ELO calculation change

[Meeplelowda]

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 adjustment for that game will be scaled by 2/3 in a 4-player game. Similarly, if there is a game where the recommended number of players is 5 (ed.: there is at least 1 Heat), the Elo adjustment for that game will be scaled by 5/8.

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

[Ceaseless]

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.

I wouldn't put any weight on a "recommended number of players" category.

[Meeplelowda]

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.

[dschingis27]

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).

[Ceaseless]

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.

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.

[FrankJones]

Yeah, I mean, the factors listed in the FAQ indicate, among other things, "player count".

it does NOT say anything about using "recommended player count" as part of the Equation for calculating Elo change.

Nor does it give any indication that different games with the same player count might use a different Elo calculation.

So, if any of that is actually happening, the FAQ is needlessly misleading.

[Meeplelowda]

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.

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.

The key part was "if this is true," "this" being what was in dschingis27's post. But in retrospect I see it's confusingly worded. This is what happens when I try to be more conversational and less mathematical.

[FrankJones]

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).

Wow. the information in that thread is truly bizarre. I am baffled. 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.

[Meeplelowda]

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.

As you point out, we have at least one example of a 6-player game where c=0.6, not 1 as reported in that thread. c=1 for 6 players does not follow either of 1/2 x [N/(N-1)] or 2/(N-1).

As for the secrecy, it gives us a nice fun little puzzle to work on.

As for basing it on the recommended player count....that's seem weird. I don't know why that should matter at all. Also, are they hard coding the player count data, or does BGG have an API used to pull it? Either way, it seems like too much effort for something that doesn't seem to have a sound basis to begin with.

[ufm]

Seems this issue is still ongoing: https://boardgamearena.com/bug?id=29568