Crazy Valkyries Math

Today I shall briefly explain the math behind a contrarian Clash of Clans war tactic dubbed, “Crazy Valkyries“. The strategy is akin to a football team risking to go for it on fourth down in lieu of punting.

In 2005 Berkeley economist David Romer published a wonderful paper that proved football coaches kick on fourth too often and should go for first downs more. (Think sabermetrics of football.) Despite objective math stating otherwise, most football coaches haven’t changed their fourth down habits. Why not? — Because going for it on fourth down is a high risk/high reward proposition–when attempts fail, fan reaction is not pretty.

Similarly, Crazy Valks is high risk/high reward strategy.

TH8 Anti Dragon Bases

Source: Jayceooi.com

Assume you are in a clan war with a ‘bottoms up’ strategy, in which all TH8s must be three starred. By far, the most popular strategy at this level is dragons. But there are many TH8 bases with centralized level six air defenses that are difficult to three star with dragons.

Further, let’s assume (as is the case with me currently) that you do not have level 4 hogs yet, nor do you have level 3 pekkas. In short, you have limited alternatives. This is how the Crazy Valkryie tactic was born.

Crazy Valks aren’t sexy. I could walk through the finer points another time but, essentially, it involves tossing a bunch of valks and wizards at a base and hoping for the best. Considering the valks’ unpredictable AI, it’s mostly about spray and pray. So why use it?

THE LOGIC

Assume you are tasked with attacking an anti-dragon TH8 base that is already two starred. If you fail, a TH9 clanamate will have to step down to three star it. What should you do? Without going overboard on statistics, let’s think about probabilities for a moment.

Option 1: Dragon Attack

More than likely, your clanmates have already attacked the base with dragons and failed. Some might have come close to three starring it before running out of time. If you try the same tactic hoping for a different result, let’s assume the odds are:

• 10% chance you will 1 star the base
• 80% chance you will 2 star it, and
• 10% chance you will 3 star it.

This is an expected result of 2.0 stars per dragon attack.

Option 2: Crazy Valks

Crazy Valks is a high risk high reward proposition. Assume the odds are:

• 40% chance you 1 star
• 40% chance you 2 star, and
• 20% chance you 3 star

This tactic has an expected result of 1.8 stars per valk attack. (With higher standard deviation from the mean.)

If the average amount of stars for dragons is higher than valks, why would you pick valks?

Analysis

Like the risk averse football coach facing fourth down, if your main goal is to save face and not look bad, then you should punt and use dragons. Why? Because there is a 90% chance you will get at least two stars on the base. i.e. The odds of you looking bad are slim.

What if your goal is to three star the base so that a TH9 clanmate can can attack a higher base and, as a result, increase the overall clan’s odds of winning the war? In this case, you should use Crazy Valks.

With Crazy Valks, there is a significant chance (40%) that you will fall on your face and only earn 1 star.

So what? The base is already two starred. Anything short of earning three stars doesn’t help the team. So you might as well swing for the fences and go with the high risk/high reward strategy. You have twice the chance of three starring with Valks (20%) than with dragons (10%). Mathematically, it is a no brainer to go with the non-traditional Crazy Valk attack.

Psychological Consequences

If the math is true, then why don’t we see people use high risk attacks more often? Because people are stupid.

One star attacks negatively impact morale. Regardless of logic and probabilities, if you are a player who usually gets three stars, and your clanmates see you fail miserably with one star, it has a negative impact on team morale.

Like the arrogant Monday morning quarterback/football fan who thinks he knows more about football than the professional coaches, COC is full of conceited people too. Some people think they have it all figured out, but in reality can’t begin to comprehend all the variables of the finely balanced game. These negative Nancy’s come out of the wood work at times like this and start pity parties. And guess what? Discussing statistical probabilities with these know-it-alls is an act of futility.

Conclusion

TH8 players who are tasked with attacking anti-dragon bases, and do not have level 3 pekkas or level 4 hogs, have the option of using the high risk tactic called Crazy Valks. Players should weigh the risk of failed attacks negatively impacting morale of the clan.

My take is that if leadership in your clan is so weak that they can’t understand there are times for all or none tactics–or if they are unable to comprehend the fact that TH8 players do not have access to TH9 troops–then screw ’em. COC players who are too mentally limited to comprehend statistical probabilities shouldn’t spoil the fun for those of us who can.

Incidentally, for the record, actual in-war results of Crazy Valk strategy are:

• 25% 1 Star
• 25% 2 Star
• 50% 3 Star