Wednesday, June 11, 2014

Damage Compared - D92-U vs. D92-F

In yesterday's analysis of the new prizes, I showed the lower salvo number of the D92-U means that a reload bonus helps the U more than the F.  What I wasn't sure of is whether having more shockwaves created by the U would balance out the greater base DPS of the F.  So I built a calculator and came up with an answer.  

I made some assumptions here... the key assumption is that with either launcher type, you need 120 hits within a 10 second period to trigger a shockwave.  (from the Battle Pirates Wiki) I also assumed a 0.1 second delay between shots within a salvo. The other simplification I made is that no hits or damage is wasted (no overkill, no firing at dead targets).  

For my calculator inputs, I take into account three general areas:  the Weapon, Attacker, and Defender.

Weapon: I use the statistics from the game, and also document the assumption that you need 120 hits in a  10 second period to start generating shockwaves.  If you want to try other assumptions or statistics, go ahead.

Attacker: In this area, the number of launchers used, the attacker's reload bonus, and the attacker's accuracy bonus (or penalty) should be entered.

Defender: In this area, select "Y" for a ship target, or a "N" for a building target.  The evade and Radioactive Defense percentages should be entered as well.

The outputs are as follows:

Net Accuracy (NA): This is the percentage of shots that are expected to hit, given the target type, accuracy, accuracy bonus, and evade.  NA = Accuracy * ( 1 + Accuracy Bonus) * (1 - Evade)
Net Reload Time (NRT): This is the total time between the end of one salvo to the start of the next salvo.  NRT = Reload Time / (1 + Reload Bonus)
Net Damage Per Hit (NDPH): This account for the target type, salvo number, and resistance.  NDPH = (Damage * (1-Defense)) / Salvo
Number of Launchers (NL): (from the attacker area)
Launcher Weight (LW): Number of launchers times weight per launcher - lets you compare total weight.
Hits per Second (HPS): Average number of shots expected to hit the target per second HPS = NL * (NA * salvo) / (NRT + salvo delay * (salvo -1))
HPS/hton: (HPS / total weapon weight) * 100
No Shock Damage Per Second (NSDPS): The weapon DPS without any shockwaves.  NSDPS = HPS * NDPH
NSDPS/hton: (NSDPS / total weapon weight) * 100
Shockwaves per second (SHpS): Given the number of hits per second, the average number of shockwaves generated per second.  If the average time to generate a shockwave is longer than the Shockwave Threshold time (10 seconds), this number goes to zero.  SHpS = HPS / Hits to shockwave (unless less than 1 / Shockwave Threshold Time)
SHpS/hton: (SHpS / total weapon weight) * 100
Shock DPS: DPS from the shockwaves only. Shock DPS = SHpS * Shockwave Damage * (1 - Defense)
Shock DPS/hton: (Shock DPS / total weapon weight) * 100
Total DPS: No Shock DPS + Shock DPS
Total DPS/hton: (Total DPS / total weapon weight) * 100

So here's some example scenarios with enough launchers to ensure shockwaves:

Reload Bonus
Accuracy Bonus
Evade
total DPS/hton
D92-UD92-FD92F DPS Margin
0%0%0%20.5327.0732%
50%0%0%29.2336.2124%
100%0%0%37.0943.5717%
150%0%0%44.2249.6312%
100%-20%0%29.6734.8617%
100%35%0%50.0758.8217%
100%35%-20%60.0970.5917%
100%35%20%40.0647.0617%
100%35%50%25.0429.4117%
25%0%Building28.9457.5099%
100%0%Building42.9478.5483%
180%0%Building55.8095.1170%

The first three columns show the relevant statistics on the attacker or defender, then the next two columns show the DPS/hton for the D92-U and the D92-F, and then the last column shows the percentage more DPS/hton done by the D92-F.

So, for any scenarios where shockwaves are being triggered, the D92-F ALWAYS does more damage per weight than the D92-U.  Of course, if shockwaves are NOT being triggered, it is obvious that the D92-F will be doing more damage, because of its much higher base damage.

The only other factor to take into consideration is whether there are loadouts where using D92-U will trigger shockwaves where an equal weight of the D92-F won't.  I'm going to skip the big table and say... yes there are situations like that, but there aren't many.  This calculator will tell you a shockwave threshold, but it isn't quite accurate because the nature of salvo fire.  For example, if you have 8 D92-F firing at a target with 100% net accuracy, you will trigger the first shockwave after 3.9 seconds (during the second salvo), even though you will trigger a shockwave every 5.5 seconds on average. 

So... play with the calculator below, if you try to compute the number of launchers you will need to trigger a shockwave, you'll end up with at least as many as you need.