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Subject: Balance statistics: your help needed! rss

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Hi,

I created a spreadsheet to record games and try to see how the scenarios are balanced.
You can find it here: https://goo.gl/WrIvbY
(it might still be a bit buggy, please tell me if you find things going wrong)


(this is just a representation of what the table looks like, the actual latest updated version is accessible through the link above)

It will be much appreciated if you record the results of your games to improve the statistical prediction.

Thank you !
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Re: Balance statistics: your help needed
The spreadsheet is currently populated with previous results from the community of the French website Cwowd.

I still miss some information (name of additional scenario from SG box in English for example). Can you give send me them?

If you want me to create a panel for another language, just give me the needed translation.
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Mirko Zennaro
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Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.
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Mathieu Hatt
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mizenn wrote:
Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.


Perhaps there is something wrong on your side then. Or on their side.
ALl the more reasons to add your stats in
 
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Anders Olin
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As a stats-nerd I approve this list
 
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Shawn Garbett
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Using the provided numbers, how much confidence can we have in these results to determine if a scenario is "balanced", e.g. 50/50 chance for the heroes? Since we are not comparing any of these results to one another, and considering each separately a straight 95% confidence interval is computed. Also, I'm taking a fixed point in time from the spreadsheet which is approximately now.

Results:

> prop.test(wins, games)

11-sample test for equality of proportions without
continuity correction

data: wins out of games
X-squared = 16.244, df = 10, p-value = 0.09285
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3 prop 4 prop 5 prop 6
0.6101695 0.5384615 0.3636364 0.4000000 0.5000000 0.2857143
prop 7 prop 8 prop 9 prop 10 prop 11
0.0000000 0.5625000 0.5833333 1.0000000 0.2500000

Warning message:
In prop.test(wins, games) : Chi-squared approximation may be incorrect

> binom.exact(wins, games)
x n proportion lower upper conf.level
1 36 59 0.6101695 0.47437851 0.7345085 0.95
2 28 52 0.5384615 0.39469823 0.6776897 0.95
3 8 22 0.3636364 0.17197944 0.5934233 0.95
4 8 20 0.4000000 0.19119006 0.6394574 0.95
5 7 14 0.5000000 0.23036054 0.7696395 0.95
6 2 7 0.2857143 0.03669257 0.7095791 0.95
7 0 1 0.0000000 0.00000000 0.9750000 0.95
8 18 32 0.5625000 0.37662573 0.7363619 0.95
9 7 12 0.5833333 0.27666969 0.8483478 0.95
10 6 6 1.0000000 0.54074187 1.0000000 0.95
11 2 8 0.2500000 0.03185403 0.6508558 0.95


There is insufficient evidence to claim the game overall with the first 11 scenarios is unbalanced, with p-value = 0.09285. In looking at individual scenarios, the scenarios that have evidence of unbalance (i.e. lower and upper do not overlap 0.5) is only Infernal pursuit (2/2).

Code Used:


library(epitools)

heroes <- c(0.61, 0.54, 0.36, 0.4, 0.5, 0.29, 0, 0.56, 0.58, 1, 0.25)
games <- c(59, 52, 22, 20, 14, 7, 1, 32, 12, 6, 8)
wins <- round(heroes * games)

prop.test(wins, games)

wins <- wins[games > 0]
games <- games[games > 0]
binom.exact(wins, games)
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William Aull
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This is less about balance and more about people's personal experiences.
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Mirko Zennaro
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mathhatt wrote:
mizenn wrote:
Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.


Perhaps there is something wrong on your side then. Or on their side.
ALl the more reasons to add your stats in


There is a topic for that scenario on bgg where other report the same.
And there are no report of OL wins.

I'd like to wrong about this
 
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Jimmy Brazelton
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Played it on Saturday with 5 players and OL won. And I've been very active on the boards and played quite a few scenarios now, so I'm pretty confident that we didn't have any significant rules problems when we played. Those archers with a free reroll from Zapatero are pretty deadly...
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Shawn Garbett
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Hillean wrote:
This is less about balance and more about people's personal experiences.


The same numbers can be viewed in this light. Assuming that your group experiences similar play, the true winning ratio will be within the upper and lower bounds with 95% confidence.
 
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Stephan Beal
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mizenn wrote:
mathhatt wrote:
mizenn wrote:
Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.


Perhaps there is something wrong on your side then. Or on their side.
ALl the more reasons to add your stats in


There is a topic for that scenario on bgg where other report the same.
And there are no report of OL wins.

I'd like to wrong about this


The first time i played it, the Archers rolled exceptionally well and wiped the floor with the heroes in the first 2 turns. It was an absolute slaughter. Highly demoralizing. Spent half an hour wiping up the blood before playing it again (at which point the heroes won because i (mis)played the LOS rules as written, which makes the mast spaces immune to ranged attacks (because the LOS rules, as written, don't correspond to the reality of that particular board)).
 
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CyberGarp wrote:
Using the provided numbers, how much confidence can we have in these results to determine if a scenario is "balanced", e.g. 50/50 chance for the heroes? ...

Yeah an other stat-nerd !!!

Don't hesitate to suggest me anything you want to see added.
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Mirko Zennaro
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Conan reach Zapotero in the first turn.
The wizard give his gem to Conan.

Conan and the thief shot Zapotero. In every turn.
Belith only defend with his guard. At least five gem per turn plus guard sacrifice ability. No way her take 9 wound on 8 turn.

If There are no los to Zapotero, thief target the other boss or archer.

Zapotero in few turn (depend on roll) die. If other boss is just become demon... Ol lost. If not... lost after few turn becuse the last boss is week.

Your hero play in this way and you win? I don't think so.
If so... explain the OL strategy please.

We try this scenario a lot, also play with OL to try if he can win.
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Jonathan Walters
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We've played the scenario once, and with only two heroes at that, and the heroes carried the game. LOS was slightly problematic for us to figure out (like is the rear deck of BOTH ships elevated?), but overall the archers didn't feel overpowered at all in our game. Looking forward to playing OL on this scenario again now that I have a much better grasp of the rules.
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Stephan Beal
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mizenn wrote:
Conan reach Zapotero in the first turn.
The wizard give his gem to Conan.


What do you mean by the wizard giving gems to Conan? You cannot transfer gems between characters.

mizenn wrote:
Conan and the thief shot Zapotero. In every turn.


How does Conan shoot? He doesn't start with a ranged weapon. There is a Crossbow in 1 of the 5 chests, but Conan cannot collect that crossbow AND reach Zappy in the first turn - he doesn't start out with enough gems to do that. Only 2 of the 5 chests are on Conan's side of the boat, so there's only a 40% chance that the Tigress has the Crossbow at all, and Conan doesn't have enough energy on his first turn to reach and loot more than 1 of those chests (reducing the odds to 20% that he will find the Crossbow) AND cross over to the other ship AND reach Zappy's space.

i'm confused.

OTOH, if Shivvy can find the Crossbow on his first turn (on the Tigress), the Archers don't stand much of a chance against him.
 
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Mirko Zennaro
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sgbeal wrote:
mizenn wrote:
Conan reach Zapotero in the first turn.
The wizard give his gem to Conan.


What do you mean by the wizard giving gems to Conan? You cannot transfer gems between characters.

mizenn wrote:
Conan and the thief shot Zapotero. In every turn.


How does Conan shoot? He doesn't start with a ranged weapon. There is a Crossbow in 1 of the 5 chests, but Conan cannot collect that crossbow AND reach Zappy in the first turn - he doesn't start out with enough gems to do that. Only 2 of the 5 chests are on Conan's side of the boat, so there's only a 40% chance that the Tigress has the Crossbow at all, and Conan doesn't have enough energy on his first turn to reach and loot more than 1 of those chests (reducing the odds to 20% that he will find the Crossbow) AND cross over to the other ship AND reach Zappy's space.

i'm confused.

OTOH, if Shivvy can find the Crossbow on his first turn (on the Tigress), the Archers don't stand much of a chance against him.


The wizard have a mage that transfer his gem to a ready area of one hero.
Conan Jump to the other ship and reach Zapotero in melee.
 
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Stephan Beal
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mizenn wrote:
The wizard have a mage that transfer his gem to a ready area of one hero.


Aha - the "Gift of Life" spell does that. i didn't realize that.

Quote:
Conan Jump to the other ship and reach Zapotero in melee.


Ah, okay. You said Conan and Shivvy are shooting Zappy every turn.

(Sorry at the OP for thread-jacking. My bad.)
 
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Mirko Zennaro
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sgbeal wrote:
mizenn wrote:
The wizard have a mage that transfer his gem to a ready area of one hero.


Aha - the "Gift of Life" spell does that. i didn't realize that.

Quote:
Conan Jump to the other ship and reach Zapotero in melee.


Ah, okay. You said Conan and Shivvy are shooting Zappy every turn.

(Sorry at the OP for thread-jacking. My bad.)


Sorry... my bad English... I used shot as generic type of hit (range and melee)

Sorry OP me too. Would be better continue in the appropriate topic (is under session section).

But I'll double check that statistics. For that scenario the data seem inverted.
 
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Stephan Beal
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mizenn wrote:
sgbeal wrote:
(Sorry at the OP for thread-jacking. My bad.)

...
But I'll double check that statistics. For that scenario the data seem inverted.


It occurred to me later that if you are using Haddy in that scenario then you are using 4 heroes. Even minor changes in Conan scenarios (different characters, spells, or even small changes to starting equipment) can drastically alter the balance. i recommend trying it again with 3 heroes instead of 4.
 
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mizenn wrote:
Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.

Sorry my bad, there was a stupid bug; I inverted the column of Heroes and Overlord when importing previous data set.
It is fix now and goes your way.
With between 90% and 96% of heroes winning it seems to be one of the most unbalanced scenario.
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Mirko Zennaro
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Romn wrote:
mizenn wrote:
Hunting the tigres 100% win for OL in 5p??

There are no way to win for OL in 5p in our (and our friends) experience.

Sorry my bad, there was a stupid bug; I inverted the column of Heroes and Overlord when importing previous data set.
It is fix now and goes your way.
With between 90% and 96% of heroes winning it seems to be one of the most unbalanced scenario.




The link is ok.
The image on the first post is yet wrong
 
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CyberGarp wrote:
Using the provided numbers, how much confidence can we have in these results to determine if a scenario is "balanced", e.g. 50/50 chance for the heroes? Since we are not comparing any of these results to one another, and considering each separately a straight 95% confidence interval is computed. Also, I'm taking a fixed point in time from the spreadsheet which is approximately now.

Results:

> prop.test(wins, games)

11-sample test for equality of proportions without
continuity correction

data: wins out of games
X-squared = 16.244, df = 10, p-value = 0.09285
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3 prop 4 prop 5 prop 6
0.6101695 0.5384615 0.3636364 0.4000000 0.5000000 0.2857143
prop 7 prop 8 prop 9 prop 10 prop 11
0.0000000 0.5625000 0.5833333 1.0000000 0.2500000

Warning message:
In prop.test(wins, games) : Chi-squared approximation may be incorrect

> binom.exact(wins, games)
x n proportion lower upper conf.level
1 36 59 0.6101695 0.47437851 0.7345085 0.95
2 28 52 0.5384615 0.39469823 0.6776897 0.95
3 8 22 0.3636364 0.17197944 0.5934233 0.95
4 8 20 0.4000000 0.19119006 0.6394574 0.95
5 7 14 0.5000000 0.23036054 0.7696395 0.95
6 2 7 0.2857143 0.03669257 0.7095791 0.95
7 0 1 0.0000000 0.00000000 0.9750000 0.95
8 18 32 0.5625000 0.37662573 0.7363619 0.95
9 7 12 0.5833333 0.27666969 0.8483478 0.95
10 6 6 1.0000000 0.54074187 1.0000000 0.95
11 2 8 0.2500000 0.03185403 0.6508558 0.95


There is insufficient evidence to claim the game overall with the first 11 scenarios is unbalanced, with p-value = 0.09285. In looking at individual scenarios, the scenarios that have evidence of unbalance (i.e. lower and upper do not overlap 0.5) is only Infernal pursuit (2/2).

Code Used:


library(epitools)

heroes <- c(0.61, 0.54, 0.36, 0.4, 0.5, 0.29, 0, 0.56, 0.58, 1, 0.25)
games <- c(59, 52, 22, 20, 14, 7, 1, 32, 12, 6, 8)
wins <- round(heroes * games)

prop.test(wins, games)

wins <- wins[games > 0]
games <- games[games > 0]
binom.exact(wins, games)


Keep in mind that someone's first plays of a scenario is usually not an optimal play --being that the owners of the game will usually play overlord when teaching others to play, the overlord will usually be more experienced with the system. Just something to consider.
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mizenn wrote:



The link is ok.
The image on the first post is yet wrong

Yes, the image doesn't necessarily aimed to be accurate, it is more here to incite people to click on the link.
I still updated it with a more up to date version.
 
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Nathan Hoffmann
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So the balance is all over the place from scenario to scenario, but for what it's worth based on the current statistics the average odds are 57% hero victory.
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Mathieu Hatt
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The problem with the statistics is that they are likely to include a lot of games that did not follow the rules correctly (due to both the rulebooks to be unclear and the translation errors and such), and also a lot of "first games" in which neither the heroes nor the overlord know the game well enough. As such they may reflect more the lack of experience of gaming groups/players, as well as lack of clarity in the rules, than actual balance of each scenario.
Hopefully the V2 of the rules as well as time with additional games with more experience will tend to even these numbers.
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