadratic).

Yes, if you're a good player, you'll get more masterpoints playing in bigger tournaments. But that's not because the awards for tiny tournaments are wrong; it's because they're too small to gauge your skill level to enough precision (you can't come 'higher' than first).

[riverwalk3]

 smerriman, on 2022-May-28, 01:16, said:

This is mathematically nonsensical / impossible.

The basics of awarding points for a single tournament is very straightforward. Coming first is twice as hard as coming second, so second should receive 1/2 the reward of first. Third should receive 1/3 the award, and so on.

Let's consider a basic example - suppose there is a 10-player tournament, we reward the top 40%, and we have 10 "masterpoints" total to give out (obviously way more than real life, just for the sake of nicer numbers).

If the top award is N, then we're giving out N + N/2 + N/3 + N/4 points in total, so want that to add to 10. That makes N = 4.8 - so #1 gets 4.8, #2 gets 2.4, #3 gets 1.6, and #4 gets 1.2.

With me so far?

Now let's say we have a 100 player tournament. By your logic, this tournament should award 100 "masterpoints".

If the top award is N, we're giving out N + N/2 + ... N/40 points total, and want to make that add to 100. That makes N = 23.37. Finishing 5th will give you 4.67 masterpoints, slightly less than winning the 10 player tournament.

But coming 5th out of 100 people is twice as hard as 1st out of 10 people. So a tournament 10 times the size has to give out double the masterpoints to keep the award proportional to the achievement.

Mathematically, the sum 1/1 + 1/2 + 1/x grows proportional to log(x), so the total award for a tournament with N entries should be proportional to N log(N), not linear with regards to N. That extra log factor is what you're seeing with BBO tournaments (as opposed to quadratic).

Yes, if you're a good player, you'll get more masterpoints playing in bigger tournaments. But that's not because the awards for tiny tournaments are wrong; it's because they're too small to gauge your skill level to enough precision (you can't come 'higher' than first).

You don't get N/2 points for finishing second. In a very large tournament, first might get 30 masterpoints and second would get around 29.

[smerriman]

Oops, you're right, it's a slight different decay curve. But the same point applies - when you sum the values of a decaying curve, you don't get something proportional to N, so it makes no sense to award points as if it was.

In simplest terms, if it were linear, the top 10 out of 100 would have to average the same prize as winning a 10 player tournament, which means half would get less for a more impressive feat. (If all players were equal, you'd come 9th out of 100 less often than 1st out of 10, so should get a bigger reward).

[mycroft]

having said that, the ACBL (and BBO) overalls scale 70% per place, not 50%.

But yes, larger fields (and coming soon to ACBL, it looks like, "stronger fields" *) are worth more to win, because it's more of an accomplishment to do so.

Which has triggered all the "points-hunting 'guests'" conversations (here, with McBruce), and the "combine to build an area game that pushes the rest of the clubs out" conversations (on BW, with several).


* Adding "strength of field" to MP calculations, scheduled for second reading next NABC. My opinion of that, from two units where it's already much harder to get MPs than Toronto, say, or Florida, or the rest of District 16, will have to be inferred, given the givens.

[barmar]

Remember that masterpoints are not a rating system, they're a marketing mechanism. A very successful one -- tournament and club attendance increased significantly when ACBL first created them.

That's why you win more masterpoints for tournaments that charge more -- it's an incentive to play in these tournaments.

BBO doesn't tie masterpoints directly to the price, but the price is tied to the number of boards and the sponsoring organization. So ACBL tourneys cost more than BBO tourneys (because ACBL Masterpoints are considered more valuable than BBO points, and also we have to pay ACBL sanction fees), and 18-board tourneys cost more (and award more masterpoints) then 12- and 8-board tournaments.