Damage Calculation

[mattp169]

@Zack

If you don’t accept the hundreds of data points in the diagrams, I can provide some screenshots as well:

EXCELLLENT!!!
THANK YOU!!!
Finally we have evidence we can discuss.
SO lets look at your math:

@Zack

Total attack of 4791, defense is 153, actual damage is 925, 918 and 929.

The exponential formula gives
(100*(.606x31.3137)^1.35)/3 = 3484 for the average value that you would expect to get most of the times

boundaries are
(100*(.606x31.3137)^1.35)/3 = 1171 for the minimum
and
(100*(1.649x31.3137)^1.35)/3 = 6844 for the maximum

First there are 2 issues with your math. That’s ok, you are human and we all make mistakes.
The first mistake is that this is PVP and you must add in the 20% making the actual defense 183.6.
Also we do not know if they have adjusted this value. it was announced in the last update they are adjusting this 20% on HIGH END raids. I do not think this value would be adjusted here but since this is a total mismatch and the attacking team would be considered high end, it is possible that the 20% is not 20% any more

The second issue is you have

@Zack

(100*(.606x31.3137)^1.35)/3 = 348

and

@Zack

(100*(.606x31.3137)^1.35)/3 = 1171

Same formula with two different answers.

Regardless I did the math myself using the 20% bonus and I concede that these data points do not line up with the original formula.

Now we can discuss that.

It has been discussed in multiple places there are soft caps built into the game.
For example this thread

These caps are an unknown and easily explain this discrepancy. Soft caps have been observed and recorded multiple times and for me are a reasonable explanation to this discrepancy

Let’ s look at how you obtained this discrepancy. You are using a fairly powerful teams against a basic beginner team. This is not normal. In fact getting to a ratio of 4791/183.6=26.09477124 is not something most players are going to see often unless they are trying to do it. That is not normal game play, even if using such a team on low level Season 1 maps is normal, you are at a point that the discrepancy does not matter and you are killing mobs and bosses with 1 or 2 tiles, making the discrepancy a non issue for actual game play purposes.

Now lets look at this graph because I think it illustrates one of your main points wonderfully.

@Zack

Looking at this explains some of the confusion I am having. Multiple times after I started posting the ratio of 5 was given as where the original formula fails. This graph puts it at least at 10 and actually closer to 15. My evidence showed up to 10.52342488 was still within the ranges of the formula.

Perhaps stating that after a ratio of 15 the formula starts to fail is a more accurate statement based on your own data.

Now i did some tests above 15 and had mixed results. Some data points matched yours and some data points worked perfectly with the original formula.

I admit there seems to be an issue when the ratio gets high, but i disagree that 5 is where the problem becomes apparent it is much higher and may only occur in circumstances either not anticipated by the designers when the actual code was written, in outside or normal game play anticipated by the designers such as your raid example above, or in new scenarios created by the heroes that have been released since the writing of the original code which can now create unforeseen ratios.

In any case these can all be explained by a soft cap. n my personal opinion the soft cap is likely based on the defense number itself.

@Zack

For practical use you want a formula that gives a good fit or at least a reasonable fit. The average value should already be close to the actual damage. Ranges where the maximum is 3.9 times the minimum value are not practical at all - it is nearly impossible to NOT be in this range! But here we are and did it

and now we get to the heart of the matter, what my original question was all about and why I started posting in the first place.

I agree with you that the ranges are horrible. I do not view the formula as a method to accurately predict the exact damage I can do. The formula serves as an educational tool to new players. It is accurate enough in NORMAL circumstances to show the following:

@SolemnWolf

Having several heroes of the same color only increases tile damage. They are calculated by adding the attacks of these heroes
Lowering the enemy defense is more effective than increasing the attack.
Combining defense penalties and attack bonuses has a devastating effect.

This is true and factual even if the formula is not perfect.

You have not proven the formula does not work and does not serve as an excellent basic idea for beginners to learn how the game works. The discrepancies you have encounter come at extremely high ratios barely even possible when the original formula was conceived and posted. The discrepancies can be explained away by soft caps, and not the formula being wrong. There is plenty of data in this thread that shows the formula works just fine under normal circumstances. Please stop saying the formula is wrong or doesn’t work.

What you are trying to do is make a formula that is more accurate and possibly determines if there are soft caps and what those caps are.

I applaud you for the effort and encourage you to do so. I hope you succeed.

What I disagree with is the disparaging of the original formula given that

1. it does work under normal circumstances
2. only ratios previously unavailable when the formula was posted are where the problem seems to arrive
3. the discrepancies can be attributed to soft caps
4. This thread is under player guides and has been used as a guide for many years and is established as the best understanding of the damage calculation we have to date
5. Your new formula is not ready.
6. All of these posts in the GUIDE make it confusing to use as a guide. If i were new to the game and started reading this guide I would be unsure how damage is calculated because it starts with a formula, the formula is shown to work then a new discussion starts with tons of what can be confusing charts and data to those uncomfortable with math. And now I do not know if the original formula is right or not. When the truth is, the original formula is good enough to get the basics and your new formula when complete could possibly be more accurate and be more useful, but until it is ready and thoroughly tested we just don’t know.

and MOST IMPORTANTLY
7. Solemn Wolf is not here to defend their work.

SO once again
@moderators
respectfully request that this thread be decluttered.
The original content be left alone
The new discussion of a new formula be moved to it’s own discussion under General Discussion where Zack and others can continue their work.
A link be provided in this thread for others to see Zack’s work and contribute
And when Zack and the others have a workable formula that can be tested and explained clearly to the novices that it be given its own Player’s Guide and both threads link to each other.