The Math behind Guild Wars [Pt.2.2]

Hello,

This is the second post in the series of ‘The Math behind Guild Wars’. In the previous part, we looked into the ‘best case scenario’ strategy and how having battle frenzy affects the overall score based on the number of participants.

As a continuation to Part 2.1, we now look into differing Win Rates instead.

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) 
Part 2.2: Making sense of Battle Frenzy (Win Rate)
 [you’re here now!]
Part 3: Guild War Calculator

P.S.: Yep, still procrastinating…  

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).

To recap, Part 1 lists the assumptions and explains the course of actions to obtain the highest possible war points. Part 2.1 discusses the methodology of comparison and gets down to the first comparison: using different number of participants to see how the strategy performs in comparison to a non-Battle frenzy one.

Like the previous post, 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 and pretty graphs after each section makes it more comprehend-able by highlighting the key points in each post.


Mentioned in the last post, this comparison aims to the do the following:

Using a 30 vs 30, 15 vs 15, 23 vs 23 and 15 vs 30 configuration, different win rates are tested within this setup.

This win rates that will be tested are:

  • 100.00% – perfect score
  • 75.00% – winning 3 out of 4 battles
  • 66.67% – winning 2 out of 3 battles
  • 50.00% – winning half of the battles
  • 33.33% – winning 1 out of 3 battles
  • 25.00% – winning 1 out of 4 battles

I’ll probably not go any lower as a below these rates means that you’re horribly over-matched and that implementing either strategy might not make a large impact to your overall score.


Comparison #2: Different Number of Participants

For ease of viewing, the final score has been tabulated and written in the front. If you want to see the workings of the calculator, kindly click on the individual image thumbnails below.

Furthermore, each section comes attached with its graph plotting the scores (y-axis) against the win rate (x-axis). Each showing the score difference:

  • a negative number means without Battle Frenzy has a higher score
  • a positive number means with Battle Frenzy has a higher score.

To make the post easier to read, I’ll shorten the name of the strategies to its respective color in the graph as its descriptor instead of typing the full term out:

  • Red: With Battle Frenzy
  • Green: Without Battle Frenzy

30 vs 30 setup

 Win Rate (%) with
Battle Frenzy
without
Battle Frenzy
Score Difference
25.00 1578 1580 -2
33.33 2438 1910 528
50.00 3518 2750 768
66.67 4418 4220 198
75.00 4868 4290 578
100.00 6848 4800 2048

As concluded in the previous post, the 30 vs 30 setup naturally rewards the highest score for both strategies.

Seeing the war points for different win rates proves a general trend that anything above 25% win rate would prevail for a strategy that does adopt Red. Despite the peak in the Green line at 66.67% win rate, the overall difference between scores is rather wide and demonstrates that the Red strategy is worthwhile for larger numbers.

TL;DR: Just use Red when you see max players for both sides. You probably won’t regret it.

30v30 rates
Chart of War Points for 30 vs 30 setup


15 vs 15 setup

Win Rate (%) with Battle Frenzy without Battle Frenzy Score Difference
25.00 658 1010 -352
33.33 1288 1160 128
50.00 1778 1580 198
66.67 2118 2860 -742
75.00 2298 2890 -592
100.00 3698 3150 548

In contrast, the 15 vs 15 setup has a much bigger score gap between both strategies, making it questionable whether Red is worthwhile unless the entire guild is able to achieve the full 100% score.

As observed, the Green strategy doesn’t lose out very much to the Red one with half of the stated win rates prevailing over the Red strategy. If you’re a strong guild, I’m predicting that most likely a 66.67% to 75% win rate is attained on the average, which easily falls within the better score of Green.

Even for the rates that it loses, the point difference is not very big either (<200 war pts), and hence it can be concluded that it’s a much safer option to take the Green strategy.

TL;DR: No Red for low numbers of players. Just stick to Green.

15v15 rates
Chart of War Points for 15 vs 15 setup


23 vs 23 setup

I then thought to myself, why not have an average number of player setup instead to see the correlation. Here’s the results of that:

Win Rate (%) with Battle Frenzy without Battle Frenzy Score Difference
25.00 1118 1310 -192
33.33 1928 1580 348
50.00 2698 2180 518
66.67 3318 3580 -262
75.00 3638 3630 8
100.00 5378 4030 1348

Like the other graphs, the Green strategy peaks at the same location of 66.67% win rate but fails to bring a significant difference in comparison to the battle frenzy strategy (262 war pts). The battle frenzy strategy is also well-sustained throughout, similar to the 30 vs 30 configuration.

Overall for 23 vs 23, the Red strategy excels in most instances of win rates (~30-60% & >75%) by a respectable amount on the average.

However, if you’re scoring very low (<30%) in terms of win rates, then resorting to a Green strategy would be more feasible in terms of scoring.

TL;DR: Red strategy makes more sense for a higher number of players on both sides

23v23 rates
Chart of War Points for 23 vs 23 setup


15 vs 30 setup

Win Rate (%) with Battle Frenzy without Battle Frenzy Score Difference
25.00 658 510 148
33.33 788 660 128
50.00 1278 1580 -302
66.67 2118 2000 118
75.00 2298 2150 148
100.00 2918 2750 168

With an overwhelmed configuration of 15 vs 30, one can see that the win rate for Red peaks much earlier than Green. This is attributed to the additional war points rewarded from the 1st battle quest (+500 pts). Green strategy gains it at 50% win rate, while Red strategy gains it later at around 66.67% instead.

Thus, looking at the trends, it’s safe to say that Red strategy generally provides a better option for scoring, unless you’re pretty certain that your guild is able to hit the specific 50% win rate.

Something which is not shown here visually would be that the smaller the difference between your guild and your opponent’s, that peak in score for the Red strategy will come much sooner, allowing a much larger range of win rates to perform better than Green. This means that the bigger your guild, the higher chance for your guild with the Red strategy to score better than the Green one.

Nonetheless, something to note would be that the point difference is not very huge between both Red and Green. But as mentioned above, the smaller the difference in numbers, the higher point difference will be. Thus, making Red even more suitable when the player count difference is smaller.

TL;DR: The larger your guild, the higher than chance for Red to be better than Green and the more points you’ll get.

15v30 rates.PNG
Chart of War Points for 15 vs 30 setup


Discussion of Results

For Part 2.2, we looked at how win rate influences the score between the Red and Green strategy. Below are some learning points to take away from these comparisons:

(A) For an equal number of players for both sides, Green’s score comes the closest to Red’s score when the win rate is 2 out of 3 (66.67%). This is because of the gain of the 2nd battle quest for Green (+1000 pts).

(B) The Red strategy is generally stable and performs exceptionally beyond 75% win rate as that is when they gain the 2nd battle quest.

(C) Also for the equal number of players for both sides, the higher the total number of players, the more worthwhile the Red strategy is.

(D) If you’re facing a larger guild, it still makes more sense to use Red as it wins in scoring for most win rates if you score over 25% of the raids.

(E) The smaller the player number difference between Guilds, your guild has a higher range of win rates for Red to excel over Green with a higher war point difference.

TL;DR: Just read (C), (D) and (E) if you don’t want math.


That concludes the comparison segment for this series of posts and the next will present a more refined and flexible version of the calculator.

Have fun and good luck for this week’s Guild Wars. 🙂

 

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5 thoughts on “The Math behind Guild Wars [Pt.2.2]

  1. I’d like to understand the non-linearity in your “green” results: specifically the consistent peak at 66.7% win rate vs it’s neighbors at 50 and 75. There must be something I’m missing about your model since it otherwise doesn’t make sense. Subject to aliasing due to the discrete nature of your data (you can’t win a fractional amount individually), 2/3 of 150 attacks is 100 wins vs 3/4 of 150 being 113 wins for, approximately a difference of 390 points, not 70 as reported.

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  2. Hi Michael,

    Thanks for taking interest in the post!

    The consistent peak at 66.67% is due to the attainment of the 2nd battle quest (+1000 war points) for the ‘Green Strategy’. This means that all of the stars of the opponents can be cleared if the win rate is greater than a 2 out of 3.

    This is of course, taking into assumption that all of the players know who to hit and not experience a scenario of cross-fire (ie. attacking an opponent more than 3 times).

    As for the second issue of fractional wins, the number of wins have been rounded downwards to the nearest figure and the calculator takes into account each time frame (ie. 0min, 25mins, 50mins) individually, instead of holistically This means that:

    At 0 mins – It calculates 75% of 30*3 attempts at battle = 67 wins

    At 25 mins – It calculates 75% of 30*1 attempts at battle = 22 wins

    At 50 mins – It calculates 75% of 30*1 attempts at battle = 22 wins

    Hence, the grand total would be 111 wins (for a 30 v 30 guild war scenario at 75% win rate).

    However…I did spot a small mistake in my calculations for the final time frame (50 mins) (specifically, that it took into account a smaller figure than required). Thus, the difference in points would actually be 110 instead of 70…which thankfully doesn’t make too much difference in the final graph line. Hence, I’ll update it once I’ve fixed the calculator.

    Like

  3. Hi,
    sometimes you’ll get 8 gw-points for a victory and sometimes 11.
    Do you know if there is a math behind or just random?
    Br from Austria
    Armin

    Like

    1. Hi Armin, unfortunately this is a random occurrence similar to the additional VP you get from WC.

      While this has been contested a number of times, an official explanation has yet to be given. :/

      Like

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