Point scoring

[redleppard1]

Has anyone else noticed the odd way that winning/losing points goes on? I just played a 3 player game where I was the winner but the runner up scored more points than I did. At times the loser may lose 35 points even though in a 3 player game it was pretty close between all players..... this is happening a lot lately.

[Jellby]

https://boardgamearena.com/faq?anchor=faq_account_elo

[Meeplelowda]

Has anyone else noticed the odd way that winning/losing points goes on? I just played a 3 player game where I was the winner but the runner up scored more points than I did. At times the loser may lose 35 points even though in a 3 player game it was pretty close between all players..... this is happening a lot lately.

How does the ELO change calculation work?
How is my ELO updated?

Elo calculations do not factor in how close a game is at all. The only inputs are win/lose/draw, the ratings of the players, and the K-factor. It's the K-factor that could cause someone who finished behind you to gain a more points than you if their rating was much lower than the person in third place and your rating was much higher than the person in second place.

Unfortunately, in the recent revision to the FAQ they removed the explanation of how K-factor works on BGA. It used to explain that:

K, the 'elasticity factor,' has a value that depends on the number of games you have played: 60 for your first 10 games, 40 between your 11th and 20th games, 20 for your 21st onwards.

A person with a K-factor of 60 will gain (or lose) three times as many points as someone with the same rating who has already finished a game 20 or more times.

Before concluding that something is wrong, you have to examine the games and look at the K-factor of the player in question.

Edit:
I got curious, so I found the game. As I suspected, the person in 2nd place has only played Azul 4 times (on BGA at least) and had an Elo of 1 before the game in question. So their rating was much lower than both you and the person in third place, and their K-factor is still 60.

The purpose of the K-factor is to account for the fact that a new player's rating almost never reflects their true skill (especially if, like on BGA, the Elo starts at 0). So at the beginning the adjustments are extreme to get the person closer to their "true" rating faster. Then the adjustments taper off over time. [Also, a rating of 100 doesn't necessarily reflect true skill, because that's an artificially set floor. But that's a discussion for another day....]

[SchengW]

We use the example of this game

Before the game the Elo ratings were:

• redleppard1: 109.55, K = 30
• Klaarherman1: 1, K = 90 (higher K because it is still within the first 10 games)
• ignax: 144.24, K = 30

Note: BGA’s Elo system actually works with a hidden offset of +1300. So the real values used for calculation are:

• redleppard1: 1409.55, K = 30
• Klaarherman1: 1301.00, K = 90
• ignax: 1444.24, K = 30

Because Elo is only defined for 1v1 games, in a 3-player game we treat it as multiple duels:

• 1st place wins against both opponents
• 2nd place wins against 3rd, loses against 1st
• 3rd place loses against both

Now let's start with redleppard1 vs Klaarherman1
A player's expected score is their probability of winning plus half their probability of drawing.
with the formular

E_A = 1 / (1 + 10 ^ ((R_B - R_A) / 400))

Thus your probality of winning is:
E = 1 / (1 + 10 ^ ((1301 - 1409.55) / 400)) ≈ 0.651 (65.1%)

Elo change:
ΔR = 30 × (1 - 0.651) = +10.47

Since it is a 3-player game (split across 2 duels):
ΔR = 10.47 / 2 = +5.23

redleppard1 vs ignax
E = 1 / (1 + 10 ^ ((1444.24 - 1409.55) / 400)) ≈ 0.450 (45.0%)

Elo change:
ΔR = 30 × (1 - 0.450) = +16.50

After split:
ΔR = 16.50 / 2 = +8.25

Then the result for redleppard1
Total ΔR = 5.23 + 8.25 = +13.48

Klaarherman1 vs redleppard1
Klaarherman1 lost this duel:
ΔR = 90 × (0 - 0.349) = -31.40 → after split = -15.70

Klaarherman1 vs ignax
E = 1 / (1 + 10 ^ ((1444.24 - 1301) / 400)) ≈ 0.305
ΔR = 90 × (1 - 0.305) = +62.56 → after split = +31.28

Result for Klaarherman1
Total ΔR = 31.28 - 15.70 = +15.59

Final summary:
redleppard1: +13.48
Klaarherman1: +15.59
ignax: (loses both, ΔR= -18.67)

When you hover your mouse over your Elo on BGA, a tooltip appears showing detailed information:

• Current Elo and games played
• Elo change (ΔElo) for this match
• Expected score vs. each opponent
• Win/loss result for each duel

The numbers in the screenshot match perfectly with the calculations we did above.

[Jellby]

Note: BGA’s Elo system actually works with a hidden offset of +1300.

It doesn't matter, does it? Only elo differences are used in the formulas, so it could be +1300 or +10000000, as long as it's the same for everyone.

[SchengW]

Note: BGA’s Elo system actually works with a hidden offset of +1300.

It doesn't matter, does it? Only elo differences are used in the formulas, so it could be +1300 or +10000000, as long as it's the same for everyone.

Exactly, it does not matter since the winning probablity is only based on the difference of the elo ratings. I still wonder why bga does it.

[FrankJones]

Note: BGA’s Elo system actually works with a hidden offset of +1300.

It doesn't matter, does it? Only elo differences are used in the formulas, so it could be +1300 or +10000000, as long as it's the same for everyone.

Exactly, it does not matter since the winning probablity is only based on the difference of the elo ratings. I still wonder why bga does it.

Well, I would prefer starting at 1500 with no floor, since starting at zero means Elo decreases that should happen, don't happen. And then once you get to 100, don't you always stay at 100 even when you lose?

All of which inflates the overall Elos, right?

[Meeplelowda]

All of which inflates the overall Elos, right?

Indeed, and not just for that person. With a floor of 100, someone who wins against someone rated 100 who should actually be rated 65 gains more than they should, and someone who loses against someone rated 100 who should actually be rated 65 loses less than they should. By "should be rated 65," I mean that would be their rating if there were no floor set.

[SchengW]

It doesn't matter, does it? Only elo differences are used in the formulas, so it could be +1300 or +10000000, as long as it's the same for everyone.

Exactly, it does not matter since the winning probablity is only based on the difference of the elo ratings. I still wonder why bga does it.

Well, I would prefer starting at 1500 with no floor, since starting at zero means Elo decreases that should happen, don't happen. And then once you get to 100, don't you always stay at 100 even when you lose?

All of which inflates the overall Elos, right?

Yes. In a pure Elo system without floors, the total rating remains constant since it’s a zero-sum transfer between players. But with a 100-point floor or a 0 starting rating, the average Elo keeps increasing.