# Hero durability - statistics

Thanks to @SolemnWolf and his excellent work to back-solve the damage formula (Damage Calculation) we can now really weigh how Def and Health stats balance.

To help people relate to a metric, I’ve computed the number of “Sonyas” for each 4* and 5* hero. A ranking of 1.00 Sonya says that one special attack from Sonya will kill the hero (ignoring the color weak/strong, assuming both heroes are fully leveled, ignoring troops, buffs, attack/defense bonuses on raid defense, etc.). The higher a hero’s Sonya’s are, the more durable they are.

Here are the hero rosters, listed from most durable to least, and the “Sonyas” for each. The new characters for the summer event are included with their preliminary stats from beta:

Legendary Heroes (5*):

Epic Heroes (4*):

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Nice work, thanks for putting that together! Now I know I have the squishiest 4*, and 2nd squishiest 5* on the roster…

They do make up for it in the hitting-hard-and-fast department of course.

A little curious as to why “Sonya” is our unit of measure here?

Exactly – this list doesn’t change its order very much if I sort by Attack stat, from low to high. There’s no “free lunch” on the stats: what you give up in one, you gain in the other (within a * class).

Sonya is a familiar hero with a middling Attack stat and a secondary effect that doesn’t deal damage, so she seemed like a fairly neutral and relatable measure. It’s trivial to recompute for any other character, e.g. Lianna, and doesn’t change the rankings.

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Would you share the formula for number of Sonya’s? Her attack is 607, her special would push that to 345% of that attack which would be roughly 2094. Then we would take HERO_HEALTH/(100*(2094/HERO_DEFENSE)^1.35) but my numbers are larger than yours. Can you help me spot the flaw?

There was a revision in the damage calculation formula (as we know it); your number should be more accurate.

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thanks! 20 characters

If you want it to be accurate to raiding experience, so you can compare what it “feels like” if you hit that hero on defense with Sonya, you might want to incorporate the 20% defense boost for defenders into your calculations.

So, if you’re used to how many hits it takes for Sonya to kill a defender in raids, your “Sonya equivalents” number would be:

Health / (100 * (2094/(Hero_Defense*1.2))^1.35)

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OK, I baked in the 1.2 for raid tanks. Using the class tool (https://docs.google.com/spreadsheets/d/1NEZtG_elBzNV4DA94Tbo-tkVahlUjrUun1NvhsvvSGo/edit#gid=1696971776) and this Sonya ranking I ran through some tanks of mine to test the difference between “always take defense then health” vs “always take health then defense”. In every case I’ve tried taking defense then health gives the higher Sonya quotient.

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Thank you for this proof. In the original version, you could choose 30 HP or 20 Def. I complained that 20 Def >> 30 HP. You’ve just proved that 20 Def > 40 HP, so at least it’s not as badly unbalanced as it had been.

The next place I would like to go with this kind of thinking is towards a way to weight attack against defense by simulating an idealized cage match. If my attack goes up there are less rounds of endurance and such. Any thoughts in that area?

It’s going to be very tricky because of the non-linearity in damage combined with the effects of color stacking. Because tiles are such a huge part of the kill proceess, you really need to know who you’re pairing with before you can tell how much of a boost +Attack really gives in a raid. Unless you want to limit yourself to rainbow teams. Then things get much cleaner.

By the way, it’s really nice to see another one of us people who are interested in the math of the game. Thanks for engaging with this interesting problem!

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So I like the Sonya Score as a simplification of the details in order to capture “tankiness”.

Anecdotal aside, I wasn’t on the forums when Aegir came out. I saw his tanky stats, didn’t have a proper tank yet, burned my telescopes, raced him to the top only to be a bit disappointed. In practice I’ve enjoyed using him on raid teams and I tend to tank with Alasie which has pretty decent results. These classes make me wonder, can I salvage Aegir? I have an Onatel now, will she be my imagined tank?

So the Aegir story makes me want to answer this question: If you had a tank with no special skill at all, what stats would you want to compensate for that fact?

In the long run we will have to just build a monte carlo simulator that let’s us see win rates of specified defenses against specified offenses.

A MC simulator of combat sounds like a fun but very challenging project, since targeting is such a huge issue. If you figure it out, though, maybe you can get SG to buy it off you so that defenses actually run smartly

Tanks are definitely getting shaken up by the whole class upgrade. That’s an interesting question you pose about whether classes salvage Aegir. The big problem I see with him on defense is that he shares damage without a general defense buff to everyone protected. So you can just target the weakest hero next to him and hurt everyone being protected.

The boosts that Aegir gets with classes makes him significantly more able to survive himself, but does nothing that I can see about the risk to those he’s protecting.

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I wanted to update the “Sonya rankings” I discuss in the OP. The following screen shots (one per color) all show the “SonyaD” which is the notional “how many shots from Sonya could this hero sustain”. The “SonyaRank” column gives the ordinal rank of this hero among all 4* and 5* heroes (1=strongest, 105=weakest). The “SonyaD4Rank” column gives the ordinal rank only among the 4* heroes (1=strongest, 41=weakest).

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Thank you for this.

Looking at it, I’ve been using a spreadsheet which does similar calculations, although it calculates hits from an “average 4*/5* special” (Attack 692; 400%) which hits somewhat harder than Sonya but not as hard as Lianna. I believe it uses the same reverse engineered damage calculation, with two other differences.

1. It estimates stats at a hero’s current tier/level so you can see how your current work-in-progress hero performs and how 5*s stuck at 3/70 work.
2. It hasn’t been updated for a while; it has the summer sand people in it, but not the next two seasons or newer HOTM or Atlantis heroes.
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I thought about using a “generic hero” as the attacker, but in my experience it’s best to have a familiar unit of measure. We’ve all faced and/or used Sonya, and her stats seem unlikely to change.

You’ll not i have “Sand Vizier” and “Sand Fortress” on the sheet instead of Gafar and Jabbar. Yeah, it’s tough to stay up to date.

I like the “standard yardstick” idea, and I agree that "Sonya"s are a good one

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Now it’s updated and a bit optimized as well

edit: and on topic - reason why I opted for comparing to some arbitrary number, in my case averages, is because not everyone has some hero (even Bane, since many of us eaten him )

And also, I didn’t want to imply relation to some fixed hero, eg specials usability depends on speed and spec hit depends on both % and base attack and so on.

edit2: however, I think it’s good that we have options of various tables and calculations, so that everyone can find something they understand better / can use faster, or, they create their own

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