tl:dr at the bottom.

Apologies on the long title and the very long post ahead (over 1100 words). It would have been a disservice to not spell out all of the details and simply sum up the results in one or two lines. My goal with this point and more to come is to slowly peel back the cover of the "black box" that SP uses for the battle mechanics, especially when it comes to how much damage a dragon does.

**Overview**:

Ranking heroic and mythical dragons relative to one another by their combined attack strength is a commonly used metric by dragon city players when determining how good or bad a dragon is. In this post I will show that the attack power of dragons have little effect on the damage output and that a new metric should be adopted. To show this I will need to prove two things, damage output is uniformly spread and damage difference is minimal. Uniformity of damage spread is necessary to allow for simple comparisons of the means (average). This analysis was done using a level 70 Kratus, using the following attacks: Giant Crack (638 power), War Fist (1500), and Pure Light+ (2100) with 208, 155, and 239 data points respectively.

**Damage Uniformity**:

I will use 3 different charts to show why I am confident that the damage is uniform. Something to consider is damage spread is ten percent of the mean in both directions, resulting in minimum damage being 90% of mean and maximum damage being 110% of mean. The first will be a trend fit using a spreadsheet, showing that the spread is linear across the spectrum. Second will be a scatter plot of each data point inside of a 200 damage window. And third will be a box and whisker plot to show that there are no outliers and each quartile are similar in size.

**Trend Lines**– This diagram is graphing the different data points after they have been put in order of increasing value. The data matches very closely with the linear line and there are no visible jumps in the data, this gives evidence that the data is possibly uniform and complete. In excel you are able to have a trend line assigned to the data and it will attempt to assign a function that matches the format that you chose, in this case a linear line. The equation that it found best fit the data is the equation given in the upper left of each equation, the R2 is a means to show how well the equation fits the data. For R2, the higher the better though the cutoff for this varies by the area of study and is well beyond the scope of this post (math of the trend line as well).

**Scatter Plots**– At first glance this looks very “scattered” and does not seem to show much, the important aspect from this output is more that there are no glaring omissions. This data is grouped into sets of 200 damage, for example all damage between 80000 and 80200 each give a +1 to the value assigned to that range. As the data range is very large, it is difficult to draw much conclusion from this diagram on its own, but it lends evidence that there is no gaps or skewing of data in any attack.

**Box Plot**– The box and whisker plot is a plot to show how the distribution of data, it groups the data into an equal number of data points for each region, so the lowest quarter are in the bottom “whisker” and the highest quarter are in the top “whisker”, with the middle two quarters forming the “box”. If any of the regions had data that was spread out more or less than other regions, it would appear with that section being longer or shorter respectively. The data I present all has similarly sized regions and thus I can conclude that no quartile has a different spread than the rest

With these three things presented, the data is both uniform and complete, allowing the comparison of the means to determine the relative strengths of damage output between attacks.

**Damage Comparisons**:

- Giant Crack – (155 data points)
- Minimum: 68853 (90.26% of mean)
- Maximum: 84061 (110.20% of mean)
- Mean: 76279.6

- War Fist – (208 data points)
- Minimum: 72760 (90.65% of mean)
- Maximum: 88680 (110.48% of mean)
- Mean: 80266.8

- Pure Light+ – (239 data points)
- Minimum: 75644 (90.05% of mean)
- Maximum: 92283 (109.86% of mean)
- Mean: 84004.0

**Numbers**:

The mean damage outputs will be used to compare the relative damage done between each move.

- 2100 vs 1500 – 84004.0/80266.8 = 1.04656 (4.656% more)
- 2100 vs 638 – 84004.0/76279.6 = 1.10126 (10.126% more)
- 1500 vs 638 – 80266.8/76279.6 = 1.05227 (5.227% more)

**Conclusion**:

From the data above the following conclusions can be reached. A 2100 power attack deals roughly 5% more damage than a 1500 power attack and roughly 10% more than a 638 power attack, while a 1500 power attack deals roughly 5% more than a 638 power attack. This goes against what is often argued on here that high nucleus is much weaker when compared to the high resolution, the damage spread is similar with the best of high resolution being 2300 and worst of high nucleus being 650. With this data, the best attack of high resolution will deal a little over 10% more damage than the worst attack of high nucleus. Therefor, I propose that the metric by which we compare mythical and heroic dragons to be changed to that of considering type coverage and defending element.

**Going forward**: Current research is being done to test if a trained move inherits any damage boost and determining the impact of dragon power on damage output. No timeline for either of those analysis as they are time consuming.

**P.S.** As I finish typing this and from having commented about this in the past, I will make a quick note to those of you who want to counter with "But my kratus did 90000 with pure light+ and only 70000 with Giant crack, so there actually is a big difference." I am going to stop you with mentioning that two data points does not prove anything and given the wide range of damage possible, it is meaningless on its own. Enough data points must be used to be able to confidently get the full picture of how the data is distributed, in this case I have a total of 602 data points.

Also, yes this took a long time and a lot of effort to get the data and do this analysis. This was not done overnight.

**tl:dr** – 2100 attacks deals 10% more than 638 attacks and 5% more than 1500 attacks. Attack power is not a large factor in damage and rankings should be done with consideration of type coverage and defending element.