Some first edition stats

[laggercat]

I've posted stats from around 18,000 second edition results here: https://boardgamegeek.com/thread/269712 ... unbalanced.

Here are stats from first edition, around 1,000 results. I'm not going to do much more than this. Four player games. There are not enough stats for the A sides, but there is around 120 games each for the B sides, which is not bad.

EDIT - see post later for updated stats

In terms of average score:
54.7 Hali
53.2 Rhodes
52.5 Ephesus
51.5 Giza
51.5 Olympia
51.2 Alexandria
48.9 Babylon

Average win percentage
39.2 Rhodes
31.4 Hali
30.8 Olympia
24.8 Ephesus
23.8 Alexandria
23.7 Giza
17.0 Babylon
(the average here is greater than 25% because some games include A sides)

Average last percentage
16.7 Rhodes
18.6 Hali
18.6 Giza
23.0 Alexandria
23.2 Ephesus
25.0 Olympia
32.0 Babylon

So, for first edition, Rhodes B looks the strongest wonder, with Hali second. Babylon is comfortably the worst of the B sides.

Although the sample sizes are small, most of the A sides look very bad, BUT the average ELO of those playing the A sides is a lot lower than for the B sides, so it might just be worse players.

Is first edition more 'even' across the wonders? If we just look at B sides then yes, but that's because second edition Olympia B is so horrible (11% win rate). Looking at the same stats for second edition B sides and Olympia A, we get these average win percentages for four player games (400 results for each wonder):

38.7 Hali
30.4 Rhodes
28.1 Babylon
25.6 Ephesus
23.2 Giza
22.9 Olympia (A)
16.0 Alexandria

That's a similar spread to first edition.

[Wonderful Plays]

Thank you for doing the hard work with these.

[6element]

This statistical exercise doesn't really help with understanding the game or improving your skills.

The game is not about comparing wonders, or finding the best/worst one. It has sufficient depth, variety, and flexibility. For example, there are cases where you have to guess what your opponents will pick right now, so it either requires memorizing play styles of particular opponents or some level of psychology.

[Lumin_S]

Thanks so much for calculating these, laggercat. I don't know how much manual effort went into this but it had to have been sizable.

@6element - for some context I don't think anyone is trying to apply these stats to improve at the game. Myself and others have been debating which edition of the game is more balanced, and the spread of win rates and scores is very helpful towards getting answers in that debate.

[laggercat]

Thanks so much for calculating these, laggercat. I don't know how much manual effort went into this but it had to have been sizable.

@6element - for some context I don't think anyone is trying to apply these stats to improve at the game. Myself and others have been debating which edition of the game is more balanced, and the spread of win rates and scores is very helpful towards getting answers in that debate.

This analysis didn't take that long as I had the spreadsheet set up from the analysis of second edition games.

Yes, I am not trying to improve anyone's game. All the stats show is that some wonders are very significantly better than others, and that the second edition did not make the wonders any more balanced compared to the first edition, which is very disappointing.

[laggercat]

I've done some more stats, going back into the pre-second edition times, with higher ELO players. About 1,300 results.

All four player still, B sides only

Average scores:
55.4 Hali
53.8 Rhodes
52.8 Ephesus
52.0 Alexandria
51.6 Olympia
51.5 Giza
49.9 Babylon

Average win %:
36.5 Hali
35.9 Rhodes
25.9 Olympia
25.4 Alexandria
25.1 Ephesus
22.5 Giza
17.1 Babylon

Average last %:
14.8 Rhodes
15.4 Hali
22.5 Giza
23.8 Alexandria
24.6 Ephesus
25.2 Olympia
32.9 Babylon

Not much different, except Hali has the best win rate now, although Hali and Rhodes are still pretty close, and way ahead of third place.

The distribution still looks pretty similar to second edition.

[ppsantos]

Data for 3,431 7-player games (7p games played by top players, from August 2020 and older):

--Win%-- % 1st+2nd place-- % 6th+7th place
Hb-- 45 64 6
Rb-- 29 48 9
Eb-- 27 48 12
Gb-- 27 42 10
Ab-- 25 45 14
Ob-- 25 42 16
Bb-- 20 35 16

Ha-- 23 38 18
Ra-- 27 38 19
Ea-- 17 40 15
Ga-- 31 51 11
Aa-- 25 39 14
Oa-- 30 44 16
Ba-- 11 32 21

Even with the old edition, among the B sides, Halikarnasus b wins most often (45%), also having the most stable performance (64% of games either as 1st or 2nd place, and only 6% of games placing as 6th or 7th ). Babylon b was the weakest, with win rate of only 20%.

Notable for the A sides are Giza A and Olympia A, having win rates higher than their B counterparts, with the much smaller data sample coming mostly from random board setup. Very few players pick Giza and Olympia A over their B sides, under choose board setup.

Comparing the old and new versions, what strikes me most is not so much how strong or ‘ahead of the pack’ Halikarnasus is (observed in both editions) but how close or ‘balanced’ the rest of the boards are compared with each other. In the old edition Hb’s win rate (45%) vs the weakest, Bb’s win rate (20%) is only 2.25 times compared to the new edition win rate disparity of 4.74 times (new edition, 7p games, Hn win 36.5%, An win rate 7.7%, posted in boardgamegeek thread). The win rate disparity between 2nd strongest board in the old ed, Rb 29% vs Bb’s 20% is just 1.45 times. But in the new ed, win rate of 2nd strongest board, En’s 14.6% is almost twice (1.9) compared to the weakest board An’s 7.7%

In the old edition, it feels like Halikarnasus b is the strongest and the rest are relatively ‘balanced’ compared to each other. Whereas in the new edition, not only Halikarnasus is still the strongest, there are now boards which feel obviously weakest (Alexandria and Olympia). It’s in this win rate disparity in the new edition between the strongest board and how it compares with the weakest and how the weakest compare with the rest of the boards that I believe the balance got worse in the newer edition.

[laggercat]

Data for 3,431 7-player games (7p games played by top players, from August 2020 and older):

--Win%-- % 1st+2nd place-- % 6th+7th place
Hb-- 45 64 6
Rb-- 29 48 9
Eb-- 27 48 12
Gb-- 27 42 10
Ab-- 25 45 14
Ob-- 25 42 16
Bb-- 20 35 16

Ha-- 23 38 18
Ra-- 27 38 19
Ea-- 17 40 15
Ga-- 31 51 11
Aa-- 25 39 14
Oa-- 30 44 16
Ba-- 11 32 21

Even with the old edition, among the B sides, Halikarnasus b wins most often (45%), also having the most stable performance (64% of games either as 1st or 2nd place, and only 6% of games placing as 6th or 7th ). Babylon b was the weakest, with win rate of only 20%.

Notable for the A sides are Giza A and Olympia A, having win rates higher than their B counterparts, with the much smaller data sample coming mostly from random board setup. Very few players pick Giza and Olympia A over their B sides, under choose board setup.

Comparing the old and new versions, what strikes me most is not so much how strong or ‘ahead of the pack’ Halikarnasus is (observed in both editions) but how close or ‘balanced’ the rest of the boards are compared with each other. In the old edition Hb’s win rate (45%) vs the weakest, Bb’s win rate (20%) is only 2.25 times compared to the new edition win rate disparity of 4.74 times (new edition, 7p games, Hn win 36.5%, An win rate 7.7%, posted in boardgamegeek thread). The win rate disparity between 2nd strongest board in the old ed, Rb 29% vs Bb’s 20% is just 1.45 times. But in the new ed, win rate of 2nd strongest board, En’s 14.6% is almost twice (1.9) compared to the weakest board An’s 7.7%

In the old edition, it feels like Halikarnasus b is the strongest and the rest are relatively ‘balanced’ compared to each other. Whereas in the new edition, not only Halikarnasus is still the strongest, there are now boards which feel obviously weakest (Alexandria and Olympia). It’s in this win rate disparity in the new edition between the strongest board and how it compares with the weakest and how the weakest compare with the rest of the boards that I believe the balance got worse in the newer edition.

Thanks for posting these stats! How did you collate them?

7 player games are the subject of some debate. Some players think that results from 7 player games are much more random than for lower player numbers - e.g. Wonderful Plays in this thread, which you are involved in already: https://boardgamegeek.com/thread/269712 ... unbalanced

I don't know if that's the case or not, however.

[ppsantos]

I manually collated them, from BGA game results, from 2017-2020. Back then, I'd look at the top ELO players (and decent rated players who consistently played 7p), and check their history for 7p games and record the results -win-or lose and what wonder was played.

I don't interpret the lower win rate for 7p due to randomness, but to increased competition amongst players, ie, it's easier to win when you are playing against only 2 opponents compared to when you are playing against 6. Since ELO rating is biased against higher player counts (the more players the bigger the 'normalizing factor to 4p' of ELO points gained/lost in the game) and in the absence of arena for 7p, I just track my win rate to get a sense of how good or bad my performance is for 7p games - 30% win rate is decent, 35%,good, and above that is excellent.

[Ratincage27]

I'm considering switching to playing Giza A (day) in many 3 player starting circumstances. I see that in 3 player games with good and bad players (new edition), Giza A has a slight scoring advantage over Giza B (54.9 vs. 54.7). But I'm wondering if that holds up with strong or 250+ ELO players.

Any thoughts/suggestions?

Specifically, I'm thinking about playing Giza A when neither of my opponents are Rhodes (tough to beat both opponents in military) or Olympia (side B advantaged because of the brick and, again, tough to beat both opponents in military if the Olympia player is a good player).