Statistics: Quest for gold

[GrandAt]

4p - tournament!
Statistics after third round

Unofficial scoreboard (gold)
1) JZ7777: 61 (the only one to win all three games)
2) Master_of_Buckland: 58
3) Lepture and jibro3o: 57

Most gold (rank after 2nd round)
1) Leonardo 299 (1)
2) Carolijn 291 (2)
3) Sophie 280 (4)
4) Urs 271 (3)

The statistics below are calculated by considering each 4p game as 3 duels for each character. The character ending on 1st place in a game wins 3 duels. Ties gives both characters 0,5 victory.

% victories
1) Leonardo: 52,78%
2) Sophie: 50,93%
3) Carolijn: 49,07%
4) Urs: 45,37%

Each adventurers favorite opponent (winrate)
1) Leonardo has 55,88% winrate against Urs (55,56% against Carolijn and 50% against Sophie)
2) Sophie has 52,78% winrate against Urs (50% against Carolijn)
3) Carolijn has 52,78% winrate against Urs.
4) Urs has no winrate above 50%.

Total: 2p tournament + 4p (so far)
Avg gold per game (change this round)
1) Sophie 17,51 (-0,21)
2) Leonardo 17.03 (+0,09)
3) Carolijn 16,98 (no change)
4) Urs 16,25 (-0,28)

[GrandAt]

4p - tournament!
Statistics after forth round

Unofficial scoreboard (gold)
1) JZ7777: 81 (still undefeated!)
2) Master_of_Buckland: 77
3) AADSiepen and jibro3o: 71

Most gold (rank after 3rd round)
1) Leonardo 399 (1)
2) Carolijn 384 (2)
3) Sophie 377 (3)
4) Urs 357 (4)

The statistics below are calculated by considering each 4p game as 3 duels for each character. The character ending on 1st place in a game wins 3 duels. Ties gives both characters 0,5 victory.

% victories
1) Carolijn: 52,08%
2) Leonardo: 51,39%
3) Sophie: 50,00%
4) Urs: 45,14%

Each adventurers favorite opponent (winrate)
1) Carolijn has 56,25% winrate against Urs (54,17% against Sophie)
2) Leonardo has 54,35% winrate against Urs (54,17% against Carolijn)
3) Sophie has 52,08% winrate against Urs and Leonardo.
4) Urs has no winrate above 50%.

Total: 2p tournament + 4p (so far)
Avg gold per game (change this round)
1) Sophie 17,38 (-0,13)
2) Leonardo 17.00 (-0,03)
3) Carolijn 16,83 (-0,15)
4) Urs 16,06 (-0,19)
Note: Interesting to see all characters lower their avg gold per game. My guess is that this is due to this statistics mixing results from 2p games and 4p games.

[GrandAt]

4p - tournament!
Statistics after fifth round

Unofficial scoreboard (gold)
1) JZ7777: 95 (no longer undefeated, AADSiepen found a way)
2) Master_of_Buckland and AADSiepen: 91
These three battle it out in the final

Most gold (rank after 4rd round)
1) Leonardo 516 (1)
2) Sophie 476 (3)
3) Carolijn 473 (2)
4) Urs 452 (4)

The statistics below are calculated by considering each 4p game as 3 duels for each character. The character ending on 1st place in a game wins 3 duels. Ties gives both characters 0,5 victory.

% victories
1) Leonardo: 57.78%
2) Carolijn and Sophie: 48,89%
4) Urs: 43,33%

Each adventurers favorite opponent (winrate)
1) Leonardo has 60,34% winrate against Urs (60% against Carolijn and 55% against Sophie)
2) Carolijn has 55% winrate against Urs (51,67% against Sophie)
3) Sophie has 53,33% winrate against Urs.
4) Urs has no winrate above 50%.

Total: 2p tournament + 4p (so far)
Avg gold per game (change this round)
1) Sophie 17,31 (-0,07)
2) Leonardo 17,21 (+0,21)
3) Carolijn 16,65 (-0,18)
4) Urs 16,04 (-0,02)

Note: This round (the 5th) was Leonardos round! He seems to dominate 4p games, but lets see if the final round changes anything.

[GrandAt]

4p - tournament!
Statistics after final round

Unofficial scoreboard (gold)
1) JZ7777: 113
2) AADSiepen: 111
3) Master_of_Buckland: 109

Most gold (rank after 5th round)
1) Leonardo 619 (1)
2) Carolijn 589 (3)
3) Sophie 570 (2)
4) Urs 539 (4)

The statistics below are calculated by considering each 4p game as 3 duels for each character. The character ending on 1st place in a game wins 3 duels. Ties gives both characters 0,5 victory.

% victories
1) Leonardo: 58.33%
2) Carolijn 54,17%
3) Sophie: 47,69%
4) Urs: 38,89%

Each adventurers favorite opponent (winrate)
1) Leonardo has 64,29% winrate against Urs (56,94% against Sophie and 55,56% against Carolijn)
2) Carolijn has 61,11% winrate against Urs (56,94% against Sophie)
3) Sophie has 56,94% winrate against Urs.
4) Urs has no winrate above 50%.

Bonus statistics - winrate per round of tournament
Character - round 1 - round 2 - round 3 - round 4 - round 5 - round 6 - total (also above)
Leonardo - 47,22% - 50,00% - 61,11% - 47,22% - 83,33% - 61,11% - 58,33%
Carolijn - 58,33% - 27,78% - 61,11% - 61,11% - 36,11% - 80,56% - 54,27%
Sophie - 38,89% - 69,44% - 44,44% - 47,22% - 44,44% - 41,67% - 47,69%
Urs - 55,56% - 52,78% - 27,78% - 44,44% - 36,11% - 16,67% - 38,89%

I wanted to share this statistics with you since i found it interesting. Just looking at the numbers for this tournament we can clearly see how Urs in the 2 first rounds manages well, but after that performs much worse. Could there be a reason for this? I'm interested to know if you have any thoughts about the dynamics of 4p Treos and to discuss it here in this thread. The tournaments setting makes it so that later in the tournament you play against players that been roughly as successful as you have so far. Those matches tend to be between players of similar ELO, while the first rounds see bigger difference in ELO between players (generally). Is there a connection to Urs performance?
The 2p tournament had Sophie as the (slightly) dominant character. Here she's just on 3rd spot. Is there a reason Sophie might perform worse in a 4p setting than in 2p? Maybe opponents try to block Sophie the most because many consider her very strong. In 4p it's easier to get blocked by highwaymen, i would say.

Total: 2p + 4p tournament
Avg gold per game (change this round)
1) Leonardo 17,21 (+-0)
2) Sophie 17,18 (-0,13)
3) Carolijn 16,88 (+0,23)
4) Urs 15,92 (-0,12)

Note: Sophie has had the best avg gold per game all the way since the end of the 2p tournament. But now in the final round of 4p tournament Leonardo takes the 1st place!

[shlïtn]

With the 4p tournament being over, here again some more statistics:
There were 36 4-player games. Everything of the following that includes gold/turn ratios was taken from 35 of the 36 games because 1 replay has been lost (empty archive file).

mean gold/turn ratio
1) Yellow: 0.91 gold/turn (2.72 gold/day)
2) Red: 0.87 gold/turn (2.62 gold/day)
3) Purple: 0.85 gold/turn (2.56 gold/day)
4) Green: 0.81 gold/turn (2.42 gold/day)

median gold/turn ratio
1) Yellow: 0.94 gold/turn (2.83 gold/day)
2) Red: 0.89 gold/turn (2.67 gold/day)
3) Purple: 0.86 gold/turn (2.59 gold/day)
4) Green: 0.79 gold/turn (2.37 gold/day)

average placements (with tied players receiving the mean of their tied ranks; these values are equivalent to GrandAt's "% victory")
1) Yellow: 2.22
2) Red: 2.38
3) Purple: 2.56
4) Green: 2.82

gold/turn ratios >= 1: 30.7%
gold/turn ratios >= 1 for 1st place: 82.9%
gold/turn ratios >= 1 for 2nd / tied for 2nd place: 34.1%
gold/turn ratios >= 1 for 3rd / tied for 3rd place: 0%
gold/turn ratios >= 1 for 4th place: 0%

Comparing the colors based on placement:
For this type of data structure, considering the dependencies that come with the grouping of 4 players into 1 game, using a mixed-effects model would be best. For simplicity, I opted for a non-parametric approach instead.
As in the 2p tournament, skill level (Elo) has a significant influence on the final placement (this can just be assumed to be true). However, skill level is independent from assigned color (which is a fact; but still tested for this sample of games: the chi-squared test of independence - grouping Elo values into the intervals [100, 200), [200, 300), [300, 500) - is non-significant with p-value = 0.7669). Therefore, assuming that each color has been played by similarly distributed Elo values, I compared the placements of the colors with the Friedman test (null hypothesis: apart from an effect of blocks (all 4 colors playing 1 game), the location parameter of the colors (placement) is the same in each of the colors). This test has a non-significant result (p-value = 0.1959).
To conclude, using this approach, the data gathered from this 4p tournament does not provide enough evidence that the 4 colors perform differently just based on final placement. (And just to clarify, this non-significant result does not mean evidence for balance, but rather a lack of sufficient evidence for imbalance.)

[GrandAt]

Interesting! The game is indeed very well balanced between the characters and these tournaments provide a small database to make statistics from. Still very interesting! What can be said is that green (Urs) ends up in the bottom both in the 2p and 4p statistics, even if it's not significant it seems to be a trend. Urs is the hardest character to block, so in a tighter more chaotic 4p game he should have an advantage. But maybe he is slightly harder to play effectively.

I always find it very interesting than assymetric games like Treos still are so well balanced. The characters special abilities are very different, their decks are different and what they gain from the forts are different. In the end though it seems very hard to see any inbalance. But the differences forces us players to play the game according the the strengths of the character we have. A game as Urs is often very different from a game as Sophie, and the same goes for all of them.

[GrandAt]

3p - tournament!
Statistics after first round
Only statistics from games that finished in time

Unofficial scoreboard (gold)
1) qwermish: 21
2) Master_of_Buckland, Galnar, Harvepin, Shaevor and Petee75 all on 20 gold.

Most gold
1) Carolijn: 80
2) Sophie and Urs: 71
4) Leonardo: 60

Average gold/game (3p)
1) Sophie and Urs: 17,75
3) Carolijn: 16,00
4) Leonardo: 12,00

The statistics below are calculated by considering each 3p game as 2 duels for each character. The character ending on 1st place in a game wins 2 duels. Ties gives both characters 0,5 victory.

% victories
1) Carolijn: 70,00%
2) Sophie and Urs: 62,50%
4) Leonardo: 10,00%

Each adventurers favorite opponent (winrate)
1) Carolijn has 100% winrate against Leonardo (66,67% against Urs)
2) Sophie has 66,67% winrate against Carolijn and Leonardo (50% against Urs)
3) Urs has 100% winrate against Leonardo.
4) Leonardo has no winrate above 50%.

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Total: 2p + 4p + 3p tournament
Avg gold per game (change this round)
1) Sophie 17,21 (+0,03)
2) Leonardo 16,89 (-0,32)
3) Carolijn 16,82 (-0,06)
4) Urs 16,01 15,92 (+0,09)

[GrandAt]

3p - tournament!
Statistics after second round
Only statistics from games that finished in time

Unofficial scoreboard (gold)
1) Master_of_Buckland, Galnar and Harvepin all on 20 gold (and battling it out in the top-match of round 3).

Most gold
1) Carolijn: 170 (+90)
2) Sophie: 160 (+89)
3) Yrs: 152 (+81)
4) Leonardo: 97 (+37)

Average gold/game (3p)
1) Sophie: 17,78 (+0.03)
2) Urs: 16,89 (-0,86)
3) Carolijn: 15,45 (-0,55)
4) Leonardo: 13,86 (+1,86)

The statistics below are calculated by considering each 3p game as 2 duels for each character. The character ending on 1st place in a game wins 2 duels. Ties gives both characters 0,5 victory.

% victories
1) Sophie: 63,89% (+1,39)
2) Urs: 52,78% (-9,72)
3) Carolijn: 50,00% (-20,00)
4) Leonardo: 28,57% (+18,57)

Each adventurers favorite opponent (winrate)
1) Sophie has 75% winrate against Urs (62,50% against Carolijn)
2) Urs has 100% winrate agains Leonardo
3) Carolijn has 66,67% winrate against Leonardo
4) Leonardo has 50% winrate against Sophie.

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Total: 2p + 4p + 3p tournament
Avg gold per game (change this round)
1) Sophie 17,24 (+0,03)
2) Leonardo 16,93 (+0,04)
3) Carolijn 16,69 (-0,13)
4) Urs 16,02 (+0,10)

[GrandAt]

3p - tournament!
Statistics after third round
Only statistics from games that finished in time

Unofficial scoreboard (gold)
1) Harvepin 60 (still undefeated!)
2) qwernish 56
3) Master_of_Buckland 55

Most gold
1) Sophie: 248 (+88)
2) Carolijn: 244 (+74)
3) Urs: 202 (+50)
4) Leonardo: 158 (+61)

Average gold/game (3p)
1) Sophie: 16,53 (-1,25)
2) Carolijn: 16,27 (+0,83)
3) Urs: 15,54 (-1,35)
4) Leonardo: 14,36 (+0,50)

The statistics below are calculated by considering each 3p game as 2 duels for each character. The character ending on 1st place in a game wins 2 duels. Ties gives both characters 0,5 victory.

% victories
1) Sophie: 58,33% (-5,56)
2) Carolijn: 56,67% (+6,67)
3) Urs: 44.23% (-8,55)
4) Leonardo: 36,36% (+7,79)

Each adventurers favorite opponent (winrate)
1) Sophie has 75% winrate against Urs
2) Carolijn has 62,50% winrate against Leonardo (60% against Urs)
3) Urs has 83,33% winrate agains Leonardo
4) Leonardo has 50% winrate against Sophie

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Total: 2p + 4p + 3p tournament
Avg gold per game (change this round)
1) Sophie 17,08 (-0,16)
2) Leonardo 16,85 (-0,08)
3) Carolijn 16,77 (+0,08)
4) Urs 15,86 (-0,16)

[GrandAt]

3p - tournament!
Statistics after fourth round
Only statistics from games that finished in time

Unofficial scoreboard (gold)
1) Harvepin: 79
2) Master_of_Buckland and justgman47: 75

Most gold
1) Sophie: 341 (+93)
2) Carolijn: 311 (+67)
3) Urs: 249 (+47)
4) Leonardo: 246 (+88)

Average gold/game (3p)
1) Sophie: 17,05 (+0,52)
2) Urs 15,56 (+0,02)
3) Carolijn: 15,55 (-0,72)
4) Leonardo: 15,38 (+1,02)

The statistics below are calculated by considering each 3p game as 2 duels for each character. The character ending on 1st place in a game wins 2 duels. Ties gives both characters 0,5 victory.

% victories
1) Sophie: 61,25% (+2,92)
2) Carolijn: 47,50% (-9,17)
3) Urs: 45,31% (+1,08)
4) Leonardo: 43,75% (+7,39)

Each adventurers favorite opponent (winrate)
1) Sophie has 79,17% winrate against Urs (56,25% against Carolijn)
2) Urs has 75% winrate agains Leonardo
3) Carolijn has 50% winrate against Leonardo and Urs
4) Leonardo has 50% winrate against Sophie and Carolijn

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Total: 2p + 4p + 3p tournament
Avg gold per game (change this round)
1) Sophie 17,15 (+0,07)
2) Leonardo 16,89 (+0,04)
3) Carolijn 16,59 (-0,18)
4) Urs 15,86 (no change)