Wizard fireball math

I was looking at a well known issue regarding wizard’s firestaff combo and the amount of damage it does. I did some Goldbrook testing on dummies and got two interesting observations. Below are the numbers we have when doing direct damage to target dummies. Defense values of a target do not change, no combustion fire damage bonus, so the observed values are stable. Testing was done with 3 gear variants (0, 15 and 50% damage bonus from gear) and two fire staffs (junk and blue). You will notice some percentage fluctuations, looks like those are a result of number rounding. They do not change the pattern/formula.

Here are the numbers (charge lvl 1 is a tap):

Junk Staff, +0% damage from gear

Fireball Damage Scaling Damage Overload %

charge level (No Overload) Lvl-to-Lvl (With Overload) overall bonus

1 84 N/A 109 29.76%

2 132 57.14% 172 30.30%

3 186 40.91% 242 30.11%

4 323 73.65% 420 30.03%

Junk Staff, +15% damage from gear

Fireball Damage Scaling Damage Overload %

charge level (No Overload) Lvl-to-Lvl (With Overload) overall bonus

1 96 N/A 121 26.04%

2 152 58.33% 192 26.32%

3 214 40.79% 270 26.17%

4 371 73.36% 468 26.15%

Junk Staff, +50% damage from gear

Fireball Damage Scaling Damage Overload overall

charge level (No Overload) Lvl-to-Lvl (With Overload) % damage increase

1 125 N/A 150 20.00%

2 198 58.40% 238 20.20%

3 279 40.91% 335 20.07%

4 484 73.48% 581 20.04%

Blue Staff, +0% damage from gear

Fireball Damage Scaling Damage Overload overall

charge level (No Overload) Lvl-to-Lvl (With Overload) % damage increase

1 123 N/A 160 30.08%

2 195 58.54% 254 30.26%

3 275 41.03% 357 29.82%

4 476 73.09% 619 30.04%

Blue Staff, +15% damage from gear

Fireball Damage Scaling Damage Overload overall

charge level (No Overload) Lvl-to-Lvl (With Overload) % damage increase

1 142 N/A 178 25.35%

2 224 57.75% 283 26.34%

3 316 41.07% 398 25.95%

4 548 73.42% 690 25.91%

Blue Staff, +50% damage from gear

Fireball Damage Scaling Damage Overload overall

charge level (No Overload) Lvl-to-Lvl (With Overload) % damage increase

1 184 N/A 221 20.11%

2 293 59.24% 351 19.80%

3 412 40.61% 494 19.90%

4 714 73.30% 857 20.03%

Quite a lot of numbers you may say. However, they show two patterns:

1. Non-linear scaling of fireballs charge levels (the main problem).

   On average, lvl 2 charge (lvl 1 is a tap) has 58% scaling, following by 41% at lvl 3 (dip, feels like a punishment) and a biggest increase (payoff for full charge?) of 73% at lvl 4.

2. Looks like Overload has additive nature, thus suffers from diminishing returns.

   If we look at a comparison of damage outputs on every fireball charge level that happened with and without Overload. We can see that the Overload baseline damage buff is 30%. However, it being additive to the % damage bonus you have from gear and other sources, the overall damage increase decreases the more gear you have. Meaning the more damage bonus you have from gear, the lower final yield you receive from Overload.

To sum up:

The problem is that the fireball has non-linear (seems like hardcoded) scaling values per charge level. Between 3 charge levels (excluding lvl 1 tap) we see that the current scaling formula “punishes” you for throwing lvl 2 charged fireball and provides a massive reward for a fully charged fireball. This scaling does not have diminishing returns, it is always the same, not matter how much % damage bonus you have from gear (and other resources) nor flat fire damage bonus from the weapon.

Overload on the other hand, by having additive damage application, suffers from diminishing returns, thus produces a lower yield with higher % damage bonuses from gear (and other resources).

Proposed solution:

Having a linear scaling of 50% per charge level, across all fireball charge levels will fix several fireball issues. Huge damage output with Overcharge fully cooked fireball and doing lower damage with not fully charged fireballs. It will also slow down clearing speed in pve (because we are mostly using fully charged fireball).

This change will not punish a player for using “mid charged” fireballs in terms of damage scaling per charge level. The fireball will deal the same damage on tap, a little lower on lvl 2 charge, higher damage at lvl 3 charge (which is fair) and around 23% less damage on fully charged fireball (including the one with Overcharge combo).

If we try to nerf fireball with some baseline % reduction, the scaling formula will stay the same and in my opinion this is the main source of the problem of fire combo doing too much damage.

Overload does not look like a main culprit in the combo (there is a talk about changing shoulders that give Overload), its the massive scaling of fully cooked fireball. When the shoulder piece is changed/reworked, the scaling of the fireball will not change and the issue will persist.

This might not be news to some players, but it was interesting to figure these things out. Hope this info helps to balance fireball damage. Sorry for big post, tried to be as detailed as possible.

Share your thoughts in the comments.