The Math behind Guild Wars [Pt.2.1]

Hello,

This is the second post in the series of ‘The Math behind Guild Wars’. In the previous part, we looked into a strategy that is able to reap the highest amount of war points.

However, what was yet to be addressed would be how this strategy would fit in different scenarios, such as changing win rates and participant count. Additionally, we will also examine what is the cut-off point where a non-battle frenzy strategy actually makes sense.

The posts will be structured as such:

Part 1: The Basic Math and Deriving a Strategy 
Part 2.1: Making sense of Battle Frenzy (Player Count) [you’re here now!]
Part 2.2: Making sense of Battle Frenzy (Win Rate)
Part 3: Guild War Calculator

P.S.: Yes, I’m still procrastinating on the second post of the combat formula.  

Before I commence, here’s your obligatory disclaimer notice that comes attached to all Guild war posts.


Disclaimer

Due to the unique scenarios for every guild war, it is near impossible to come up with an ‘universal‘ strategy that is applicable to every scenario. Thus, the strategy, itself, is focused upon finding out the highest number of war points that a guild can gain without resorting to paying (the ultimate rule-breaker in any instance).

This part of the post would be to make the strategy (and its math) less questionable by applying the strategy to different scenarios (eg. different number of players/opponents, different win rates etc.) and see how the math adds up.

As always, criticisms about the posts’ methodology, assumptions and the formulas that I’ve used are welcome here. If nothing were to make sense to you, hopefully the TL;DR quotes after each section is able to highlight the key points in each post.

Also, a bit of caution as this post contains high dosages of math so if you’re not into it, hopefully you can enjoy the pretty graphs and understand what I’m writing from the TL;DR notes.


News Update

Reported in the forums by developer Gameloft_DPS (source: Let’s Talk forums), the schedule of the Guild Wars has been slated for a 10 week cycle, alternating between the armor first followed by the weapon in each elemental run…

While no interpretation has been given, my guess is that the rank 1 and 2 will now reward the weapon for this weak, while rank 1 holds the armor…but that’s my guess and no confirmations yet until it’s out. 

“We started with Water, and will progress to Light, Dark, Nature, Fire in that order. This means a 10 week cycle to release rewards for all elements.

This is the current plan, but may be subject to change. We will be reviewing the release plan and rewards based on player participation and feedback.”

– Gameloft_DPS


Methodology of Comparison

As voiced in the former entry, an overly optimistic strategy was previously presented with certain conditions which are either tedious to achieve or near impossible to meet, depending on one’s guild’s play style, rigor and the opposing matched guild.

With a further developed calculator, we look into how this proposed strategy can be made more feasible under the different scenarios:


(1) Different Number of Participants

This varies the number of participants for each side (your guild vs opponent guild), with three different configurations of 30 vs 30, 15 vs 15 and an overwhelmed option of 15 vs 30.

These configurations take into account with Battle frenzy and without, while the win rate is kept at a constant of 100% for consistency.


(2) Different Win Rates*

*This has been postponed to the next post as the current one is getting too long.

Using a 30 vs 30, 15 vs 1523 vs 23 and 15 vs 30 configuration, different win rates (100%, 75%, 66.67%, 50%, 33.33%, 25%) are tested within this setup. (Basically it’s option (1) with the win rates factored in.)

By the way, this is where it gets interesting… 


Comparison #1: Different Number of Participants

30 vs 30 setup

30v30

15 vs 15 setup

15v15

As examined the last post, the 30 vs 30 setup yielded a large point difference of 2,048, demonstrating that the Battle Frenzy strategy is more beneficial than the non-Battle Frenzy one.

However, as the number of participants fall, there is a natural decline in war point difference, which drops to a smaller 548, indicating that the strategy is more worthwhile when there are a higher number of participants on both sides.

A graph is plotted below to add some color to the post and show the linear relationship between the point difference, keeping the number of both sides the same. Bear in mind that the win rate is still maintained at 100%.

linear vs.PNG
Chart showing the war points difference (y-axis) between 2 guilds of equal number of players (x-axis)

TL;DR: It’s more worthwhile to do battle frenzy when you have more players on both sides.

15 vs 30 setup

From the results, the strategy still holds up when your guild is pit against a larger one by the numbers. With a 15 member difference and no chance of achieving the second battle quest (ie clearing all of the opposition’s stars), the Battle Frenzy strategy still wins, but by a small increase of 168 points.

15v30

Frankly, when facing off a larger guild, one might consider opting for the non-Battle Frenzy strategy as one needs to recognise that these set of calculations are based on a 100% win rate and the minute point difference might not be worth it…

…or is it?

Before I go into that (in the next post), here’s another nifty graph that shows the relationship of war point difference between a range of 15 to 30 players vs a guild with a fixed number of 30 opponents. This is also based on the 100% win rate.

vs30.PNG
Chart indicating the war points (y-axis) between the 2 strategies for the number of participants (x-axis) against a fixed number of 30 opponents

And here we get to see the potential backlash of using the battle frenzy strategy as certain scenarios (ie. when the participating player count is between 18 to 21).

The non-linear relationship of the strategies is mainly attributed by achieving the 2nd battle quest for a player count of 18 (for non-Battle Frenzy strategy), which adds an additional 1,000 war points and explains the sudden increment of score. Likewise, for the Battle Frenzy strategy, this phenomenon is witnessed at above 24 players.

Nonetheless, one might argue that this window is indeed small and it is predicted that this level of specificity might not be applicable once win rates are factored into the picture. However, that is for the next post to address…

 TL;DR: There are specific conditions where having battle frenzy loses out to a non-battle frenzy strategy.


Okay, that’s about it for today. I’ll finish up the next post by sometime tomorrow and get into the specifics of win rate applied to these scenarios.

Hopefully, I’ve not lost too many readers after posting such a math-heavy post. 🙂

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