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dschingis27 wrote: ↑09 December 2025, 17:09 Ahhh, I think sprockitz got it all right already (2nd post in the link I shared).

This is for 7Wonders, I verified it for 5p and 6p:
players -> factor * opponents = "2p equivalent"
(2p -> 1.0 * 1 = 1)
3p -> .75*2 = 1.5
4p -> .66*3 = 2.0
5p -> .50*4 = 2.0
6p -> .40*5 = 2.0
7p -> .33*6 = 2.0
Since 7Wonders is recommended with 4p, the net multiplier does not go up when you increase players above 4.
Example: Winning in a 3p game is equivalent to winning a 2p game 1.5 times. Winning a 4p game is equivalent to winning a 2p game 2 times. Winning a 5p game is also equivalent to winning a 2p game 2 times. It seems that the Elo change calculation wants to keep this parameter at 2 when the player number is above the recommended number for a game. That means no one has to finetune these factors but they depend on the recommended player number.

So, here is my take:
Up to the recommended number of players for a game, it choses the factor based on the formula found by Meeplelowda:
1/2 x [N/(N-1)]
Beyond that, it choses the factor based on this:
2/(N-1)

Meeplelowda wrote: ↑09 December 2025, 19:21

dschingis27 wrote: ↑09 December 2025, 17:09 Ahhh, I think sprockitz got it all right already (2nd post in the link I shared).

This is for 7Wonders, I verified it for 5p and 6p:
players -> factor * opponents = "2p equivalent"
(2p -> 1.0 * 1 = 1)
3p -> .75*2 = 1.5
4p -> .66*3 = 2.0
5p -> .50*4 = 2.0
6p -> .40*5 = 2.0
7p -> .33*6 = 2.0
Since 7Wonders is recommended with 4p, the net multiplier does not go up when you increase players above 4.
Example: Winning in a 3p game is equivalent to winning a 2p game 1.5 times. Winning a 4p game is equivalent to winning a 2p game 2 times. Winning a 5p game is also equivalent to winning a 2p game 2 times. It seems that the Elo change calculation wants to keep this parameter at 2 when the player number is above the recommended number for a game. That means no one has to finetune these factors but they depend on the recommended player number.

So, here is my take:
Up to the recommended number of players for a game, it choses the factor based on the formula found by Meeplelowda:
1/2 x [N/(N-1)]
Beyond that, it choses the factor based on this:
2/(N-1)

If this is true, if there is a game out there where the recommended number of players is 3, the Elo should be scaled by 2/3 in a 4-player game. Similarly, there should be a game where the recommended number of players is 5 that is scaled by 5/8.

I don't know if those recommended player counts exist for any game.

Ceaseless wrote: ↑09 December 2025, 22:44 I wouldn't put any weight on a "recommended number of players" category.

Meeplelowda wrote: ↑09 December 2025, 23:54

Ceaseless wrote: ↑09 December 2025, 22:44 I wouldn't put any weight on a "recommended number of players" category.

We are hypothesis testing. No one said anything about whether the recommended number of players is useful. What we are concerned with in this discussion is whether it is used to influence the weighting of Elo adjustments. We don't care for the purposes of this discussion whether it should be used.

Meeplelowda wrote: ↑09 December 2025, 19:21 If this is true, if there is a game out there where the recommended number of players is 3, the Elo should be scaled by 2/3 in a 4-player game. Similarly, there should be a game where the recommended number of players is 5 that is scaled by 5/8.

I don't know if those recommended player counts exist for any game.

Ceaseless wrote: ↑10 December 2025, 00:10

Meeplelowda wrote: ↑09 December 2025, 23:54

Ceaseless wrote: ↑09 December 2025, 22:44 I wouldn't put any weight on a "recommended number of players" category.

We are hypothesis testing. No one said anything about whether the recommended number of players is useful. What we are concerned with in this discussion is whether it is used to influence the weighting of Elo adjustments. We don't care for the purposes of this discussion whether it should be used.

I misunderstood your previous post. My bad.

Meeplelowda wrote: ↑09 December 2025, 19:21 If this is true, if there is a game out there where the recommended number of players is 3, the Elo should be scaled by 2/3 in a 4-player game. Similarly, there should be a game where the recommended number of players is 5 that is scaled by 5/8.

I don't know if those recommended player counts exist for any game.

I read these bolded "should be" in a different light than you meant it.

dschingis27 wrote: ↑10 December 2025, 00:08 So, finally, I found the very relevant thread again.
https://boardgamearena.com/forum/viewtopic.php?p=60122

If it is true what is posted there, then my take from above was wrong (or only partially true, depending how you look at it).

FrankJones wrote: ↑10 December 2025, 00:36 Why would any game have a C-factor that follows the pattern discovered in this thread but then abruptly increase banc to 1 once it reached 6 players? (but only for some games, apparently, since for "Earth", it continues the downward trend to 0.6).

Is there any reason for this level of secrecy?

Also, basing any part of the Elo equation on the designer's "recommended player count" just seems asinine to me.