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Subject: Mermaids opening statistics - revisited rss

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Robert
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Mermaids opening statistics revisited
(data collected via https://flat1701.github.io/tmstats/; if you don't understand the abbreviations, look up the reference here: *click*)
Unless stated otherwise in the text, the statistics use the following filters:
* 4p games
* played by players rated >= 1100 (i.e. "Rating Quartile" is set to "Best + Good")
* original map
* Cultists Errata
* no F&I factions allowed (and thus no present )
* even in stats which include games that allowed F&I factions (e.g. "All factions"), my stats never include games which allowed variable factions before the official rule update ("v5")
* no additional scoring (Outposts aka "edge", distance, SA/SH distance, Settlements aka "clusters")
* don't care about whether the game allowed VTO, TW6-8, BON10, or TE>>4 round scoring

These filters pretty much represent the settings of a 4p game with the TM base game (plus VTO and mini-expansions) as it's used in the Terra Mystica tournament. You may rightfully argue that VTO or the presence of some mini-expansion (or not) will affect the chances of a faction, but the sample sizes just get too small and the differences are not overly relevant (and where I suspect they may be, e.g. BON10 and Mermaids, I'll check). This is about round 1 where only the starting order matters, so VTO (variable turn order) or not is less relevant.

The data lines focus on the relevant information - most filters will be mentioned in the text instead. All observations should be taken with a grain of salt, as some of the sample sizes are quite small.

The main comparisons are based on the column labeled "Margin". It contains the VP difference of the given faction compared to the average VPs in the game. So if a game between factions A, B, C and D ends 130:120:110:100VP, then the average VP count is 115VP, and the margins are +15, +5, -5 and -15 for factions A, B C and D respectively. If another game between the same factions ends 150:140:130:120, the respective margins will be exactly the same.
Still there is also a column labeled "VP" which gives the average VPs in the given scenario. Both "VP" and "Margin" come with an indicator of an error range (the number behind the '±') - the smaller this number, the more reliable is the value itself. This is usually correlated with the number of samples which are given in the "Count" column: a low number of samples (less than 50 or so) can be tainted much easier by some freak results than a large sample size.
Mermaids are a prime example that a faction which wins significantly more than one quarter of its 4p games can still have a not-so-great margin.

Included in "Observation 1" is a benchmark for games played by the remaining players (I'll refer to this group as "rated less than 1100" even though it includes unrated players too): the delta between their average with all factions compared to the faction whose openings I'm checking may give an indication how "difficult"/"forgiving" the faction is.


Observation 1: Mermaids give a worse-than-average margin in the hands of good players, and also sub-par in the hands of players of lower rating. This is a good example that margin isn't everything, since Observation 5 shows us that Mermaids win 35% of their games and come in 2nd in another 28%.
In my previous analysis, Mermaids also performed better margin-wise than average for players rated in the upper 50%. Still Mermaids seem to be an "easy-to-play" faction, and the rulebook recommends them for the first game when playing with 4p or 5p.
The margin situation improves dramatically on the new maps (without expansion scoring), especially for players with ratings above 1100 where they look OP both regarding win rate and average margin. Note that the sample sizes for the F&I maps are quite small.
Desc. VP Margin Count
ORIGINAL MAP
games played by players rated >= 1100
All factions 128.58 ± 0.09 6.01 ± 0.09 33615
No F&I factions 128.62 ± 0.09 6.01 ± 0.09 33058
Mermaids 128.81 ± 0.27 5.21 ± 0.27 3241 (set for further analysis)

games played by players rated less than 1100
All factions 108.96 ± 0.10 -5.40 ± 0.09 37453
No F&I factions 108.97 ± 0.10 -5.42 ± 0.09 36718
Mermaids 108.68 ± 0.37 -6.19 ± 0.33 2976

NEW F&I MAP ("side 1")
games played by players rated >= 1100
All factions 126.00 ± 0.52 5.29 ± 0.50 1129
No F&I factions 127.77 ± 0.67 6.12 ± 0.64 702
Mermaids 131.74 ± 2.20 11.17 ± 1.86 73

games played by players rated less than 1100
All factions 107.44 ± 0.57 -4.66 ± 0.52 1283
No F&I factions 108.19 ± 0.67 -4.54 ± 0.62 946
Mermaids 107.67 ± 2.07 -4.66 ± 1.87 98

REVISED MAP ("side 2")
games played by players rated >= 1100
All factions 128.38 ± 0.48 5.63 ± 0.45 1296
No F&I factions 129.35 ± 0.58 6.63 ± 0.55 859
Mermaids 137.34 ± 1.83 14.04 ± 1.72 85

games played by players rated less than 1100
All factions 107.26 ± 0.61 -6.23 ± 0.52 1699
No F&I factions 108.59 ± 0.58 -5.16 ± 0.53 1105
Mermaids 113.46 ± 2.02 -1.49 ± 1.91 87



Observation 2: A whopping 78% of all Mermaids open with a temple, which seems like a good decision since it yields above-average results if accompanied by at least three dwellings or a TP (which 64% of the temple-building Mermaids achieved). But to really shine, temple-building Mermaids should end round 1 with TE+4D or TE+TP+D (more dwellings won't hurt ). 8% of all Mermaids achieved this.
Unlike most other factions, going on a total dwelling spree resulting in all 8 dwellings on the map at the end of round 1 is doable for Mermaids, given the right conditions. For good results, this should lead to at least seven dwellings (achieved by 6% of all Mermaids), otherwise it results in sub-par margins.
SA and SH openings don't work well - the increased shipping range is way to expensive in round 1.
Desc. VP Margin Count
SH 111.27 ± 1.50 -6.88 ± 1.49 103
SA 123.60 ± 9.38 2.90 ± 12.92 5
1TE 130.02 ± 0.29 5.87 ± 0.30 2513
0TE 126.84 ± 0.67 4.53 ± 0.65 620

breakdown of temple builders:
2TE 128.82 ± 5.71 2.89 ± 5.13 11
TPTE 131.29 ± 1.58 7.99 ± 1.62 92
* 0DTPTE 126.75 ± 2.33 2.24 ± 2.37 32
* DTPTE 131.36 ± 2.26 10.32 ± 2.40 47
* 2DTPTE 142.23 ± 3.82 13.67 ± 3.89 13
D0TPTE 126.06 ± 0.79 1.47 ± 0.79 343
2D0TPTE 127.83 ± 0.65 4.62 ± 0.67 511
3D0TPTE 131.17 ± 0.40 6.71 ± 0.40 1353
4D0TPTE 133.79 ± 0.91 10.03 ± 1.03 197
5D0TPTE 142.67 ± 4.18 12.33 ± 3.89 6

breakdown of non-TE/SH builders:
2TP0TE 123.89 ± 2.10 1.36 ± 2.19 55
* 0D2TP0TE 87.00 ± NaN -26.00 ± NaN 1
* D2TP0TE 116.58 ± 5.24 -3.92 ± 3.80 12
* 2D2TP0TE 125.79 ± 2.19 2.29 ± 2.82 34
* 3D2TP0TE 126.00 ± 4.49 6.88 ± 7.56 6
* 4D2TP0TE 147.50 ± 10.50 14.50 ± 3.25 2
TP0TE 123.49 ± 1.11 1.04 ± 1.08 204
* DTP0TE 128.00 ± 16.26 4.17 ± 15.58 3
* 2DTP0TE 115.20 ± 3.39 -9.52 ± 3.40 15
* 3DTP0TE 116.20 ± 3.53 -2.79 ± 3.24 20
* 4DTP0TE 120.40 ± 1.82 -0.56 ± 1.78 62
* 5DTP0TE 127.92 ± 1.53 4.25 ± 1.55 103
* 6DTP0TE 115.00 ± NaN -4.25 ± NaN 1

2D0TP0TE0SA0SH 109.33 ± 13.54 4.58 ± 13.49 3
3D0TP0TE0SA0SH 120.22 ± 4.63 1.83 ± 5.53 9
4D0TP0TE0SA0SH 114.42 ± 2.66 -3.10 ± 2.85 24
5D0TP0TE0SA0SH 121.77 ± 1.68 3.79 ± 1.86 81
6D0TP0TE0SA0SH 126.79 ± 1.94 3.74 ± 2.01 56
7D0TP0TE0SA0SH 134.12 ± 1.73 9.59 ± 1.68 96
8D0TP0TE0SA0SH 137.36 ± 1.51 12.26 ± 1.49 92



Observation 3: The most popular (22%) starting bonus tile for Mermaids is BON4 (ship+1 +3pw), followed by BON10 (Ship VP +3pw) with 21% and BON1 (spade) with 16% and BON5 (1w +3pw) with 15%. Of these, only BON4 leads to margins above average regardless of TE opening or dwelling spree, while BON5 only does reasonably well with a TE.
The next best results come from BON8 (priest), but it's with a TE - and it's the games ending round 1 with TE+3D which make this a successful bonus tile. Maybe in these cases the priest is used to advance ship for those Mermaids who didn't get a chance for BON4 yet want to reach out to blue hexes which require ship+2.
Note: 7D and 8D openings are exclusively achieved using BON4.
Desc. VP Margin Count
BON1 (Spade) 128.15 ± 0.63 4.33 ± 0.64 524
* TE 129.57 ± 0.65 5.14 ± 0.69 438
BON2 (Cult) 128.03 ± 1.31 3.33 ± 1.23 145
BON3 (6C) 128.44 ± 1.07 4.88 ± 1.00 207
BON4 (Ship+1) 130.24 ± 0.61 6.89 ± 0.60 701
* TE 129.55 ± 0.81 6.61 ± 0.79 370
* only D 133.22 ± 1.11 9.15 ± 1.07 229
BON5 (3pw,1W) 128.94 ± 0.67 6.03 ± 0.66 495
* TE 130.35 ± 0.69 6.78 ± 0.69 433
BON6 (SA/SH VP) 122.10 ± 1.63 1.73 ± 1.46 103
BON7 (TP VP) 116.77 ± 6.25 4.23 ± 7.09 13
BON8 (1P) 129.12 ± 0.79 5.50 ± 0.83 378
* TE 131.07 ± 0.82 6.43 ± 0.92 308
* TE+3D 135.23 ± 1.28 10.15 ± 1.42 118
* only D 120.84 ± 2.71 3.73 ± 2.54 37
BON9 (D VP) 122.80 ± 3.91 0.75 ± 4.42 10
BON10 (Ship VP) 129.18 ± 0.59 4.49 ± 0.61 665
* TE 131.16 ± 0.62 6.02 ± 0.65 553



Observation 4: Mermaids are twice as often picked from first seat than from last.
For each seat, I've listed the most popular bonus tiles picked from that seat. From the two first seats (which more than 60% of all Mermaids held) the best bonus tile by far was BON4 (ship+1), which interestingly is not true for Mermaids picked from seats #3, and only barely for those picked from seat #4.
Desc. VP Margin Count
seat 1 129.44 ± 0.47 5.55 ± 0.47 1063 (32.8%)
* BON3 (6C) 128.83 ± 1.35 4.39 ± 1.21 133
* BON4 (Ship+1) 131.94 ± 1.13 8.39 ± 1.12 181
* BON5 (3pw,1W) 130.13 ± 1.28 7.02 ± 1.27 116
* BON10 (ShpVP) 129.46 ± 0.78 4.32 ± 0.79 401

seat 2 128.91 ± 0.50 5.67 ± 0.50 912 (28.1%)
* BON4 (Ship+1) 131.72 ± 1.00 8.60 ± 0.97 229
* BON5 (3pw,1W) 127.63 ± 1.12 5.20 ± 1.17 160
* BON8 (1P) 129.37 ± 1.16 5.71 ± 1.23 149
* BON10 (ShpVP) 128.49 ± 1.12 4.76 ± 1.17 184

seat 3 128.54 ± 0.60 5.47 ± 0.59 730 (22.5%)
* BON1 (Spade) 128.17 ± 1.21 4.73 ± 1.16 171
* BON4 (Ship+1) 128.62 ± 1.28 5.25 ± 1.28 182
* BON5 (3pw,1W) 129.80 ± 1.34 7.17 ± 1.26 156
* BON8 (1P) 130.71 ± 1.63 7.38 ± 1.65 101
* BON10 (ShpVP) 128.05 ± 1.82 3.33 ± 1.89 65

seat 4 127.75 ± 0.65 3.39 ± 0.66 536 (16.5%)
* BON4 (Ship+1) 126.99 ± 1.70 3.53 ± 1.55 109
* BON5 (3pw,1W) 127.94 ± 1.78 3.52 ± 1.71 63
* BON8 (1P) 126.30 ± 2.14 -0.22 ± 2.58 50



Observation 5: Mermaids are a prime example that a faction which wins a way more than one quarter of its 4p games can still have a not-so-great average margin. The reason may be that Mermaids who win games do so with a smaller margin than other factions.
The fact that more than 60% of all Mermaids are picked from seats #1 and #2 seems to have a reason, as it leads to a higher probability to do well (i.e. win or come in 2nd).
Desc. VP Margin Count
winner 141.15 ± 0.33 20.18 ± 0.28 1146 35.4%
* seat 1 141.71 ± 0.56 20.46 ± 0.49 382 * 33.3%
* seat 2 140.39 ± 0.61 19.46 ± 0.51 342 * 29.8%
* seat 3 140.95 ± 0.65 20.27 ± 0.56 276 * 24.1%
* seat 4 141.84 ± 0.95 20.99 ± 0.88 146 * 12.7%

2nd place 129.57 ± 0.34 6.19 ± 0.22 893 27.6%
* seat 1 130.08 ± 0.58 5.76 ± 0.36 304 * 34.0%
* seat 2 129.05 ± 0.63 6.55 ± 0.45 244 * 27.3%
* seat 3 129.19 ± 0.78 6.66 ± 0.45 187 * 20.9%
* seat 4 129.83 ± 0.83 5.9 ± 0.49 158 * 17.7%

3rd place 120.35 ± 0.41 -4.82 ± 0.23 704 21.7%
* seat 1 119.82 ± 0.73 -5.48 ± 0.4 230 * 32.7%
* seat 2 120.57 ± 0.76 -4.34 ± 0.45 187 * 26.6%
* seat 3 120.07 ± 0.99 -4.9 ± 0.49 151 * 21.4%
* seat 4 121.23 ± 0.82 -4.3 ± 0.49 136 * 19.3%

last 111 ± 0.56 -16.84 ± 0.36 498 15.4%
* seat 1 111.25 ± 0.96 -16.35 ± 0.63 147 * 29.5%
* seat 2 111.64 ± 1.14 -16.37 ± 0.7 139 * 27.9%
* seat 3 108.97 ± 1.22 -18.18 ± 0.8 116 * 23.3%
* seat 4 112.11 ± 1.2 -16.64 ± 0.8 96 * 19.3%



Observation 6: About 37% of all Mermaids were picked in games which had D>>2 scoring in round 1, and that worked significantly better if it was the Fire variant. The reason is probably that the D>>2 of the Water variant in many of such games came later, when the Mermaids could actually benefit from the cult bonus.
Desc. VP Margin Count
R1: SPADE>>2 130.61 ± 0.63 6.41 ± 0.65 576
* built TE 132.15 ± 0.65 7.17 ± 0.67 491
* built only D 123.78 ± 2.90 6.81 ± 3.26 40

R1: D>>2 (watr) 128.34 ± 0.58 4.80 ± 0.59 671
* built TE 128.44 ± 0.71 4.91 ± 0.73 427
* built only D 130.61 ± 1.25 6.89 ± 1.21 163

R1: D>>2 (fire) 129.48 ± 0.73 6.62 ± 0.70 517
* built TE 130.09 ± 0.88 6.92 ± 0.89 332
* built only D 131.38 ± 1.57 8.39 ± 1.44 117



Observation 7: Now we look at relevant (sample size >50) openings with a margin above 8: A successful dwelling rush (to 7/8D) is almost always (185 out of 188 cases) requires BON4 (ship+1 +3pw). For the TE+4D/TE+5D crowd, 171 of the 203 used BON5 (+1w +3pw), which gives them a) the 3pw to use ACT6 (2 spade power action) and b) the extra worker for the 4th dwelling.
Desc. VP Margin Count
7D/8D
* BON4 (Ship+1) 135.83 ± 1.17 11.09 ± 1.14 185

TE+4D/5D
* BON4 (Ship+1) 129.94 ± 3.74 4.13 ± 3.30 16
* BON5 (3pw,1W) 134.27 ± 0.95 10.47 ± 1.06 171



Observation 8: This observation only covers the 2513 temple builders (who reached a 5.87 margin on average). FAV11 (Earth1, D>>2) is the dominating favor (almost 85%), and FAV6 (Water2, cult step) is the other favorite, often taken if there was a cult bonus from water in round 1.
Desc. VP Margin Count
FAV6 (W2) 126.34 ± 0.99 4.95 ± 1.07 185
* D>>2 (Water) 127.61 ± 1.77 5.95 ± 1.85 75
* TP>>3 (Water) 126.07 ± 1.78 5.49 ± 1.77 54
FAV7 (E2) 122.31 ± 2.53 1.05 ± 3.00 36
FAV8 (A2) 120.45 ± 2.19 3.08 ± 2.16 44
FAV9 (F1) 126.58 ± 1.92 2.75 ± 1.69 71
FAV10 (W1) 123.66 ± 1.91 -2.18 ± 1.93 58
FAV11 (E1) 130.95 ± 0.32 6.40 ± 0.32 2130



Observation 9: 62% of the Mermaids' games used VTO (variable turn order), which is slightly higher than the general VTO percentage of 59%. I.e. Mermaids were slightly more popular since VTO was introduced. Mermaids did significantly worse in games with VTO, but so do most factions (cf. this statistic on BGG). The delta in margin of 2.9 VP is minimally higher for Mermaids than it is for the average base factions (2.8 VP).
89% of the non-VTO games were recorded before April 2015, only 134 since. Just 28 VTO games were recorded before April 2015.
Desc. VP Margin Count
no VTO 127.79 ± 0.46 7.64 ± 0.45 1214
VTO 129.42 ± 0.33 3.75 ± 0.33 2027



Observation 10: Mermaids seem to get less leech in round 1 than the average faction, but when they get a lot, it significantly improves their margin. A dwelling rush leads to particularly low leech values (215 out of 361 leeched three or less, and another 115 leeched 4-7).
Desc. VP Margin Count
Power leeched by all factions in the tournament setting
0-3 125.29 ± 0.17 4.41 ± 0.17 9483 (28.7%)
4-7 128.83 ± 0.14 6.14 ± 0.14 13643 (41.3%)
8-11 131.09 ± 0.19 7.17 ± 0.18 7748 (23.4%)
12-15 133.15 ± 0.39 8.15 ± 0.36 1938 (5.9%)
16+ 131.89 ± 1.17 7.77 ± 1.04 246 (0.7%)

Power leeched by Mermaids in the tournament setting
0-3 124.87 ± 0.46 3.05 ± 0.46 1210 (37.3%)
4-7 130.19 ± 0.39 5.75 ± 0.4 1417 (43.7%)
8-11 132.83 ± 0.61 7.82 ± 0.63 559 (17.2%)
12-15 138.45 ± 2.07 11.88 ± 1.91 53 (1.6%)
16+ 148.5 ± 8.5 17.5 ± 4.75 2 (0.1%)



Special Observation: Since Mermaids and BON10 (ship**3VP, +3pw) go together nicely, here's how allowing BON10 affected the usage and success of Mermaids. Note that this covers just the fact whether BON10 was allowed in a game, but not whether it was actually present. Statistically, the probability of BON10 being in a 4p game when it is allowed is 70%.
As expected, players pick Mermaids more often when BON10 is enabled, and they make more VP.
Desc. VP Margin Count
BON10 disabled
No F&I factions 125.98 ± 0.27 9.29 ± 0.26 4392 (13.3%)
All factions 125.97 ± 0.27 9.30 ± 0.26 4512 (13.4%)
Mermaids 122.89 ± 1.10 5.93 ± 0.99 272 (8.4%)

BON10 enabled
No F&I factions 129.03 ± 0.10 5.51 ± 0.09 28666
All factions 128.98 ± 0.10 5.50 ± 0.09 29103
Mermaids 129.35 ± 0.28 5.14 ± 0.28 2969



Conclusion: Mermaids with the ship+1 bonus tile start the game with 12pw in bowl II. This means they can take power action ACT6 (2 spades) right away, and in combination with the temporary ship range of 2 they have no problems to place a lot of blue dwellings on the map, ideally with D>>2 scoring in round 1.
Ship+1 also works well with a temple opening - better than a temple opening with the spade bonus tile and about as good as using the +1w, +3pw bonus tile. In order to do well, temple builders need to end the round with TE+3D - TE+4D being a bit more difficult but also significantly more rewarding.


=================


New opening statistics for base factions:
- Alchemists: Alchemists opening statistics - revisited
- Mermaids: Mermaids opening statistics - revisited
- Witches: Witches opening statistics - revisited


Older opening statistics for base factions:
- Alchemists: Alchemist opening statistics
- Auren: Auren opening statistics
- Chaos Magicians: Chaos Magicians openings statistics
- Cultists: Cultists opening statistics
- Darklings: Darklings opening statistics
- Dwarves: Dwarves opening statistics
- Engineers: Engineers opening statistics
- Fakirs: Fakirs opening statistics
- Giants: Giants opening statistics
- Halflings: Halflings opening statistics
- Mermaids: Mermaids opening statistics
- Nomads: Nomads opening statistics
- Swarmlings: Swarmling opening statistics
- Witches: Witches opening statistics

Older opening statistics for expansion factions:
- Riverwalkers: Riverwalker opening statistics
- Yetis: Yetis opening statistics
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Luke J
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Thank you for updating this!

I am very surprised that Mermaids clock in as below average. In my games they almost always seem competitive.

A couple thoughts: Could the improved performance against the new maps actually result from the fact that those games are almost always played with Bon10 and often with the additional scoring tile (distance and cluster, in particular)?

My other thought was that bridges were more valuable on F&I Side 1 and Mermaids generally get to opt out of that competition, but then they also score very well on F&I Side 2 which is less bridge-dependent, so that explanation doesn't seem to suffice.

My biggest fear with Mermaids is ending up without sufficient neighbors. The leech statistics at the end seem to support that.
 
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Robert
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ljwoodw wrote:
A couple thoughts: Could the improved performance against the new maps actually result from the fact that those games are almost always played with Bon10 and often with the additional scoring tile (distance and cluster, in particular)?
The numbers above for the new maps are exclusively for 4p games without additional scoring or the possibility to pick F&I factions. That's why the numbers are so low: most games on F&I maps also allow additional scoring and/or F&I factions.

ljwoodw wrote:
My other thought was that bridges were more valuable on F&I Side 1 and Mermaids generally get to opt out of that competition, but then they also score very well on F&I Side 2 which is less bridge-dependent, so that explanation doesn't seem to suffice.
Less dependency on bridges certainly helps on all maps - on F&I side 2 the color distribution is more friendly for blue than on the other maps - Swarmlings are almost as OP as Mermaids.
 
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Silly Words
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Nice work Doc.
 
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