webdiplomacy.net

tideshome wrote: ↑

Thu Nov 09, 2023 10:39 pm

One difference between the current points and GR is that if points go below 100 they are topped up so the player can carry on taking part in games. Would there be something similar to the GR if points were scrapped?

I'm sensing some confusion about what GR is and how it works.

We already have GR scores on this site. It's not an exhaustible resource like Dip Coins, it's a ranking system. Your bid would be proportional to how well you're ranked vis-a-vis your opponents. If there were a game open to all skills levels, then even the lowest-ranked player on the site could join.

A strange difference between the ghost rating adjustments of the scoring schemes:
In a classic game where 6 of the players have the same Ghost Rating (G, say), the seventh, player P, has a rating of 2G, and the game ends in a 2-way draw with one of the 6 and the other player P, with exactly 17 centers each, then it seems with Draw Size Scoring player P will get a larger ghost rating adjustment than with Sum of Squares scoring:
Based on how I THINK the code in https://github.com/kestasjk/webDiplomacy/blob/master/ghostratings/calculations.php works:
In DSS: P's ratingAdjustment = 8G/17.5 * (1/2 - 2G/8G) = 8G/17.5 * (1/2 - 1/4) = 2G/17.5
In SoS: P's ratingAdjustment = 8G/17.5 * (17*17/(17*17 + 17*17) - 2G*2G/(6*G*G + 2G*2G)) = 8G/17.5 * (1/2 - 4/10) = 8G/17.5 * (1/2 - 2/5) = G/17.5

echidna wrote: ↑

Fri Nov 10, 2023 4:43 am

A strange difference between the ghost rating adjustments of the scoring schemes:
In a classic game where 6 of the players have the same Ghost Rating (G, say), the seventh, player P, has a rating of 2G, and the game ends in a 2-way draw with one of the 6 and the other player P, with exactly 17 centers each, then it seems with Draw Size Scoring player P will get a larger ghost rating adjustment than with Sum of Squares scoring:
Based on how I THINK the code in https://github.com/kestasjk/webDiplomacy/blob/master/ghostratings/calculations.php works:
In DSS: P's ratingAdjustment = 8G/17.5 * (1/2 - 2G/8G) = 8G/17.5 * (1/2 - 1/4) = 2G/17.5
In SoS: P's ratingAdjustment = 8G/17.5 * (17*17/(17*17 + 17*17) - 2G*2G/(6*G*G + 2G*2G)) = 8G/17.5 * (1/2 - 4/10) = 8G/17.5 * (1/2 - 2/5) = G/17.5

I have the intuition that it's harder to achieve this outcome in a DSS game than an SoS game, so it should provide a bigger GR uplift. Of course, a more experienced player / someone with access to game outcome data might be able to prove me wrong on this point.

I played around with the code in GPT and I think I have an accurate analysis of some of illustrative GR change examples, which are pasted in detail below the line.

In short, the GR consequences of a game vary a lot based on the scoring system used:
- To your earlier point, two-way draws in SoS are always better than in DSS.
- It is much better to just survive with just a few centres in a DSS game than in an SoS game.
- It can be a bit better to solo under SoS than DSS, but only if you're the underdog.

I think each of these disparities can be justified by the difficulty of achieving these outcomes given the incentives of each scoring system, but of course more experienced folks / real player data could definitely change my mind.
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Variables Explanation:
P_GR: The initial Ghost Rating of the player in question.
O_GR: The initial Ghost Rating of each other player.
n: Total number of players in the game (7 in classic Diplomacy).
d: Number of players surviving to the draw, including the player in question.
s: Number of supply centers controlled by the player in question at the end of the game.
S: Total supply centers in the game (34 in classic Diplomacy).

General Formulas for GR Adjustments:

Draw-Size Scoring (DSS)
GR Adjustment_DSS = (8 * (P_GR + (n - 1) * O_GR) / 17.5) * (1/d - P_GR / (P_GR + (n - 1) * O_GR))

Sum-of-Squares (SoS)
GR Adjustment_SoS = (8 * (P_GR + (n - 1) * O_GR) / 17.5) * (s^2 / (s^2 + (S - s)^2 * (d - 1) / (n - 1)) - P_GR^2 / (P_GR^2 + (n - 1) * O_GR^2))

Illustrative Scenarios:

Four-way Draw, Player Has Fewer Centers (Player controls 4 centers)

Assumption: Other players' centers are evenly distributed.
P_GR | O_GR | DSS Adjustment | SoS Adjustment
200 | 100 | 0.00 | -133.73
100 | 100 | 34.29 | -34.73
50 | 100 | 51.43 | -1.68

Solo Win by the Player (Player controls 18 centers for a solo win)

Assumption: Remaining centers are evenly distributed among other players.
P_GR | O_GR | DSS Adjustment | SoS Adjustment
200 | 100 | 274.29 | 219.43
100 | 100 | 274.29 | 274.29
50 | 100 | 274.29 | 285.26

Two-way Draw, Player Has Half the Centers (Player controls 17 centers)

Assumption: Player controls exactly half of the total centers.
P_GR | O_GR | DSS Adjustment | SoS Adjustment
200 | 100 | 91.43 | 167.18
100 | 100 | 114.29 | 228.57
50 | 100 | 125.71 | 242.81

Nice! A possible correction - I think there is an unnecessary factor of 8 in both your adjustment formulae.

There could totally be an error, but I believe that the eight in the "(8 * (P_GR + (n - 1) * O_GR)" term is the same as your "8G", it just allows for the player in question to have a different initial GR than their partners (though their partners' GR scores all have to be the same, = O_GR).

Ah, I may have inadvertently misled you. Since I was reporting only the case of six players each with equal ghost ratings of G, and a seventh with a ghost rating twice as much, 2G, I instantiated the "$grSum" in the code with 8G (1*2G + 6*1G).
In your formulae, you have both that factor of 8, AND the factor formed of sum of GRs "(P_GR + (n-1)*O_GR)".
A clue is if you look at your computed results, an SOS adjustment of over 200 if a 100 rated player solo'd a single SoS game against 6 other 100 rated players would result in that player's rating jump to 300 - wow!

echidna wrote: ↑

Sat Nov 11, 2023 12:39 am

Ah, I may have inadvertently misled you. Since I was reporting only the case of six players each with equal ghost ratings of G, and a seventh with a ghost rating twice as much, 2G, I instantiated the "$grSum" in the code with 8G (1*2G + 6*1G).
In your formulae, you have both that factor of 8, AND the factor formed of sum of GRs "(P_GR + (n-1)*O_GR)".
A clue is if you look at your computed results, an SOS adjustment of over 200 if a 100 rated player solo'd a single SoS game against 6 other 100 rated players would result in that player's rating jump to 300 - wow!

I would love if there were some definitive formulae out there for this and some examples. Would be good to know how GR actually works here then lol.

Okay I think I bullied GPT into giving me the right answer lol, the 8 was erroneous and these new values make a lot more sense. That said, I'd still appreciate more info on how GR is calculated on WebDip in case this still suffers from some profound misundertandings - maybe I'm missing it, but extra info on GR is not where I'd expect to find it (e.g., https://webdiplomacy.net/points.php)

----------------------------------------------------------------------------------------------------

Variables Explanation:
P_GR: The initial Ghost Rating of the player in question.
O_GR: The initial Ghost Rating of each other player.
n: Total number of players in the game (7 in classic Diplomacy).
d: Number of players surviving to the draw, including the player in question.
s: Number of supply centers controlled by the player in question at the end of the game.
S: Total supply centers in the game (34 in classic Diplomacy).

General Formulas for GR Adjustments:

Draw-Size Scoring (DSS):
GR Adjustment_DSS = ((P_GR + (n - 1) * O_GR) / 17.5) * (1/d - P_GR / (P_GR + (n - 1) * O_GR))

Sum-of-Squares (SoS):
GR Adjustment_SoS = ((P_GR + (n - 1) * O_GR) / 17.5) * (s^2 / (s^2 + (S - s)^2 * (d - 1) / (n - 1)) - P_GR^2 / (P_GR^2 + (n - 1) * O_GR^2))

Illustrative Scenarios:

Four-way Draw, Player Has Fewer Centers (Player controls 4 centers):
P_GR O_GR DSS Adjustment SoS Adjustment
200 100 0.00 -1.29
100 100 4.29 0.56
50 100 6.43 1.06

Solo Win by the Player (Player controls 18 centers for a solo win):
P_GR O_GR DSS Adjustment SoS Adjustment
200 100 34.29 42.86
100 100 34.29 39.18
50 100 34.29 36.92

Two-way Draw, Player Has Half the Centers (Player controls 17 centers):
P_GR O_GR DSS Adjustment SoS Adjustment
200 100 11.43 36.33
100 100 14.29 33.47
50 100 15.71 31.62

Just had to stop being lazy and actually read the FAQ lol: https://webdiplomacy.net/ghostRatings.php

Upon seeing this, I *think* the analysis above is actually right (i.e., after removing the erroneous 8)

A while back I posted to Feedback/Bug Reports
https://webdiplomacy.net/contrib/phpBB3/viewtopic.php?f=17&t=4831#p356479
to say that (for SoS I should have made clear):

https://webdiplomacy.net/ghostRatings.php states:
expectedScore = yourGR / sumOfEachPlayersGR

yet the code to be found at
https://github.com/kestasjk/webDiplomacy/blob/master/ghostratings/calculations.php
uses GRs SQUARED.

This thread got a little sideways on specific scoring issues, but to bring it back to the more interesting question of GR vs. Dip Points:

Maybe a simpler solution would be to just add the potential for game creators to use GR minimums/maximums win the "Advanced Settings"? Noob and/or expert games could be more accurately safeguarded in this way without asking anyone to give up the dip coin system that some seem to prefer.

It strikes me that the GR-bid system to enter a game is something that's already happening in the background right now. I guess it just makes people uncomfortable when the GR consequences of a game are explicit rather than just calculated in the background. I really don't have much sympathy for this position lol, I still strongly believe it would be better if people knew the exact GR consequences of a game rather than the Dip Coin consequences, but if the current system prevents riling people up I guess let them focus on their coins - I'll be looking at their GR ranking, not their dip point balance, to see if they're any good at the game.

Of course, GR can still be fixed up a bit (CDs count as losses + some elegant solution for CD-takeovers that is beyond me lol)

we really need to PUNISH quitters. It's become an epidemic. People routinely quit just before they actually lose. I see this in every game. CDs should count as a loss on your ghost rating, cost you TWICE your bet, anything to pummel quitters. Alternatively, we could reward people sticking it out to the end with a 20% refund of their bet for dying and not quitting. There should be severe consequences for quitting, worse than losing.

As someone who at least a few times a year misses deadlines for move inputs and CDs - I fully support this, and think it might be as effective in curbing intentional CDs as the RR drop (referring to double bet penalties and so on).

I can't think of a way to define what is accidental and what is intentional though so I think it would have to be adopted across the board for CDs - except maybe for < 24 hr cycle games. A couple of time I accidentally filled in on 12 and 14 hour cycle matches and CD'd as a result because I am a dumbass.

As many have said... and IMHO: If GR points were deducted from the original players, the incentive to CD would be removed. The distribution of GR points at the end of the game is fine as is.