Author Topic: Faction Balancing - Statistical Analysis of WNL 2013 Matches  (Read 3410 times)

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imemine

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Faction Balancing - Statistical Analysis of WNL 2013 Matches

Since it was argued many times that the factions are not balanced in Warband and that there is a need to improve the balancing, I have conducted a statistical analysis of the WNL matches 2013 to base this argumentation on empirical data. Up to now, the argumentation was rather based on personal feelings and experiences of the players than on valid empirical evidence. However, the opinions differ from each other, thus, I feel that there is a need to have empirical evidence that supports or falsify the single assumptions on the amount and kind of imbalance between factions.

1. Methods
1.1 Leading question
Do different factions have an impact on the match outcome independent of the skill of the teams (players)? Or in other words: Are the factions balanced?

Further assumptions and theoretical background:
The WNL is a kind of measurement for the skill level of the participating teams (players). So teams (players) that have a higher skill should win more often independent of the faction they have to play with. Each faction is equally frequently played by the teams, cause each team plays an equal amount of rounds with both of the available factions during a match. Due to these conditions you can analyse if the factions influence the match outcome over all teams (weak and strong ones) or not. If the factions are balanced, each faction should win 4 rounds in average over all teams and matches, cause each faction is played for 4 rounds during a match by both teams on one map (Note: The matches were divided into two separate sets cause different maps have different conditions and in each WNL match 2 maps are played).
Since different factions have different advantages and disadvantages in the three available troop classes (infantry, archers/crossbowmen, cavalry) and these advantages can be used to a higher or lower amount on open vs. closed maps, it can be assumed that the map type might influence the impact of the factions on the battle outcome as well. Thus, the map type was included in the further analyses to test whether it moderates the faction's impact on the outcome or not.
(click to show/hide)

1.2 Data (sample): Which data were analysed?
The match results in WNL 2013 were confirmed by screenshots, which show how many rounds were won by a certain faction during a match (see WNL Archive, or WNL Week Fixtures). I have included all data that was available until 27th July. I will conduct a reanalysis of the data and include the matches that are still missing as soon as the WNL 2013 will be finished. However, since there are only a few matches that are still missing, the results shown below won't change that much.
Remember, the WNL matches took place before the patch 1.157 was released and even after the release the WNL continued to use the 1.153 settings.
In the spoiler below you find further information on how missing data was dealt with (e.g., no screenshots available, some screenshots missing, default win).
(click to show/hide)
In each WNL match 2 maps are played by both teams. The two maps were treated as separate cases, cause due to the different type of maps the rounds played on open vs. closed maps underlie different conditions.
On each map 8 rounds are played, 4 rounds for each faction. For each data set the following information was gathered from the screenshots:
  • WNL week (1-12)
  • Match # (a distinct number to identify the single matches, cause the 2 maps of one match were treated as two cases)
  • Faction 1 (Swadians, Rhodoks, Sarranids, Nords, Vaegirs)
  • Faction 2 (Swadians, Rhodoks, Sarranids, Nords, Vaegirs)
  • Map name (San'di'boush, Frosty Battle, Field by the River, Fort of Honour, Vendetta, Dry Valley, Mountain Fortress, Nord Town, Shariz Village, Ruins, Reveran Village, Verloren, Khudan Outskirts, Castle Ruins, Port Azur)
  • Map type (open vs. closed)
  • rounds won by faction 1 in trail 1
  • rounds won by faction 2 in trail 1
  • rounds won by faction 1 in trail 2
  • rounds won by faction 2 in trail 2
  • draws in trail 1
  • draws in trail 2
Note: Trail means the four rounds that were played by the same team with a certain faction on each map. There are 2 trials on each map cause the teams swap the factions after 4 rounds.

For the following analyses the variables "rounds won by faction # in trail 1" and "rounds won by faction # in trail 2" were aggregated to the variable "total rounds won by faction #". Furthermore, the variables "Faction 1" and "Faction 2" as well as "total rounds won by faction 1" and "total rounds won by faction 2" were aggregated to the variables "Faction" (including both factions played on one map in a match) and "total number of rounds won", respectively.

In total, we got 558 valid sets of data for the analyses (108 sets for Vaegirs, 114 for Rhodoks, 115 for Swadians, 117 for Sarranids and 104 for Nords, including 280 sets for open and 278 sets for closed maps).

1.3 Statistical Analyses
To test the hypothesis that the factions are not balanced and thus, there are differences in the average number of rounds won between the factions a 2 x 5 univariate analysis of variance was conducted with "map type" (open vs closed) and "faction" (Swadians, Rhodoks, Sarranids, Nords, Vaegirs) as fixed factors and "total number of rounds won" as dependent variable.
An analysis of variance is used to examine whether there are differences in the average score of a variable (called mean) comparing different conditions (called factor levels, e.g., Swadians is one level of the factor "faction" and "open" is one level of the factor "map type"). Differences in the total amount of rounds won comparing the single factions would indicate that the factions are not balanced and have an impact on the battle outcome that is independent of the skill of the teams (players). This effect might be moderated by the different map conditions (open vs. closed), this means the impact might be larger or smaller on different map types.

2. Results
2.1 Descriptive Statistics

(click to show/hide)
As you can see in the table above the factions differ in average from the expected average number of rounds won of 4.0 in the different conditions (open vs closed maps and total = over both map types). This suggests, that the factions have an impact on the match outcome independent of the skill of the participating teams (players). However, the difference is quite small, what suggests that the battle outcome is mainly based on the skill of the teams and not the faction choice.
The following inferential statistical analysis will examine with which probability our assumption that the teams are imbalance is true for the popoulation (this means the observed differences in this sample applies to all Warband matches ever played) as well.

2.2 Faction Balancing
2.2.1 Test of between-subjects effects (or are there significant differences between the factions, between the map types and concerning the interaction of map type and faction in the sample of data?)

(click to show/hide)
The analysis of variance revealed that factions have an significant impact on the battle outcome. The probability of error is 0.001, this means we can be 99,9% sure that the observed differences in the average total number of rounds won are not based on randomness and can be found in the population as well. The level of significance is usually at least set to 0.05 in scientific research. Thus, to prove that an assumption is valid you must be at least 95.0% sure that your observed effect in the sample is not based on randomness. If the probability of error is smaller than 0.05 than you have validated your assumption based on empirical evidence.
In contrast, the map type neither has a main effect on the battle outcome nor it moderates the impact of the factions on the battle outcome (statistical interaction faction x map type). Both effects (map type, faction x map type) don't reach the level of statistical significance (<0.05). However, the probability of error in case of the interaction is not that high, so we have a kind of tendency for a moderating effect of the map type on the impact that factions have on battle outcome. This means if we include more data in the analyses the effect might become significant but with the current data we just can't be sure enough that this assumption is true.

Now you might wonder, how large is this impact that the factions have on the match outcome? The analyses showed that the impact is quite small (partial eta squared = .034). In plain terms only 3,4% of the outcome of rounds is rather affected by the faction that is played than by the skill of the teams (players). Luckily this strongly suggests that in fact the factions overall are/were balanced in Warband (before the patch 1.157).

2.2.2 Test of within-subjects effects (or which factions differ significantly from each other in the total number of rounds won?)

Note: Although the figure shows that there are differences in the total average number of rounds won, this does not mean that each small difference can be observed in the population (all matches ever played in Warband) as well. Most of the differences are very small (e.g., difference between Nords and Vaegirs on both types of maps), thus we need to check with the statistical analyses if this differences are significant and if we can be at least sure with 95% probability (or a probability of error (p) below the level of 0.05).

The analyses revealed that in average Vaegirs significantly won more rounds than Rhodoks (p < .01), Swadians (p < .01) and Sarranids (p < .05). They don't differ significantly in the number of rounds won compared to Nords. Nords significantly won more rounds than Rhodoks (p < .01) and Swadians (p < .05). No other significant differences in the total number of rounds won could be found in the comparison of the single factions.
In plain terms, Veagirs and Nords are stronger than the other factions, but they don't differ in strength from each other. Swadians and Rhodoks are the weakest factions and Sarranids belongs to the weaker factions as well.

If we have a closer look at the comparison of open vs. closed maps, we can see in Figure 1, that Swadians and Rhodoks show an equal performance on both types of maps, Vaegirs and Nords are both slightly better on closed maps and Sarranids show a better performance on open than on closed maps. Since the statistical analyses revealed that the interaction between faction and map type wasn't significant, we have to assume that the differences between the factions on a certain type of map is based on randomness. So further comparisons between the factions can't be applied.

3. Discussion and Conclusions
In summary, the analyses revealed that there is an imbalance between the factions. Vaegirs and Nords significantly are more likely to win independent of the skill of the team (players) that is playing with this faction. However, the impact of the factions on the outcome of the battle is rather small, only 3,4% of the outcome is affected by the factions and not by the players' skills. Therefore, the factions are/were balanced in Warband (v1.153).

Conclusions concerning the balancing after the changes of Warband patch v1.157
To improve the balancing between the faction the patch v1.157 mainly focus on the following aspects:
  • reducing the archer athletics skill by 1 point for all faction
  • reducing the price of several equipment mainly for Swadians
  • Vaegir archers don't have access to a scimitar anymore

If we want to predict if the patch v1.157 might provide a better balancing for the factions, we have to find and discuss potential explanations for the imbalance that was proved by the empirical data.
The stats of the different classes for each faction that determine fighting performance show that the observed differences in the total number of rounds won are reflected by the amount of skill points of each faction (for reference see this thread or have a look at module_troops.py in the Warband module system of version v1.153). Beside the skill points, proficiencies and equipment might have an influence on the performance of the factions as well.
(click to show/hide)
The different distribution of total skill points and proficiencies among the faction suggests that approaches to improve the balancing between the factions should focus on a more equal distribution. If we have a look at the aproaches made by the patch, we could only find a change in skill points that affects all factions. Therefore, this approach will unlikely improve the balancing between the factions. In plain terms, the empirical data suggests that the archer nerf doesn't improve the balancing between factions. Moreover, since Swadians and Rhodoks that have crossbowmen already show a lower performance than factions with bow archers, the archer nerf might even increase the imbalance between the factions.
However, skill points and proficiencies are not that highly associated with the total number of rounds won (correlation r <.30), that they could explain the observed differences in total. It is more likely that the observed differences are based on the different equipment that is available for each faction. The improved accessibility to better armour for Swadians might help to improve their performance in matches. However, Rhodoks and Sarranids don't profit from these changes and have a similar performance as Swadians. The Vaegirs that are beside the Nords the strongest faction, might show a slightly less good performance if their archers don't have access to a scimitar anymore. However, if we take into account that Sarranid archers have access to a scimitar as well and don't show a good performance especially on closed maps, we have to assume that rather the equipment and skills of the Vaegirs infantry than the melee skills and equipment of the Vaegir archers leads to the observed strength of the faction.
Furthermore, Nords and Rhodoks are not affected by the approaches of the patch concering balancing. And since Rhodoks are one of the weaker factions compared to Nords (a faction that is as strong as Vaegirs are) this aspect of imbalance is not resolved by the patch.

Taken together, the patch will more likely bias the imbalance that exists between the factions than provide a better balance. And if we take into consideration that the imbalance is overall quite small, applying the changes is not recommendable by any account cause you will likely get another kind of imbalance and you are even at risk to increase the current imbalance .

Edit: Skill points and proficiencies were corrected in the spoiler of the discussion.
« Last Edit: July 30, 2013, 04:23:38 AM by imemine »

sotamursu123

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #1 on: July 30, 2013, 02:24:19 AM »
You should only count in high-level teams and players opinions to be honest. Many aren't using the factions to their full potential.

And the line between high-level and low-level is hard to define so hmmmng.
(click to show/hide)



Marowit

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #2 on: July 30, 2013, 02:24:36 AM »
Haven't read it yet, but looks absolutely phenomenal and thrilling.

Nicely done!
Honestly though, I don't think volunteering to fight in a war should be a merit in today's society.  :?
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imemine

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #3 on: July 30, 2013, 02:40:20 AM »
You should only count in high-level teams and players opinions to be honest. Many aren't using the factions to their full potential.

And the line between high-level and low-level is hard to define so hmmmng.
(click to show/hide)

The results concerning the faction balancing are not affected by this aspect since this effect applies systematically to all factions and high-level and low-level teams played the same amount of rounds with each faction. Moreover, I used a statistically approach that allows me to prove how balanced the factions are independent of the skill of the teams or their ability to use the full potential of a certain faction. Thus, the results wouldn't be different if only high-level teams were included.

Haven't read it yet, but looks absolutely phenomenal and thrilling.

Nicely done!

I would not have expected that someone else but me thinks statistical analyses are thrilling  :wink: So thx! :D
« Last Edit: July 30, 2013, 02:51:40 AM by imemine »

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #4 on: July 30, 2013, 03:21:17 AM »
Was a good read. I think I might have to do some math on loadout pricing between the two patches (seeing analysis makes me want to do some). Going to take some time but should should prove interesting :D
« Last Edit: July 30, 2013, 03:32:13 AM by Cradoc »

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #5 on: July 30, 2013, 05:18:12 AM »
I'm going to speculate a little bit about this:

Quote
The Vaegirs that are beside the Nords the strongest faction, might show a slightly less good performance if their archers don't have access to a scimitar anymore. However, if we take into account that Sarranid archers have access to a scimitar as well and don't show a good performance especially on closed maps, we have to assume that rather the equipment and skills of the Vaegirs infantry than the melee skills and equipment of the Vaegir archers leads to the observed strength of the faction.

Vaegir infantry equipment was somewhat reliant on Vaegir archers in the previous verison, seeing as the "common" tactic was for Vaegir archers to get 2 free scimitars and trade one of them to an infantryman for a shield. The extra shield was cheaper than buying a scimitar as infantry so that meant Vaegir infantry effectively had a discounted scimitar, allowing them to spend money on other gear such as helmets or throwing weapons for more survivability or utility. By removing the free scimitar from Vaegir archers, Vaegir infantry practically lose out on those discount scimitars except when their team's composition includes enough cavalry to provide them. It might be more of an issue on closed maps, where higher proportions of cavalry in a team composition are much more rare. I also feel that this cuts both ways as Vaegir archers will most likely still want shields and will look to their infantry teammates to provide them, but they will no longer have anything to offer in return. This (along with the lack of a free scimitar) could lead to Vaegir archers being a detriment to their teams in melee and create a statistically significant impact on the faction's performance (most likely on closed maps). I wouldn't be surprised at all if the overall performance of the Vaegirs dropped as a result of their infantry having less money to spend on utility items and/or survivability and their archers having a noticeable decrease in melee effectiveness.

My $0.02 on that aspect. I'm going to come back when I'm less tired so I can actually understand the statistics.

Golradir

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #6 on: July 30, 2013, 11:25:39 AM »
I heard you were busy with some statistics chat, but didn't expect this ;_;  I'll read it when I'm more awake :o
Did you do this alone or with oli?
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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #7 on: July 30, 2013, 01:52:14 PM »
Really great and interesting work here. The conclusions seem a little unjustified. Vaegirs haven't just had their archers needed. Much of their equipment has seen a price hike.

Swadia also gets a nice boost with some cheap gear. Both the crossbow factions benefit from jump reloading and the archer nerf. It's possible that Rhodoks have not received a high enough relative boost. Their issue has always been lack of decent mid tier armour options. Sarranids get a nice bump from price changes as well.

Honestly outside of Rhodoks, this data is pretty much in line with the changes in the patch.

Obviously the data can never be perfect since each faction needs to be looked at concerning how it matches up with other factions specifically. Outside of mirrors there are 10 matchups that should be balanced. For example I always think Rhodoks suffer very heavily against Vaegirs because the scimitar cuts through their paper armour.
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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #8 on: July 30, 2013, 02:27:08 PM »
Really impressive work, well done!

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #9 on: July 30, 2013, 02:57:29 PM »
Another important thing to note from the statistics is the exceptionally closed nature of the open maps this season. It's interesting that Rhodoks fared so poorly with such a closed map pool. It'd be nice to see how a tournament looks on the new patch.
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Lord Rich

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #10 on: July 30, 2013, 03:51:16 PM »
Rhodoks did poorly but at the same time they were included 6/10 times on open maps and while one of those times was mountain fortress (which is not really open) they were the attacking side on that map (and mountain fortress is a pretty biased map at the moment). Of the closed maps they fought at least 1 more was at a disadvantage as well attacking on vendetta. Additionally in both those circumstances the faction they were fighting was the nords. Of their remaining 3 matches 2 were on Fort of Honour which is relatively balanced I believe and one was defending on verloren. Overall I would classify them as the weakest open map faction, so perhaps it isn't a surprise that statistically they did poorly, but I would consider them as strong as nords at closed maps.

The order I classify the factions in terms of strength at the different types of maps:

Closed Maps
Nords
Rhodoks
Sarranids
Vaegirs
Swadians

Open Maps
Vaegirs
Swadians
Sarranids
Nords
Rhodoks

I don't think rhodoks really have any problems myself, they have good starting gear comparable to any other team, great 1H's, the best shields, the best selection of polearms and their crossbows are better equipped than swadia's. Their cavalry is a real weakness because of the low riding skill but they are at least equipped ok and can get hunters with some armour. The main weaknesses for rhodoks are their cavalry and the lack of good armour upgrades. The infantry one is nice but costs a ton and the xbows are the only class in the game without heavy armour. It's ok to have that sort of disadvantage though because they also have some great infantry weapons and equipment to make up for it.

Perhaps the only thing I would suggest is give the crossbows some heavy armour just so they have a money sink like all the other classes. But it should be expensive and comparable to the infantries.

imemine

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #11 on: July 30, 2013, 05:13:45 PM »
(click to show/hide)

This is a good point. So I agree that Vaegirs might show a overall lower performance if their archer equipment is limited and they can't support their infantry with free scimitars. However, to my knowledge the teams don't use this opportunity to a high extend, cause some players prefer to have the Elite Scimitar as infantry and just drop a free shield for their archers. So the reduced equipment accessibility of archers might not affect the overall performance of the teams in a high amount. It would have been nice to have data on the amount of equipment changes between the class, to prove whether this might affect the overall performance or not. But unfortunately these data is not available so far I know. In terms of balancing, a lower performance of the Vaegirs would strengthen the Nords. Nords have advantages in both melee skills and proficiencies as well as a good equipment of their infantry. But they are not affected by the patch. Therefore, I assume that Nord will become the most overpowered faction compared to the other factions in Warband and this might not improve the overall balancing.

(click to show/hide)

Another important thing to note from the statistics is the exceptionally closed nature of the open maps this season. It's interesting that Rhodoks fared so poorly with such a closed map pool. It'd be nice to see how a tournament looks on the new patch.

I have had compared the equipment settings of the factions and considered the information that is provided in the patch thread(s) so far. However, I didn't have had the time to make a detailed comparison of the equipment changes for all factions yet. I'm still working on that. I will update the discussion as soon as the reanalyses are done.
But I don't totally agree with the assumption that the changes in price might provide a better balancing between the faction at all. Since Nords are (to my knowledge) not affected by this, they will likely become the most overpowered faction (see also my statements above). The weakness of Rhodoks might be based on their weaker armour, but they have access to quite heavy shields, so their weakness might be rather based on the less fast 1H arms than on the available armour. Thus, I would appreciate if both factions Nords and Rhodoks would be more emphasized concerning the better balancing as well.

Concerning the archer nerf, you have to assume that the reduction in 1 point of atheltics would affect the bow archer factions to a higher degree than the crossbowmen if this should provide a better balancing between the factions. I'm really not sure if this is true. In contrast I assume that it strengthen factions with strong infantry and thus Nords might profit more than the other factions by the archer nerf. But Nords are already a strong faction, so the imbalance would be enlarged in this case.

With respect to the new patch it would be quite interesting to see how these changes affect the balancing and the composition of teams concerning the different classes. I will do a reanalyses for the next WNL for sure, but unfortunately, there is only a few public data available (streamed matches) that provide information on the composition of teams. (Possibly the logs of the matches, could be used as data base as well, however, I have no access to them.)


(click to show/hide)

Yep you are right, there might be a bias in the data of the WNL 2013 regarding the classification of some maps. However, the data doesn't support the assumption that Rhodoks are as good as Nords on closed maps yet. They showed a similar (poor) performance on both map types, open as well as closed. But I will check in the reanalyses if either the classification of "Mount Fortress" as open map or the position of the teams (defending vs attacking) have an impact on the battle outcome or affects the results as well. I will do the analyses as soon as the final screenshots (and hopefully some others that were still missing from AE ;)) are available for the WNL 2013 matches.

Furthermore, I will check if there is still enough information available from the previous WNL and/or other cups like 5aside and the Nations cup. If I found enough I will include this in the analysis, so the meaningfullness of the results is strengthened. I just need to find enough time to do this...   :roll:

I heard you were busy with some statistics chat, but didn't expect this ;_;  I'll read it when I'm more awake :o
Did you do this alone or with oli?

Oli did a great job as well, he supported me with coffee and guitar music! :lol:

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #12 on: July 30, 2013, 06:04:54 PM »
I would not have expected that someone else but me thinks statistical analyses are thrilling  :wink: So thx! :D
Actually, I'm with Eternal on that. That's a rather solid work, doubtless something beyond what Taleworlds has ever dreamt of doing when balancing breaking the game with the new patch. I have always supported solid data-based (as opposed to opinion- and taste-based) analyses for competitive Warband. Thank you for the solid work, Madame. Now, could you, please, do the same for North America (UNAC)? :)
« Last Edit: July 30, 2013, 09:08:37 PM by KissMyAxe »

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #13 on: July 30, 2013, 06:19:41 PM »
Thanks for the awesome work you have done here :) Very interesting to go through and it is nice to see some facts instead of opinions ;)


I would not have expected that someone else but me thinks statistical analyses are thrilling  :wink: So thx! :D
Actually, I'm with Eternal on that. That's a rather solid work, doubtless something beyond what Taleworlds has ever dreamt of doing when balancing breaking the game with the new patch. I have always supported solid data-based (as opposed to opinion- and taste-based) analyses for competitive Warband. Thank you for the solid work, Sir. Now, could you, please, do the same for North America (UNAC)? :)

Fix that and she might do it :P

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Re: Faction Balancing - Statistical Analysis of WNL 2013 Matches
« Reply #14 on: July 30, 2013, 06:30:24 PM »
I would not have expected that someone else but me thinks statistical analyses are thrilling  :wink: So thx! :D
Actually, I'm with Eternal on that. That's a rather solid work, doubtless something beyond what Taleworlds has ever dreamt of doing when balancing breaking the game with the new patch. I have always supported solid data-based (as opposed to opinion- and taste-based) analyses for competitive Warband. Thank you for the solid work, Sir. Now, could you, please, do the same for North America (UNAC)? :)
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