Help Me Workshop A New Scoring System

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Re: Help Me Workshop A New Scoring System

Postby super_dipsy » 21 Sep 2018, 07:35

mjparrett wrote:If the PDL taught me one thing, it is that you won't get consensus on something like this. And generally, if it ain't broke, don't fix it. The scoring system we have here is wonderful and works fine. So let us leave it be. That is not to say yours potentially isn't. But you'll have as many people as currently like/dislike the system in place. Everyone is treated the same by the system and there are no injustices that need solved. So what is the problem?

Actually, as long as this is a system for tournaments, I don't think that is such a problem. If you start a tourney you get to lay down your own scoring rules, and once done people can either choose to join the tourney or not. If they don't agree with the system, they wont join. Agreement is not required :)

NoPunIn10Did wrote:Since this is a fixed-sum system, it wouldn't be hard to numerically transform it to something compatible with our current Elo setup.

Um. Technically yes I guess, but on first glance it looks a much harder job. Instead of a result being a win or a draw (with n players), the system shades the draws based on centre counts. So whereas today you have to balance player strengths and whether they were in the draww or not, you now have to add in another dimension which is how many centres they had or not (only those int he draw of course since centre count is not relevant for losers). I still find the idea sits much more naturally as a tournament-only thing.

I guess the real question is the one of playing behaviour incented by the system. ALL scoring systems have an effect on play, it is just a question of what it would be with this one. There will be better placed people than me to judge this, but if I imagine I was in a tourney with this scoring, how would I play - apart from badly that is

First point is there is no additional lift for a solo. So 2 2ways are the same as a solo. Depending on how many games in the tourney and whether it is all play all etc, this might dissuade a bit from going for the solo. I know that when we introduced the bonus for solos, the solo rate increased. I'm not sure whether you could work something like this into the system? It might be hard without breaking the 0 sum thing. Second point I guess is pretty obvious; since it has a centre count element to it, I think I would be more focused on my end centre count. I don't really know how this would affect things, but I suspect that it would mean that if the game looks to be heading for a draw I would be trying to either maximize my count or as nopun said even think about throwing centres to someone to make the centre count more equal att the top.

But all in all, I think it does a good job of bringing the centre count and draw size factors together. Very neat.

If it would have any value, I can run the model against history to see what it would do, but I think you said you already did that. Is that something you would share? Would it hypothetically have changed the PDL table? Obviously it is pretty artificial because with a different scoring system players would have probably played differently, but it might be interesting.

BTW, I assume that you would handle part game players with some sort of ratio as we do today, possibly including a factor of the centre count when they joined / left? Or since this is for tourneys is the assumption that if a player leaves they get a sub and it is scored as a single player? That's probably an unimportant detail at this stage of the discussion though :)
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Re: Help Me Workshop A New Scoring System

Postby jay65536 » 21 Sep 2018, 16:23

Quick point: two 2ways are not the same as a solo and a loss in my system. That's because if I have a solo and a loss and you have two 2ways, I'd be ahead of you based on the tiebreaks--that's why "most solos" is the first tiebreak.

You have access to more history than me, but I did re-score the top league of the PDL. (Of course, as you point out, this must be taken with a grain of salt since the players were playing for a different system than mine.) It did change the order of the table somewhat, but not at the top. Basically it changed the table in 2 ways:

First, there were 7 players all of whom had one 3way draw and two losses. (Only 6 players did better than this, and their order of finish was unchanged relative to the real PDL table.) In the PDL system, all of these people were tied at 10 points (except for one who surrendered and lost some), and separating them came down to tiebreaks. The PDL tiebreak was total center count across all 3 games, minus the number of times you played Russia. So in that system, if you racked up centers but then lost to a solo, your centers helped you in tiebreaks. The table was never completed, so I'm not entirely sure how the 6-way tiebreak shakes out, but I do know that The Tibetan Blackbird would have led the tiebreak. In my system, it's not a 7-way tie to begin with; there are 4 players at 84, one at 78, and two at 75--some of the players allowed a big board top by someone else, which loses points relative to an equally shared draw. The 4-way tie was broken by the fact that of the 4 players at 84, only one of them (StarkAdder) topped the board while getting that 3way draw. The two-way tie at 75 was broken by center count in the draw, not total center count. So, for example, The Tibetan Blackbird drops from 7th to 13th. DirtyHarry, instead of being 11th or 12th, is tied for 8th. StarkAdder is 7th.

Second, there were 6 players with all losses. In the PDL system, the center count tiebreak is still there to separate those players. In my system, it's just a tie--my system deliberately does not differentiate between losses.

Now what would be really interesting is to re-score the 2017 PDET--I think some of those games would have actually tested my system and majorly changed the tournament table--but that's a LOT of games and I probably don't have time to go back and look at them all.
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Re: Help Me Workshop A New Scoring System

Postby jay65536 » 27 Sep 2018, 23:51

So I'm coming back to this thread and there are 2 points that I took away that could potentially improve my system:

1. Changing the advantage multiplier to 8.4 instead of 6. What that means is that there would then be 2 different ways of getting 126 points: either get a 2way, or get 17 centers in any size draw while your closest competitor has 11 or fewer. This would be analogous to how there are 2 different ways to get 84 points: an equally shared 3way or having 10--12 centers and a more-than-1-center lead in any size draw.

2. Breaking the zero-sum aspect to give more points to a solo (378 is probably a good number for that).

What do people think, particularly about #1?
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Re: Help Me Workshop A New Scoring System

Postby jay65536 » 18 Feb 2019, 19:44

So I had some free time to think over some more of the feedback I got the first time I made a thread for my scoring system. I've substantially revised it. Anyone still interested in giving feedback, I'd love to hear it. In particular the complaint that my system rewards throwing centers to 2nd place has been heard and (I believe) taken care of.

jay65536 wrote:My system is an attempt to make a hybrid of draw-based scoring, which a lot of the online community seems to prefer religiously, and lead-based scoring, which is very popular in FtF because it's shown to make for more fun games in that setting. Here is how it works:

-Each game is worth a total of 180 points. If you lose, you get 0. If you solo, you get 180. If you get a 2way, you get 90. In any draw in which the highest center count is 6 or fewer, the 180 points is equally split.
-In any other draw result, scoring consists of two steps: (1) We first compute the "top score" for the board. (2) The top score is taken away from the total of 180, and that number is divided by the number of draw participants minus 1. Call this the "bottom" score. All draw participants who finish 2 or more centers below the top center count earn the bottom score. All players who finish within 1 center of the lead equally split the remaining points (i.e. the top score plus however many bottom scores it takes to match the number of players).

The only other details of this system are how to compute the top score. Here is how it works:
1. If the highest center count is 7--9, the top score is 45.
2. If the highest center count is 10--12, the top score is 60.
3. All higher center counts simply add 6 points per center. So for 13--17, it would go 66/72/78/84/90.

That's pretty much it.

Examples:
1. A 3way draw where the highest center count is in the 10--12 range will be 60 points per draw participant. The top score is 60, and the bottom score is 120/2 = 60.
2. A 3way draw with a center split of 14/11/9: top score 72, bottom score 108/2 = 54. Points are split 72/54/54.
3. A 3way draw, 13/12/9: top score 66, bottom score 57. The 9-center power gets 57 but the top 2 players each get (66+57)/2 = 61.5.
4. A 4way draw where the top center count is 7--9 will be equally split, since the top score is 45 and the bottom score is 135/3 = 45.
5. A 4way draw, 15/7/7/5: top score 78, bottom score 102/3 = 34. Points split 78/34/34/34. (Note that an equally split 5way draw is worth 36 points in this system, while an equally split 6way is worth 30. This bottom score is in the middle, showing that there is a significant penalty for allowing one player to get a lead like this!)
6. 4way draw, 10/9/7/6: top score 60, bottom score 40. Points split 50/50/40/40 (the top two players equally split 60+40).
7. 5way draw, 8/8/7/6/5: top score 45, bottom score 135/4 = 33.75. The top 3 players will equally split 45+33.75+33.75 = 112.5, so the scores are 37.5/37.5/37.5/33.75/33.75.

Since I imagine this system requires tiebreaks, here's what I thought to use:
1 - Most solos
2 - Most games outscoring your opponents
3 - Most games topping the table
4 - Highest-scoring draw result (all the way down the list if necessary)
5 - Highest center count in best-scoring draw (all the way down the list if necessary)

Any questions or feedback, that's why the thread is here! Interested to hear what people think.
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Re: Help Me Workshop A New Scoring System

Postby NoPunIn10Did » 14 May 2019, 18:35

I missed jay's updates to his system back in February; he asked me via PM to come back and have a look.

I think it's addressed my complaints regarding perverse scenarios. It's still ultimately a draw-sized-scoring system and comes with those downsides, but it's interesting that as you become the board-topper, you care less about the remaining number of players in the draw and more about your own center count (and the lead you have over others).

If we were to generalize this system, possibly altering some of the specified exact point thresholds, it might look as follows:
  1. You're dividing up a pie. In this case, it's a 180 point pie, but it wouldn't have to be.
  2. Identify the board-topper: the player with the most SCs. For this step, it doesn't matter who you pick if multiple players are tied.
  3. The first piece cut from the pie is oversized, and it's based on the fraction of the map the board-topper controls.
  4. The board-topper receives that piece but doesn't get to eat it yet.
  5. Every other survivor divides up the remaining pie equally.
  6. Every survivor that came within 1 SC of the board topper becomes part of the "top" group.
  7. Every other survivor (those 2+ centers away from the board topper's total) can eat their pie now.
  8. The top group pools all pie pieces together, including the potentially-oversized first piece, making a new "topper" pie.
  9. Everyone in the top group splits the topper pie evenly.

My suggested name for this scoring approach is Animal Farm Scoring:
All survivors are equal, but some survivors are more equal than others.


Caveat: I'm not 100% sure this system would work as well in a non-DIAS context, but I think it would be something interesting to experiment with otherwise.
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Re: Help Me Workshop A New Scoring System

Postby jay65536 » 14 May 2019, 21:29

NoPunIn10Did wrote:I missed jay's updates to his system back in February; he asked me via PM to come back and have a look.

I think it's addressed my complaints regarding perverse scenarios. It's still ultimately a draw-sized-scoring system and comes with those downsides, but it's interesting that as you become the board-topper, you care less about the remaining number of players in the draw and more about your own center count (and the lead you have over others).


Unless I am missing something, the main drawback of draw-based scoring is the necessity for draw-whittling when people can't solo. But in this system, as long as the board-topper leads by more than 1 center, they don't just care less about the draw size; they don't care AT ALL. As long as the board-topper maintains a lead, their score is 100% a function of center count. This is why I consider this system a hybrid--draw size is all that matters if you are not the leader but it matters not at all if you are.

I am hoping--I have not tested this yet--that what this means in practice is that by removing the leader's incentive to draw-whittle, draw-whittling will become a far bigger risk for the powers who still have a scoring interest in doing so, since there would be a big power possibly opposing their efforts (and presumably teaming up with the smaller powers if they did). The different incentives, I hope, would create enough tension to create interesting endgames.

If we were to generalize this system, possibly altering some of the specified exact point thresholds, it might look as follows:
  1. You're dividing up a pie. In this case, it's a 180 point pie, but it wouldn't have to be.
  2. Identify the board-topper: the player with the most SCs. For this step, it doesn't matter who you pick if multiple players are tied.
  3. The first piece cut from the pie is oversized, and it's based on the fraction of the map the board-topper controls.
  4. The board-topper receives that piece but doesn't get to eat it yet.
  5. Every other survivor divides up the remaining pie equally.
  6. Every survivor that came within 1 SC of the board topper becomes part of the "top" group.
  7. Every other survivor (those 2+ centers away from the board topper's total) can eat their pie now.
  8. The top group pools all pie pieces together, including the potentially-oversized first piece, making a new "topper" pie.
  9. Everyone in the top group splits the topper pie evenly.


1. I only used the number 180 because it is divisible by lots of small integers like 2, 3, 4, 5, 6, and 9. That way the fractional pieces of the system are represented as integers still. Other than that, there is obviously nothing special about the total points.

3. So, the way the system came out, it seems like it is (based on fraction of board size), but it's not. These are the considerations that went into the top score:
(i) An equitably shared 4way draw is 9/9/8/8 or else 9/9/9/7. So I fixed the top score for 7--9 centers at 45 (180/4) to ensure that if you are topping the board with 7--9 centers, you have no incentive to either draw-whittle or randomly dot your draw partners unless you get up to 10+ centers in the process. (Note: 7 is the smallest number of centers it is possible to have while holding a lead of 2 or more centers.)
(ii) The top score for 10--12 centers is fixed at 60 for an analogous reason: 12/11/11 and 12/12/10 are the equitably shared 3way draws, and the same logic applies.
(iii) Since a 17/17 2way draw earns 90 points in this system, the top score for 17 centers should be fixed at 90, so that there is no incentive to draw-whittle in this case either.
(iv) The scores in between 60 and 90 are computed by making each center greater than 12 but short of a solo worth an equal number of points, which in this case is 30/5 = 6.

This sort of logic is almost certainly adaptable to any or almost any variant, which I presume is what you're going for here.

My suggested name for this scoring approach is Animal Farm Scoring:
All survivors are equal, but some survivors are more equal than others.


I think maybe a simpler name is Two-Tier Scoring? Because while this system allows for different scores for draw participants, there are never more than two distinct scores (as opposed to Calhamer points where there is always one, or a different system where there may be a different score for each player).

Caveat: I'm not 100% sure this system would work as well in a non-DIAS context, but I think it would be something interesting to experiment with otherwise.


I'm not sure why you think this system wouldn't be OK in a non-DIAS context. Interested to hear what makes you think that.

I am glad to know that at least one other person (besides myself) likes this system enough to want to try experimenting with it. I'd be very interested to see how an idea like this plays in practice, and in particular the kind of reactions/opinions it gets from a player pool that is used to draw-based systems (part of why I posted it here).
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