Scoring System for Second PDL Season

Suggestions to improve the concept of a PlayDiplomacy League

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Re: Scoring System for Second PDL Season

Postby V » 29 Mar 2018, 22:56

Just commenting on the “Championship” game idea (which happens to not be a favourite of mine) but advance warning of this being a deciding fixture is imperative. By the time we get to round 4 , play decisions attempting to get into 1st spot will be commonplace. If there is a playoff decider then getting above 7th will be the important issue, so could easily change a lot of things for a lot of participants.
Personally I like the idea that the player in #1 spot is the winner. Never liked playoffs.
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Re: Scoring System for Second PDL Season

Postby Riles » 30 Mar 2018, 18:13

V wrote:Just commenting on the “Championship” game idea (which happens to not be a favourite of mine) but advance warning of this being a deciding fixture is imperative. By the time we get to round 4 , play decisions attempting to get into 1st spot will be commonplace. If there is a playoff decider then getting above 7th will be the important issue, so could easily change a lot of things for a lot of participants.
Personally I like the idea that the player in #1 spot is the winner. Never liked playoffs.


I agree, I think a top board is unnecessary in a league of 21 people. In a tournament with a lot of people a top board brings together the top performers to let them go head to head since they probably hadn't played each other yet. In our league we've already played most everyone at least once (many twice), so the purpose getting them on the same board so they can play each other had already basically been done during the normal games.

If I'm third in the league going into game 4, with a championship board I only want to get a 4 way draw to solidify my position in top 7 (even if I share it with the person in first if they are in my game). However, with no championship board, I may go for a solo to try and grab the top spot.
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Re: Scoring System for Second PDL Season

Postby duckling » 30 Mar 2018, 23:21

Lots of interesting points being made here. I'm learning a lot, but I'm still confused as to what would be a good, simple system.
Running small tournaments with highly advanced scoring systems seems wrong.. the more variables you have, the more data is required to produce reliable results that even out flukes and biases.
21 people, 12 games, 4 games per player isn't really a lot. Statisticians in the crowd, please correct me!

Scoring system isn't just about what we want to be rewarded, it is also about making play work throughout the league, and about helping separate players from each other, also those who don't solo. Here Dip crashes hard with reality :)
Also, if you can run off with the league win after a lucky break in the first game, that's going to spoil a few things down the line.
IMO, the remaining players must have a way of (potentially) catching up.
And so the compromises start...

From the discussion so far, it seems to me that:
- we don't want big draws (well.. any draws, really..)
- we want to discourage too many early killings (because they lead to 2&3-ways)
- we want there to be a fight for the top, not for survival
- we want to put the solo well ahead, but not so far ahead that nobody can catch up (we must keep the fight going)

Shyvve's proposal still rewards survival more than being at the top. Three 4-ways beat two 3-ways, and I think that'll take the air out of the solo incentive.
So in the end, I still don't think the proposal is a big improvement.

I like that it rewards the solo more, though. But then you must remove the incentive to go into a big draw to avoid it.
Maybe getting rid of the 4 and 5-way points, in addition to 6 and 7, might be just as well.
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Re: Scoring System for Second PDL Season

Postby Riles » 31 Mar 2018, 09:02

Apologies in advance for the long post, like I said I like this kind of thing so I think way too much about it.

I've thought about it, and my personal opinion is to get away from "small draw is better than big draw" regardless of point spread between them. In 9 games of round 1 there was only 1 solo, 1 two-way (which could've been a three-way), 6 three-ways, and 1 four-way. I'm not sure that changing the points of each draw amount would've increased the chances for a solo in any of these games. In most any "draw whittling" system (I like the phrase from mhsmith and am now adopting it as my own) it is too easy to "spread the wealth" between 3 players making it too easy to end in a 3 way stalemate.

So my proposal is to move to Sum-of-Squares (SoS) scoring starting next season. The amount of data needed is simple, all you need is SC count at the end of the game, the size of a draw is irrelevant.

To give a summary of what SoS is for those unfamiliar, all games distribute a pool of ~100 points (rounding error will move this up or down slightly). You give solos all 100 points. In the event of a draw, you take each surviving player's end SC count and square it. Your score is the percentage of your "Squared SC count" of the total of the squared values. That's confusing to read so here's an example:

Suppose you end with 4 surviving players in a DIAS draw (all SoS games are DIAS in nature as draw size is irrelevant), Alice has 16 centers, Bob has 9 centers, Carl has 7 centers and Debra has 2 centers.

Square each player's SC count and you get 16^2=256, 9^2=81, 7^2=49, 2^2=4. Add the squares together (hence the name Sum of Squares) and you get 256+81+49+4=390. The total points each player gets is the percentage their "squared SC count" is of the Sum of the Squares.

So Alice with 16 centers would earn 256/390=65.6% or 66 points. Bob with 9 centers would get 81/390=20.8% or 21 points. Carl with 7 centers would get 49/390=12.6% or 13 points. Debra would get 4/390=1.0% or 1 point.

Alice comes away with most of the points of the game as Alice is much stronger on the board compared to everyone else (coming away with 3 times as many points as second place on the board).

Let's compare this with an even 2-way draw with 17-17 split between Eve and Frank; each player would get 50 points. So Alice earning fewer SC's than either Eve or Frank still earns Alice more points because Alice dominated her board better (by keeping her opponent's SC counts down).

Short summary of the concept behind the math which points to the strategy: You earn more points if you keep your SC count high and the SC count of your opponents low. Each additional SC that a player earns is more valuable than the SC they earned before it. So keeping your opponent's SC counts low and even between them would maximize your score, for if one of your opponents starts to earn a lot of SC's, those later centers will start taking a larger chunk of the pie per center (that's the nature of squaring the center count).

For example, suppose Bob took Debra's last two centers. Debra would go from 1 point to 0. Bob would go from earning 21 points to 28, Alice would go from earning 66 down to 60, and Carl would drop from 13 to 12. This encourages Alice to work with Debra even though Debra has only 2 centers left, perhaps even getting Debra a third center from Bob (raising Alice up to 68 points). Conversely, Bob can now try to work with Carl so they can split the remaining two centers between them from Debra, increasing each of their scores (to 24 and 15 respectively). While it can be beneficial for Bob/Carl to eliminate Debra if they split the SC's, that is not beneficial for Alice (whose score drops to 61).

The point is there is no way to eliminate Debra that would benefit Alice, Bob, and Carl at the same time. This means that the automatic assumption of "draw-whittling" does not occur and you wouldn't find cooperation between the large 3 to eliminate Debra, giving Debra negotiating power (Debra may still be eliminated, but it wouldn't be a lost cause).

Summary (without math):
1. Sum of Squares can discourage eliminations depending on circumstance, which may be a good or bad thing based on your opinion of eliminations, but in general I think more players on the board increases the likelihood of a solo as cooperation can get complicated between the anti-solo coalition. I'm also a general fan of games that eliminate late if at all, it's not fun being eliminated early so anything to slow that process is a benefit in my book (I know this is not a universal desire in players of Diplomacy). Remember that the goal is 18 centers, not to eliminate the competition (though elimination can often help, it isn't strictly necessary)

2. To further explain the above, players with small SC counts late in the game won't be automatic fodder for other players trying to whittle down the draw, they can find a natural ally in the largest power on the board (they can have similar goals that benefit both as illustrated in my example). In general, a smaller power taking an SC from a larger power (that isn't you) is good for you and can improve your score, regardless if you are the largest or smallest power on the board. That makes powers with 2 SC's potentially great allies in the right context since their success is your success.

3. Sum of Squares favors those that can keep a high SC count while keeping opponents low, which discourages "BFF" alliances (that can max at 50 points each at 17-17 split). The corollary being more stabs and alliance shifts (which I personally think is always a plus). This also dissuades settling for a draw, encouraging scrapping for those last few centers, taking risks, which all lead to higher probabilities of solos in my opinion.

4. Every SC matters, so fewer SC exchanges between allies to keep themselves balanced (goes back to point 3). In a 3-way draw in the current system all players get equal points, but in SoS each player will get a different number of points depending on their end game size, which can generate conflicting goals, which is almost always interesting in Diplomacy.

5. You can have three end results: Solo-Draw-Loss (as opposed to the multiple outcomes of Solo, 2-way, 3-way,...). Draw size is irrelevant, just your general size compared to your remaining opponents. Some would say this goes back to basics where a draw is a draw is a draw, doesn't matter the size of the draw it just means you weren't able to win (but with SoS you are still rewarded for controlling a large portion of the board so it kind of speaks out of both sides of the mouth).

6. Large powers will want lots of opponents to keep their personal scores high (by keeping SC counts of opponents distributed and low), smaller powers may want to eliminate each other if it means raising their own SC counts, which can again cause conflicting goals.

7. While scoring relies solely on a single data point (SC count), the math can be un-intuitive in the moment of a game to see what effect the previous year had on what the current score would be if a draw was called immediately. This can be a negative of the system if you are point counting mid-game trying to see where you stand. But that can also be a positive as it makes it more difficult to "game" the system to get a "good enough" result. To reiterate a previous point, gaining SC's yourself is always good, as is helping a small power take a center from a large power. The exact point impact will vary from case to case, but that's all you need to know to help form a general strategy.

8. Chances of ties after the season finishes in the rankings would be low as the distribution of points during games would usually be different from one game to another. In a league of 4 rounds of 3 games each that's ~1200 points to distribute in a relatively uneven way to 21 players, so ties are unlikely.
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Re: Scoring System for Second PDL Season

Postby duckling » 31 Mar 2018, 13:04

So my proposal is to move to Sum-of-Squares (SoS) scoring starting next season. The amount of data needed is simple, all you need is SC count at the end of the game, the size of a draw is irrelevant.


Hmm.. I quite like that.
It seems to meet all the criteria I listed previously, except the "big draws". But it compensates for that in the scoring.
It also takes the edge off that we can't get a large dataset, or lots of solo chances, in so few games.

It would really upend the scores, if you went by current results. The players strongest on their respective boards would've jumped well up, and some would be bumped significantly down.
But it would've encouraged entirely different results, of course. The draws w/eliminations we saw in this round would be less rewarding (or more risky).

This system would get my vote, I think.
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Re: Scoring System for Second PDL Season

Postby Shyvve » 31 Mar 2018, 23:49

If SoS scoring were formally proposed for future seasons, I would gladly vote for it too.
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Re: Scoring System for Second PDL Season

Postby Custer » 01 Apr 2018, 13:56

Here, here, got my vote........

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Re: Scoring System for Second PDL Season

Postby Saturos » 02 Apr 2018, 09:07

While the current system already encourages whittling a bit, SOS would really take it to the extreme. You would always drag the game on until your "team" has every center.
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Re: Scoring System for Second PDL Season

Postby duckling » 02 Apr 2018, 20:50

While the current system already encourages whittling a bit, SOS would really take it to the extreme. You would always drag the game on until your "team" has every center.


Wouldn't that just drag on until that choice is between drawing now or whittling first? (In which case whittling probably wouldn't pay off well)
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Re: Scoring System for Second PDL Season

Postby Saturos » 02 Apr 2018, 22:48

duckling wrote:
While the current system already encourages whittling a bit, SOS would really take it to the extreme. You would always drag the game on until your "team" has every center.


Wouldn't that just drag on until that choice is between drawing now or whittling first? (In which case whittling probably wouldn't pay off well)


Take for example our game of round 1 game 2.1.

Instead of letting the game drag on and maximizing measly tiebreaker points, we ended the game and let England have some tiebreaker points. If it was changed to be scoring by SoS, we would have to spend weeks slowly removing him from the board.
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