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Could this make sense as an alternative scoring system to MPs?

#1 User is offline   smerriman 

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Posted 2018-February-24, 20:40

(Was tossing up whether to post this here or in the BBO discussion forum; while it sprung from daylongs, it's sort of a general scoring idea as well so ended up going here).

I've been thinking a lot recently about the use of MPs in daylong tournaments where not everybody plays the same hands. There have been plenty of threads in the past about the fact not everyone plays the same hands, and that can have a heavy influence on the scores - if you're dealt a flat hand, you might have zero chance of winning the tournament no matter how well you play.

While winning any bridge tournament requires some luck (the optimal line may not succeed), playing the same hands is crucial to MPs, especially the way that ties are worth half a matchpoint.

Suppose for a moment that hands are always dealt in such a way that optimal play works out best. Any scoring method should therefore ensure that optimal play will place you in first place overall.

A starting idea would be to adjust the matchpoint formula so that the top score on each board is 100%. This of course doesn't work because now the situation is flipped - a flat hand that used to be worthless is now overvalued.

However, what if we extend that to the idea of a weighted average. A completely flat board gets you 100% - but that board then carries 0 weight, not counting at all. A board where you beat everyone else gets you 100%, with a full weighting of 1 board. At the end, you add up your weighted percentage, and divide by the number of 'boards' you've played, for your final score.

Consider two types of board:

Hard board: 20% of players will score maximum, 80% minimum.
Easy board: 80% of players will score maximum, 20% minimum.

Person A receives two hard boards, succeeding once and failing once. Under MP scoring, he receives a score of 65%.

Person B receives two easy boards, succeeding both times. Under MP scoring, he only receives a score of 60%.

Person C gets one easy board, and one hard board, winning the easy board only. Under MP scoring, he gets 50%.

Now considered a weighted score. Playing the first board well gets you 100%, and counts as 0.8 boards. Playing it badly gets you 0%, counting as 0.2 boards. The reverse applies to the second board type.

Person A now has a score of (100% * 0.8 + 0% * 0.2)/1.0 = 80%
Person B now has a score of (100% * 0.2 + 100% * 0.2)/0.4 = 100%.
Person C now has a score of (100% * 0.2 + 0% * 0.2)/0.4 = 50%.

Person B wins due to playing optimally. True, it was harder for Person A to win - but at least they had the opportunity, and this will balance out over a larger number of hands. The idea is the harder it is to score well, the more it should count if you do, and the less it should count if you don't. (With weightings based on how everyone else actually played - assumes enough people played to make this realistic).

Thoughts?
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#2 User is offline   manudude03 

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Posted 2018-February-24, 20:57

Who defines whether the play was optimum? And is it optimum line a priori or the optimum line given the information you have. Suppose someone overbids to 6NT where everyone else would be playing 3NT, would the overbidder be allowed to take his 5% line to only make 10 tricks 95% of the time instead of the 100% line to make eleven tricks?
Wayne Somerville
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#3 User is offline   smerriman 

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Posted 2018-February-24, 21:08

Yeah, obviously the above was a very simplified example - but the scoring system itself has nothing to do with whether anyone plays "optimally" or not; that was just an example of how it gives a different result from MPs. Someone who overbids to 6NT will get 100% or 0% at full weighting regardless of scoring.

It's solely a way of weighting hands, based on everyone's actual results for that hand, due to the fact that eg a 50% score on a flat board is not the same as a 50% on a swingy board. (I haven't defined the exact formula for what the weighting would be based on the results.)
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#4 User is offline   aawk 

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Posted 2018-February-25, 05:38

To rate or select boards, play and strength of players is a bad solution who will be the judge of that ?

In MP play (if enough boards are played) the better players will always float to the surface anyway. Just accept that there is a (small) unfairness in MP play.

My tip is play teams that is the purist form of bridge you can get.
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#5 User is offline   gwnn 

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Posted 2018-February-25, 08:14

I'm not sure what the point of this is. Maybe I should try to reread it more carefully. Board 1 and 2 are the same board, just upside down, right? I mean, NS's Board 1 ("easy") is EW's Board 2 (also "easy").
... and I can prove it with my usual, flawless logic.
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#6 User is offline   kernow 

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Posted 2018-February-25, 08:24

this seems a very good idea but i have 2 thoughts, can you not use hands that have been played previously and please discard the top 4 scores and bottom so the idiot results do not unbalance the results
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#7 User is offline   smerriman 

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Posted 2018-February-25, 13:20

View Postgwnn, on 2018-February-25, 08:14, said:

I'm not sure what the point of this is. Maybe I should try to reread it more carefully. Board 1 and 2 are the same board, just upside down, right? I mean, NS's Board 1 ("easy") is EW's Board 2 (also "easy").


I'm primarily thinking of daylongs, where there is no EW. Getting dealt a 'hard' board allows good players to get a good score; getting dealt an 'easy' board drags your score too heavily towards 50%. An 'easy' 50% should drag your score less towards 50% than a 'hard' 50% where you could/should have done better.
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#8 User is offline   smerriman 

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Posted 2018-February-25, 14:07

Also, I just realised the weighting formula is extremely trivial. It's how many people didn't tie your score.

In MPs, if 50% of people do better than you, and 50% of people do worse, it proves you are a 50% player.

If 10% of people do better than you, and 10% of people do worse, it proves you are somewhere between a 10% and a 90% player. MPs assigns a score of 50% - too small for good players, and too large for lesser players.

In my proposal, the first score would count towards a full 50% - the second score would only count as 0.2 of a board to counterbalance this.
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#9 User is offline   nullve 

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Posted 2018-February-26, 03:31

View Postsmerriman, on 2018-February-24, 20:40, said:

Consider two types of board:

Hard board: 20% of players will score maximum, 80% minimum.
Easy board: 80% of players will score maximum, 20% minimum.

Person A receives two hard boards, succeeding once and failing once. Under MP scoring, he receives a score of 65%.

Person B receives two easy boards, succeeding both times. Under MP scoring, he only receives a score of 60%.

Person C gets one easy board, and one hard board, winning the easy board only. Under MP scoring, he gets 50%.

Now considered a weighted score. Playing the first board well gets you 100%, and counts as 0.8 boards. Playing it badly gets you 0%, counting as 0.2 boards. The reverse applies to the second board type.

Person A now has a score of (100% * 0.8 + 0% * 0.2)/1.0 = 80%
Person B now has a score of (100% * 0.2 + 100% * 0.2)/0.4 = 100%.
Person C now has a score of (100% * 0.2 + 0% * 0.2)/0.4 = 50%.

Person B wins due to playing optimally. True, it was harder for Person A to win - but at least they had the opportunity, and this will balance out over a larger number of hands. The idea is the harder it is to score well, the more it should count if you do, and the less it should count if you don't. (With weightings based on how everyone else actually played - assumes enough people played to make this realistic).

Suppose that prior to this, A has scored better than B overall over the course of a zillion same-board tournaments. Then maybe A was just unlucky to get two hard boards now while B got two easy ones?

If true, why is A's bad luck under your MP scoring more acceptable than B's bad luck under standard MP scoring?

If not true, why?
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#10 User is offline   barmar 

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Posted 2018-February-26, 08:59

In short matches, like the 8-board daylongs, there's enough variance that there's probably no really good scoring method. Even if this idea has merit, it will probably only be a minor improvement.

The real solution is longer matches. The more boards you play, the less impact a few extreme boards have, especially in MP scoring. As I said in another thread, this is why the NABC Online is 3 days of 24 boards. Even with players not all playing the same boards, 72 boards is enough for skill to win out. Each board has less than 1% influence on your final score, and weighting them would make an almost negligible improvement.

Consider rubber bridge. It's not unusual to win a particular rubber due to getting good cards. But if you play a few dozen rubbers, your luck can only hold out so long -- you really need to play well to win consistently.

#11 User is offline   barmar 

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Posted 2018-February-26, 09:22

View Postsmerriman, on 2018-February-25, 14:07, said:

Also, I just realised the weighting formula is extremely trivial. It's how many people didn't tie your score.

In MPs, if 50% of people do better than you, and 50% of people do worse, it proves you are a 50% player.

If 10% of people do better than you, and 10% of people do worse, it proves you are somewhere between a 10% and a 90% player. MPs assigns a score of 50% - too small for good players, and too large for lesser players.

In my proposal, the first score would count towards a full 50% - the second score would only count as 0.2 of a board to counterbalance this.

I kind of see your point.

If there's a perfectly flat board, it probably "plays itself", and shouldn't count much towards your score.

But if there's a hand where everyone else gets the same result, but you get something different. If you did better than the rest, you presumably did something brilliant to achieve it, and should get a big bonus; if you did worse, you apparently missed something obvious and should be penalized harshly.

But doesn't the MP formula already do that? In the flat board, everyone gets 50%, which has little effect on the final score (all those players' scores are just dragged a little towards the middle). On the second board, if it's played by 25 total players, you get 100% or 0% while the others get 48% or 52% -- this will have a more significant effect on your final score than theirs.

This is, of course, dependent on the assumption that scores tend to cluster around 50%. If you were having an 80% game and then get a bottom board, that zero will drop you to 68% in an 8-board tourney, while an average would have resulted in 74%, still a really good final score. But as I mentioned in my previous reply, longer matches mitigate this -- in a 24-board tourney it's 76% versus 78%.

#12 User is offline   smerriman 

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Posted 2018-February-26, 13:24

View Postbarmar, on 2018-February-26, 09:22, said:

But doesn't the MP formula already do that? In the flat board, everyone gets 50%, which has little effect on the final score (all those players' scores are just dragged a little towards the middle). On the second board, if it's played by 25 total players, you get 100% or 0% while the others get 48% or 52% -- this will have a more significant effect on your final score than theirs.

MP does that perfectly - if everyone else plays the same boards. Your score isn't affected compared to the players who played the same board - but it is affected compared to those who didn't.
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#13 User is offline   smerriman 

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Posted 2018-February-26, 13:59

View Postnullve, on 2018-February-26, 03:31, said:

Suppose that prior to this, A has scored better than B overall over the course of a zillion same-board tournaments. Then maybe A was just unlucky to get two hard boards now while B got two easy ones?

If true, why is A's bad luck under your MP scoring more acceptable than B's bad luck under standard MP scoring?

If not true, why?


You're right, of course - in reality, there is simply no way to compare A and B based on the hands they received.

However, I would rather receive a lower score because *I* had the potential to do better - vs receiving a lower score because *others* had the potential to do better.
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#14 User is offline   barmar 

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Posted 2018-February-27, 10:16

View Postsmerriman, on 2018-February-26, 13:24, said:

MP does that perfectly - if everyone else plays the same boards. Your score isn't affected compared to the players who played the same board - but it is affected compared to those who didn't.

The expectation is that most players should get about the same proportion of swingy versus non-swingy, or hard versus easy, boards, even if they don't get the exact same boards.

#15 User is offline   smerriman 

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Posted 2018-February-27, 13:16

Yup, they should, on average - but statistically some are guaranteed to get more than average, and some are going to get less than average. Weighting them as described above removes this variation completely.
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#16 User is offline   barmar 

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Posted 2018-February-28, 09:31

I don't think any method can really help much with an 8-board tourney. This might be an improvement, but only slightly, and probably not worth the confusion of having an ideosyncratic scoring method.

#17 User is offline   Vampyr 

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Posted 2018-March-01, 11:12

The one thing that could possibly be done is the matchpoints could be normalised — the values could be stretched or shrunk to fit along a pre-arranged scale.
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#18 User is offline   barmar 

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Posted 2018-March-02, 09:37

View PostVampyr, on 2018-March-01, 11:12, said:

The one thing that could possibly be done is the matchpoints could be normalised — the valuescould be streched or shrunk to fit along a pre-arranged scale.

In online games we convert matchpoints to percentages.

In f2f games with sit-outs, or sections of different sizes that play different numbers of boards, this is done by factoring.

#19 User is offline   Vampyr 

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Posted 2018-March-02, 19:19

View Postbarmar, on 2018-March-02, 09:37, said:

In online games we convert matchpoints to percentages.


Yes. Perhaps I didn’t express myself well, or maybe what the OP wants cannot be achieved. Since presumably the number of stanzas played vari s widely, how are player scored against one another?
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#20 User is offline   smerriman 

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Posted 2018-March-02, 21:20

You play 8 hands. Each hand is against a different group of people. Your average matchpoint score is your total score.

If you look at the top scorers in every tournament, you'll see their win is always due to all 8 boards being 'swingy'. The last couple of times I've gotten in the top 200, one or two hands were in the 50-60 percentages where I couldn't do better, which immediately ruled out winning.

I actually think my suggestion would have considerably more than just a slight effect, but understand the complexities of implementing it.

(Though, to be fair, MP where everyone plays different boards is pretty ideosyncratic too! BBO scoring is very unique compared to any other tournament.)
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