Correlation between average Points and Winrate

[Chessmaster_Hex]

Hello,
this is more of a mathematical/statistical discussion, so if you are not interested in this field, the following is probably no for you.

I assume, that when I go to the game statistics and I add up:
Points for first/second/third/fourth line
and points for tourist attractions
and points for connected lines
and points for assignments
I should get the average Points that player achieves in a single game, correct?

So the Point-Average of winners as of today is e.g.
27.22 + 25.46 + 24.07 + 22.25 + 10.66 + 18.33 + 14.83 = 142,82

Looking at some of the top players of the world I realised, that this point average does not always correlate with the winrate of this player.
Example: Player B has a 9 percent-points better winrate than Player A, but a 2 point lower point average. Both have at least 500 Games.

How is this possible? There is no player interaction and at this number of games in arena I would assume both players on average get opponents of comparable skill level.

Possible Explanations I came up with:
- If one player participates in tournaments and the other doesn´t the opponents skill level might be quite different
- Denying my own assumption made above: If they play from different countrys the opponent skill level might actually differ because of the time zones. But the same effect (higher WR, but lower point-average or vice versa) can be seen with players from the same country.
- Historic reasons: Loosing a lot of games in the beginning will lower the average Winrate stronger than the average points. I would assume this effect to be small at 400+ games played.

Have you got further suggestions? Am I missing something?

Greetings
Chessmaster Hex

[sorryimlikethis]

If you're looking at BGA win rates then there are 2 things you haven't taken into account - solo games and 3+ player games.
Solo games add to your total games played but negatively impact your "win rate %". E.g. my win rate is "58%" but I have 240 solo games weighing that figure down.
Getting 1st in a 4 player game will count as 3 wins for your win rate % (you have beaten 3 people). In games like Welcome To I have over a 100% win rate because I only play 3-4 player games.

Average points won't necessarily represent player skill either. While you would expect the averages to even out over hundreds of games, having 1 less station in an otherwise full line will cost between ~6-12 points. One player may just have less stations on average than another player.

[Jellby]

Getting 1st in a 4 player game will count as 3 wins for your win rate % (you have beaten 3 people). In games like Welcome To I have over a 100% win rate because I only play 3-4 player games.

I think it counts as 2 wins, not 3. The "formula" is 0.5 times total number of players, such that if victories are evenly distributed the rate is always 50%.

I also wonder if average scores may be affected by the number of players.

[Chessmaster_Hex]

Hey,
thanks to you two for sharing your thoughts!

I agree, that one player might get a lower number of cards and thus lesser average points. I assumed that after a few hundred games for everyone compared, this effect would dwindle to nothing since it´s not dependend on the specific players style of play.

I totaly forgot about the winrate always beeing calculated to a virtual 1v1 winrate, this is a very good point. Especially good players would inflate their Winrate (if they want to or not is neither matter nor problem) in Next Station when playing it more or less often outside of the arena with 4 rather then 2 players. Since there is no Interaction between players it´s not much less likely to become first in a 4 player game than becoming first in a 2 player game.


Something else I realised: The average points one gets, when summing up the different averages don´t match the average points givin by bga at the top of the game history (the number of victorys too, doesn´t match). In my case the Sum is 166,34 while bga states 163,5. It´s not troubling me, but it triggers my curiosity .
I would assume this has something to do with matches beeing arena or non-arena or just friendly games?!

Greetings
Chessmaster Hex

[ahrnge]

Getting 1st in a 4 player game will count as 3 wins for your win rate % (you have beaten 3 people). In games like Welcome To I have over a 100% win rate because I only play 3-4 player games.

I think it counts as 2 wins, not 3. The "formula" is 0.5 times total number of players, such that if victories are evenly distributed the rate is always 50%.

I think y'all are saying the same thing. You're right that it's scored as 200% of a win, not a 300% of a win, so in that sense one could say it is counted as two wins. But a "200% win" is often more like three "100% wins" in terms of its contribution to your overall win rate, in that if you then went and lost three games it would bring your win rate for that sample down to 50% (as if your record were 3-3), like you said. Really a four player win is scored as "two wins out of one game," which often resembles three wins out of three games more than it does two wins out of two games.

Of course, "two wins out of one" looks most like "three wins out of three" for players around a 50% overall win rate. For players with very low win rates, the numerator (#wins) dominates, so you'd rather see three two-player wins than one four-player win. Conversely for players with very high win rates, the difference between the denominator and the numerator (#played-#wins) dominates, so you'd rather see one four player win than three two player wins.

This is why player count is relevant for correlating win rate and average score. For many games I think the best players tend to prefer lower player counts, so while they'd have the highest average score, they might not have the highest average win rate.