Moor’s Strategy Guide: Clan War Searches

“Clan War mismatches are preferable to no match or very long searches”

-Super Steve

Definitions

“hard-core gamer”  – arranges daily schedule around gaming

“mid-core gamer” – arranges gaming around their daily schedule

“casual gamer” – seeks gaming entertainment when time presents itself

“farmer” – CoC player focusing upgrades specifically for obtaining resources for more upgrades

“trophy hunter” – CoC player focusing base layout and army composition to win and keep trophies

“warrior” – CoC player focusing troop upgrades and base layout specifically to win clan war battles

“war base score” – the ranking of a player’s war base, consisting of structure/troop/spell levels.

Assumptions

1.  The average Clash of Clans player is a “casual” player. These players often go in-and-out of clans, have idle builders for long periods of time, and may go days between checking on their bases and emptying collectors. Casual players with idle villages and full collectors are a principle source of economics in the CoC universe.

2.  The average Clash of Clans player is Level 60-65. Player level is calculated predominantly by number of structure upgrades (excluding walls), with a minor influence of clearing obstacles, troops donations, and winning achievements. Troop upgrades do not count toward Player Level. The average player doesn’t accumulate enough troop donations to have significant impact. In summary, higher Player Level is proportional to the number of structure upgrades. Level 60-65 strongly correlates to Town Hall 7 (or equivalent base with a higher-level rushed TH).

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3.  Town Hall 7 is the transition between “casual” and “mid-core” gaming. Upgrades can take a week (i.e. Dragons or Air Defense) and are impossible to afford without farming or purchasing gems. A casual player can get to TH7 by sporadically playing and perhaps occasionally purchasing gems. Once at TH7, the player must schedule gaming sessions to organize upgrades and farm resources to continue advancing. Without scheduling regular gaming sessions, it becomes impossible to manage the upgrades available at TH7. This effectively caps the casual gamer at TH7.

4.  The average player age is 21-35 with enough disposable income to afford portable Android or iOS devices, internet service, and occasional in-game purchases. The assumption is this demographic is Supercell’s primary business interest for in-game purchases.

midcore-demographics

 

5.  The average clan has high membership throughput (revolving door) of mostly casual players (levels 50-65) and is short-lived. The average clan has half-hearted war participation, weakly coordinated strategy, and poor base design. Most players forfeit (give up) and don’t attack when facing a superior clan. These clans dominate the war search algorithm.

6.  The “mid-core” gamers invest enough time and attention to progress to TH8 and above. Their attention to the game results in more strategic base layouts, defense methods, troop upgrades, and fighting tactics. Mid-core gamers are approximately split between farmers, warriors, and trophy hunters. These players advance from the “casual” clans and build more strategic and organized clans. The “mid-core” gamers range from levels 80-120.

7.  The “hard-core” gamers invest both monetarily and time. These players gem their bases, are in the high-level leagues, and are generally inaccessible by lower classes of gamers.

The Mounting Frustration Level

The next observation is that organized clans consisting of TH8 and above players are voicing frustration on the Supercell and Reddit forums over Clan War Searches (the two most common forums for CoC aficionados). This demographic is interesting:

  • TH8 and above are probably “mid-core” gamers who schedule gaming sessions to keep their builders and laboratory busy.
  • These gamers are above-average level (>65) and have more experience with army composition, base layout, and defensive strategies.
  • Organized clans with Supercell forum participation are far beyond average. Out of the presumably hundreds of thousands of clans, only a handful engage in the Supercell forums.

This demographic lies outside of the “average” clan war search. The Supercell forum has many complaints regarding the Clan War Search:

“So we appear to be in a rut of unbalanced war matches lately and no one likes ruts. Basically this is because there are not many clans similar to ours (number of th10, th9, th8 & th7). CofC tries to match us with an equal clan, but because there are so few other clans that are our equal we are being randomly matched with clans that are significantly stronger”

“I too have been struggling with poor clan war matchups. In my clans case, our mean lvl is approximately 77. We have no members over 100 and no members under 60. In all of the matches we’ve had in the last 30 days, we have been paired with clans that have 20+ wins (we have 4). The last match we had was against a clan with 61 wins (seriously?). They also have about 10 of their top players (out of a 40 vs 40 war) that are over lvl 100 and some of their lowest members about 5, that are under 60 and even 50. But the median of their clans has been slightly higher than ours about 80.

However, what happens in this scenario, is that our top lvl players can’t attack their top lvl players. We either have no chance at a star, or can only 1 star at best. So, that pretty much means that we have to start at base 30 and below and as of such our median members are all competing for the same lvl of difficulty bases to attack which is around the middle and low end of the available bases to attack.

So, we lose the every war because their high lvl players can attack our highest players 1-10 and their median can attack our middle and so forth.”

Calculating Experience

Player level comes from accumulating experience. Experience is gained through upgrades, donating troops, clearing obstacles, completing achievements, and destroying an opponent’s town hall. The majority of experience comes from upgrading structures.

Experience is calculated by taking the square root of upgrade time (in seconds) rounded down. For example, a Level 5 Wizard Tower takes 4 days (345,600 seconds) and produces 587 experience points:

20150209 123539

These experience points are added to the player’s level progress.

Calculating Level

Levels are achieved by accumulating experience points. To calculate how much experience required for the next levels, multiply the present level by 50. For example, a player at Level 6 would require (6 x 50 = 300) experience to gain Level 7. A Level 60 player would need (60 x 50 = 3,000) experience to advance. The amount of experience required for the next level goes up according a geometric square equation:

20150209 123547

This means the difference between a Level 60 and 61 player is small (3,000 points) but the difference between a Level 120 and 121 player is much larger (6,000 points).

20150209 123729

Therefore, war matchups between average players (levels 60-65) are generally “fair”. The differences between levels are “small”. However, war matchups between high-level players can become “unfair” because the differences between levels can be huge.

Calculating War Base Score

Supercell has not commented or released any information about the clan war search algorithm, but observational analyses have been made by many professional mathematicians and postdoctoral researchers who happen to be CoC fans (i.e. Khirevich or Randal Olson).  This article combines some basic assumptions with observational analysis to create some practical methods.

Every war participant has their base scored. The “war base score” is calculated by adding together the player’s structure, troop, spell, and hero upgrades. Wall upgrades do not appear to affect the score. The exact algorithm is not known, but some upgrades may have higher weight than others. For example, some analysts suggest Inferno Towers greatly affect base scores, or Hero upgrades count a bit more toward the score than other upgrades.

It is not known exactly how the “war base score” is calculated, but because all of the other Supercell algorithms are very simple (i.e. calculating experience), the “war base score” is probably equally simple. It may work similarly to the experience algorithm by adding the square root of time of all of the upgrades, including troop upgrades. Alternatively, it may add the square root of the costs (in Gold, Elixir, or DE) of all the upgrades. This may explain why Hero upgrades have a larger effect – Heros are upgraded many times over with increasingly large sums of expensive DE.

This may result in two equivalent players with the same score but different abilities:

  • Farmers prioritize non-war troops, such as Goblins, Giants, and Healers. Their “war base score” will reflect these upgraded troops, but will have less war-fighting capability.
  • Warriors prioritize war troops, such as Golems, Witches, and PEKKAs. Their “war base score” will be the same as the Farmer, but with greater war-fighting power.
  • Farmers prioritize defenses to protect their loot during farming.
  • Warriors prioritize defenses to protect their Town Hall during Clan Wars.
  • Warriors prioritize Hero upgrades, as they are useful in both offense and defense roles.

Both of these players (Farmer and Warrior) may have the same “war base score” but have unequal war-fighting capability.

However, as a generalized assumption, similarly-leveled players will have similar upgrades (structures, spells, troops, etc.) Therefore, a rough approximation can be made.

War Base Score ≈ Player Level

Calculating the Clan’s Composite Score

All of the clan’s participating members are added together for a composite “war base score”. After the composite score is calculated, the war search algorithm seeks an opposing clan with a similar composite score.

The general consensus is the Supercell algorithm uses a Geometric Mean. This is a way of normalizing the input variables so that no value dominates the weighing. See the tabulation below. It’s not much different than just taking the average:

20150209 123912

The first observation is our clan was out-matched player-by-player with only two exceptions (positions 6 and 14, played by CEN and Gone2). I was facing a level 99 player, five levels above me. According to the analysis above, 5 levels at this range is huge – a difference of 24,000 experience! On average, each of our members (excluding Savage) was facing opponents 2 levels higher. Our average level was 76 vs. their 80. If a geometric mean is used, the numbers are even more stark, 74 vs. 79.

So was Savage useful? Removing Savage from the calculation narrowed the gap. Using the geometric mean, the matchup would have been 77.7 vs. 79.2. Still not fair, with each one of our members still facing opponents 2 levels higher. But it starts to look more plausible on paper.

Savage reduced our clan’s composite score by 2 to 3 levels, depending on the method of calculation (average or geometric mean). Is it worthwhile to give the enemy an easy three-star in exchange to reduce our overall clan composite score by 2 or 3 levels?

The answer is “yes” … if the clan search algorithm doesn’t out-match the rest of us. So how can we get a fair match?

Getting a Fair Match

We finally reach our destination. The journey has been enlightening and fun, but now we just want a fair war match. We understand some game mechanics. But how to get a fair match?

Consider the Supercell algorithm is designed for the average (casual) player, who is essentially capped at TH7 (level 60-65). The algorithm performs best with clans meeting an average distribution curve. Remember when we were all TH7? Our war matches were awesome. But when we crossed the threshold from “casual player levels” to “mid-core player levels”, war searches hit the crapper. That’s because we exited the algorithm-optimized sweet-spot and we are now outliers. The war search algorithm has a hard time matching us to an opposing clan.

“Clan War mismatches are preferable to no match or very long searches”

– Super Steve

According to Supercell, the algorithm defaults to a poor war match if an appropriate match is not quickly found! This is a normal gaming algorithm. If the game is not converging on a solution fast enough, the solution window is made wider. As time progresses, the algorithm gets less picky. The longer the search lasts, the less picky the algorithm, and the worse the matchup:

20150209 124024

The solution is simple: never let the algorithm advance to the next iteration and search for less optimal matchups. This is done by stopping the war search after a fixed time and re-starting, never letting the algorithm run long enough to widen the solution window. This forces the algorithm to find a war match in the first (most narrow) solution window.

Other clans have tried this approach and believe the iteration is performed in 5 to 10 minute increments:

“The matching code uses (probably) an iterative algorithm along with geometric mean. If the search runs longer than 5-10 minutes you will likely be paired with a significantly stronger or weaker clan. To prevent this, restart the search after 5-10 minutes.”

“Absolutely agree that time searching is deeply involved in matchmaking. I noticed that the longer we searched, the worse our matches were. Had a 5 war losing streak because of total mismatches, with searches lasting about a half hour each. The frustration was mounting big time for everyone in the clan. I came to the same conclusion reached here; basically the longer the search goes, the wider the range of potential matches. So a few weeks ago, I changed my strategy, not letting searches go over 10 minutes. Since then, we have only had 1 fairly bad match that we lost, but could have won, but we are 9-1 over that span. More importantly, our war matches have been nearly flawless. Sometimes we are a little more advanced, sometimes we are a little less advanced.”

“I’ve found that if we cancel the search every 5-8 minutes and restart the search, when a match is finally found it tends to be a lot closer match.”

Summary

  1. Our clan has moved out of average (“casual gamers” of levels 60-65) and into a more thoughtful, strategic, and organized clan (“mid-core gamers”). This has moved our clan outside of the average optimized war search algorithm.
  2. The war search algorithm deliberately seeks poorer matches as time progresses to avoid long wait times. The workaround is to re-start the war search before the algorithm resorts to widening the search window.
  3. The clan composite score adds together the cumulative upgrades (structures, troops, spells, and heros) of the war participants using either an averaging scheme or geometric mean. Adding a low-level participant may significantly reduce the composite score, but also gives the enemy an easy three-star. Are we shooting ourselves in the foot, or gaining an advantage?

 Update #1

So does the Supercell algorithm use a Geometric Mean or Standard Average? Since player Level is a geometric function of player Experience, the player Level scales non-linearly with Experience. Therefore, a standard average is not reasonable. This is illustrated by converting the clan matchup from above into Experience. Level can be calculated from Experience using the quadratic equation:

20150212 114801

So the Levels can be converted into Experience, a geometric mean taken, and the result reverted back to Levels. If everything goes well, the two results should be equal:

20150212 112721

I wanted further proof that the geometric mean of Player Level was equal to the geometric mean of Player Experience. This would further the conclusion that the Supercell clan war search algorithm attempts to match players based on Experience, or at least a metric proportional to Experience (i.e. additional experience points for troop upgrades, or hero upgrades). Over lunch, I made a mathematical proof that the geometric mean of the clan’s player levels is equal to the geometric mean of the clan’s player experience.

IMG_9699

The reasonable conclusions are:

  •  War matchups are made of the basis of the geometric average of participant experience or an expanded experience score that also includes additional factors, such as troop upgrades (the base experience does not include troop upgrades for some unknown reason). Since most Supercell algorithms are very simple, we can assume the war base scores are calculated similarly to base experience (square root of upgrade time in seconds) but with more things included. Why Supercell doesn’t count troop upgrades into regular experience score is a mystery. It seems troop upgrades should be counted as part of your experience score.
  • The war search algorithm iterates to less sensitivity (wider search window) after timeout periods, estimated to be between 5 and 10 minutes, to avoid long war search times.

Update #2

So why do longer search times result in less advantageous matchups? Here are some guesses:

  • Lower-level clans (i.e. average level of 60-65) get matched quickly, so the pool of queued clans is much smaller.
  • The queue of higher-level clans (i.e. average of level 80+) take a long time to match, so the pool of queued clans is much larger.
  • The longer a clan stays in the queue, the more urgent it gets matched.
  • We are more likely to get matched with a high-level clan that has been in the queue for a long time.

Looking at the Clan War Search graph, I envision:

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During the first iteration, the algorithm attempts to match us with another clan who has been in the queue for a long time, but within a narrow window. I suspect the algorithm attempts to avoid making disadvantageous mismatches during the first iteration. If the opposing clan is weaker, and they have been in the queue for a few iterations, they get matched with us. The advantage is on our side. However, the longer the search continues, the algorithm readily makes disadvantageous mismatches, worsening our favor. Anything past the second iteration is almost a guarantee of a highly unbalanced mismatch in the enemy’s favor.

The conclusion is a war search result within the first 10 minutes will almost guarantee an advantage in our favor. During the second iteration (presumably 10-15 minutes), the advantage may be tilt in either direction. Anything after that (>15-20 minutes) is increasing odds of being unbalanced towards the enemy’s advantage.

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