Help Me Workshop A New Scoring System, version 3

[jay65536]

So awhile back I made a thread about a new scoring system I was developing, and I included a modification based on feedback I received. I have modified it again and was reminded of it seeing the scoring system thread revived. Once again I am looking for feedback. In particular, as with the previous thread, I'm most interested in hearing feedback from players who are used to draw-based scoring, which is why I'm posting it here (though I welcome all feedback).

My system is an attempt to make a hybrid of all three criteria that are usually used for tournament scoring--draw size, center count, and center lead. It's an attempt to provide multiple ways to obtain a good score. So, in my optimistic view of the system, if you like playing for a small draw, you can get a good score that way. If you like to push for a solo and you get stopped by a large coalition of powers on your way to 18, you can get a good score that way too. It's my attempt to create a system that rewards multiple styles as long as they are executed well.

Here is how it works:

-Each game is worth a total of 180 points.
-A solo is always worth 180 points, and a loss is always worth 0.
-If exactly 2 players share a draw, they each earn 90 points.
-If a draw is called when no one has more than 6 centers, the points are equally split among draw participants.
-In all other draw results, we then find the "top score" for the board, which is a function of the highest center count and the number of players who qualify for the top score. To qualify for the top score, you must have either the highest center count or exactly 1 fewer center.
-If the board's top score times the number of draw participants is less than 180, the top score is ignored and the points are equally split among draw participants. [Note: this only happens in extreme edge cases, as you can see below.]
-In all other cases, all players who qualify for the top score receive the top score, and all remaining points are then equally split among all remaining draw participants.

The only thing that remains is to find the top score. It works like this:
If 1 player qualifies:
7 centers: 54
8 centers: 57
9 centers: 57
10 centers: 60
11 centers: 60
12 centers: 60
13 centers: 66
14 centers: 72
15 centers: 78
16 centers: 84
17 centers: 90

If 2 players qualify:
7 centers: 48
8 centers: 49.5
9 centers: 49.5
10 centers: 54
11 centers: 60
12 centers: 60
13 centers: 61.5
14 centers: 63
15 centers: 64.5
16 centers: 66
17 centers: 67.5

If 3 players qualify:
7 centers: 45
8 centers: 45
9 centers: 45
10 centers: 54
11 centers: 54
12 centers: 60 [Note: this can only happen in a 12/11/11 3way, so this is an equal split]

If 4 players qualify:
7--9 centers: 39.375

If 5 players qualify:
7 centers: 31.5

(I should note that everything past 2 players, I would consider an extreme edge case...)

And that's it. No other provisions.

Examples:
-A 12/11/11 3way draw is 60 points each. So is a 12/12/10.
-A 14/10/10 3way draw breaks down as 72/54/54.
-A 15/14/5 3way draw breaks down as 64.5/64.5/51.
-A 9/9/8/8 4way draw is worth 45 points each (since 39.375 * 4 is smaller than 180). So is a 9/9/9/7 4way draw.
-A 15/8/7/4 4way draw breaks down as 78/34/34/34.
-An 11/10/7/6 4way draw breaks down as 60/60/30/30.
-A 10/8/6/6/6 5way draw breaks down as 60/30/30/30/30.
-A 10/10/9/5 4way draw breaks down as 54/54/54/18.

Like I said, any feedback welcome!

[Shyvve]

Jay,

First, I know you've put a lot of time and thought into this for a good while now. So, thanks for that. In general I like your approach of trying to find a hybrid system that factors in draw size, center count and center count lead.

I've worked through the examples you cite for various outcomes. One thing which occurred to me though, is what happens in the extremely rare cases of large draw sizes (6- or 7-power draws). Again, these are definitely extremely rare outcomes but it's interesting to see how they play out under your system.
You specify that when draws are called in which no one has more than 6 centers, that the 180 points are divided equally among all draw participants. So, a 6wd draw yields 30 points and a 7wd draw gives 25.7 per player.
In the last example you show, "-A 10/10/9/5 4way draw breaks down as 54/54/54/18", the 5-center power is actually getting less points than would be earned from a 6wd or 7wd. Granted, part of this is because at least one player in the 4wd example has exceeded 6 centers (two players in this case are at 10). But, on the face of it, it would seem like being in a 4wd 'should' earn more points than any 6wd or 7wd, no?

[Custer]

I think in 6 or 7 way draws, all players should be awarded zero points. Takes care of that.



The SHIV

[NoPunIn10Did]

I guess one issue I see here is that you're creating an incentive for those who aren't in the lead to do one of the following:

1. Match the leader or become the leader outright.
2. Make sure the leader is at least 2 centers higher than anyone (other than yourself).

Goal #1 is great. Goal #2 is worrisome.

[Cinemascifi]

It appears to me that this system rewards volume of games over quality of games.

Example :

player A played 3 games, 1 of which was a solo, and the other 2 were losses. 180 points.

Player B played 100 games, and managed three 2-way draws. All other games were losses. 270 points.

Seems a bit unfair that someone with a 97% loss ratio, with no solos, should outrank someone with a 67% loss ratio and 33% solos.

[Mr.E]

In fairness, I'm assuming this is a tournament system, where volume of games should matter. We're not, I'm assuming, suggesting this as a scoring system for an on-going series of games. This isn't a potential site scoring system, for instance.

For me, any scoring system should really be ignoring SC count in any form, other than did I finish on 18+ SCs or none. But this is tournament scoring where there are a small number of games involved and SCs count is probably the only widely accepted way to differentiate between players in such a small number of games.

Not the only way, I should add, but probably the only widely accepted way. Comparative scoring across games, based on powers played isn't generally liked... and even those systems tend to be based on SC count in a small-minded way.

One other thing I'd say is I've come to think that a draw between x powers is no different than a draw between y powers. If all powers in a draw received the same number of points, then it would go a long way to prevent draw-whittling.

The difference would be in the scores recorded for the players who were eliminated or not included in the draw.

So in games that ended in a 5-way draw and a 3-way draw, the players that drew the games would receive the same number of points, but the players who lost the games would score differently.

In the 5-way draw, the two losing players would lose fewer points than those in the 3-way draw. This is based on the preposition that it's easier to get a 5-way draw than a 3-way draw.

I think Jay's system is intriguing, better than any system that is purely based on SC count (in any form). But I think it would need testing as a shadow scoring system over some tournaments.

[NoPunIn10Did]

It appears to me that this system rewards volume of games over quality of games.

Example :

player A played 3 games, 1 of which was a solo, and the other 2 were losses. 180 points.

Player B played 100 games, and managed three 2-way draws. All other games were losses. 270 points.

Seems a bit unfair that someone with a 97% loss ratio, with no solos, should outrank someone with a 67% loss ratio and 33% solos.

The system is framed here as a fixed-sum system. It assumes all players are playing the same number of games in a tournament. Were it used in an ongoing online environment, it’s trivial to convert it to a zero-sum system.

[jay65536]

So, to respond to Shyvve and NP:

The particular case of the 54/54/54/18 was actually thrown in there to represent a bad edge case (trying to be fair-handed in my self-analysis). I do think in that instance it is a bit of a raw deal that one player receives only 18, whereas if the game ended 11/10/9/4 instead, the breakdown would be 60/60/30/30.

This leads into NP's critique that the system contains "perverse incentives" for the small powers to want as few players qualifying for the top score as possible. I have thought about this, but the issue is that when designing this system, it seems like I have to have some kind of "perverse incentive" trade-off.

Here's what I mean. Let's imagine we have an endgame where the center counts are 10/10/7/7. If a 4way is called under my system, version 3, the scores are 54/54/36/36. (Notice that 36 is the score for an equal 5way, even though this is a 4way.) So if both 7-center powers threw one dot to the same 10-center power, it would be 12/10/6/6 and the new scores would be 60/40/40/40. The two small powers gain points while losing centers. This is a "perverse incentive" we want to avoid.

But now look at version 2 of my system, where we fix the bottom scores first. In an 10/10/7/7, the breakdown now would be 50/50/40/40. Now there is a different perverse incentive: the two powers tied for the board top would gain points by draw-whittling. If they colluded to hand all of one 7-center power's dots to the other, the final center count would be 14/10/10, so the two tied powers have actually gained points while NOT gaining centers AND giving up their board-topping status!

This is actually why I thought my system needed a revision--because I realized version 2 did not handle joint board tops in bigger-than-3way draws well at all. NP, your story from Dixie stuck with me in this case, about the 4-power endgame where you guys flipped a coin. In my old system, those two big powers would be getting 50 points each and therefore have a reason to keep trying to draw-whittle, not taking the 4way. In my new system, they'd already have their board-topping points as long as they had 11+ centers, so draw-whittling (at least without picking up significant centers) becomes less of a big deal.

I am definitely open to ideas on how my system can handle ties better. But like I said above, one important thing to me is to make sure that board-toppers don't have an incentive to draw-whittle. I think (and I think you'd agree) that when there is only one board-topper, my system handles this well; it also, I believe, handles things well when there are 2 board-toppers in a 3way draw. Beyond that, it starts to get dicey.

A really simple way to do this is to break zero-sum; it could then be that the top and bottom scores are fixed, top scores by center count and bottom scores by a combination of top score and draw size (and also solos could be worth more). Maybe another palatable way to do it is to just declare that in any 3+-way tie for board top, but not 2-way tie, the draw is equally split. Version 1 wasn't good because of the incentive to make 2-way ties; but perhaps if that incentive were taken away, the perverse incentive to engineer 3-way ties would be nullified by how hard it is to do (and the *actual* incentive of two of the tied powers to break the 3-way tie by gaining centers).

What do you guys think?