Cycle Time - Rank, Salvo, and Minimum Reload effects on DPS

I'm going to try to clear up some of the uncertainties regarding DPS calculation... I've baked in some errors over the last year.  I want to fix them and release a DPS Calculator/Survival Time calculator that people can use and agree on.

When figuring out DPS (Damage per Second), the amount of time the weapon takes to do the damage is important.  DPS is generally computed by Net Accuracy * Net Damage / Cycle Time, and this article will focus on factors that go into Cycle Time.

Some definitions:
Cycle Time = total time a weapon takes to fire a group of shots, from the beginning of one group to the beginning of the next group.  Cycle Time = Salvo Time + Reload Time
Salvo Time = Total time a weapon takes to fire a group of shots, from the beginning of the group to the end of a group.  Salvo Time = (Salvo - 1) * Salvo Delay
Salvo a group of shots that are fired in rapid succession to deal the weapon's listed damage.  Salvo is a statistic listed on the blueprint, or if none is listed the Salvo value is 1.
Salvo Delay = The amount of time delay between shots in a group
Reload Time = The amount of time between the last shot fired in a group and the first shot of the next group.  For Salvo 1 weapons, this is the entire Cycle Time.  The basic value for this is listed on each weapon's blueprint.  Rank, Hull, Specials, Fields, and Alliance can all apply modifiers to the reload time.  Retrofits change the Reload Time listed on the player's blueprint.

RANK EFFECTS ON RELOAD
The conventional way to calculate reload time (with salvo 1 weapons), was to add all the reload bonuses, and apply the following formula:  
Reload Time = Blueprint Reload / (1 + sum of hull/special/alliance/rank bonus)

When potential rank bonuses were increased from 25% to 75%, some players began noticing some discrepancies when ships were very highly ranked.  Recently I have been assuming that the rank bonus was applied separately from the other reload bonuses, so that it would compound when you had a high rank combined with other bonuses like alliance or hull bonuses.
Reload Time = blueprint reload / (1+sum of hull/special/alliance bonus) / (1 + rank bonus) 

However, it seems that doesn't fit the data either.  This forum post put together some evidence that the actual rank bonus is applied as follows:
Reload Time = blueprint reload * (1 - rank bonus) / (1 + sum of hull/special/alliance bonus)

See here: https://www.kixeye.com/forum/discussion/503010
and here: https://www.kixeye.com/forum/discussion/519038

I wanted to see this for myself, so I recorded some video of ships firing, applied the potential formulas, and found which one matched the data best.  

I agreed that the final formula, using (1 - rank) as a reload multiplier is the correct formula.

This means that a for ship with a Salvo 1 weapon, Legendary rank multiplies the DPS by a factor of 4, not 1.75.  THAT'S HUGE!  See the charts below:

I compared a generic salvo 1 weapon (all reload time) to a Torrent missile (salvo 16, reload 12.5 seconds).  The Torrent gets less of an increase in damage from rank because the salvo time is not affected by bonuses, but 253% is still a big increase.  The other takeaway from this graph is that even though the % rank bonus drops as rank gets higher, the DPS effect increases for each rank through rank 20, and is still very significant for each rank through Legendary rank.  

The Chart on the right shows the weapon's DPS increase % for each rank (compared to the previous rank).

Thanks to Hwasung0181 from the Kixeye forums for pointing me in the right direction on this one, and Tengam for doing some of the original work.

MINIMUM RELOAD TIME
Kixeye has said that weapons have a minimum reload time of 0.2 seconds. and that was the reason some weapons in the retrofit lab were changed to have additional damage instead of  a reload time reduction.

Robot's reference: https://www.kixeye.com/forum/discussion/509974

If this is the case, some weapons with short reload times may be affected, particularly Inferno rockets which start with a 0.75 second reload, and are often mounted on Hellstrikes with cluster warheads.  Looking back at the reload bonus (x4) from rank, this could mean that any legendary-ranked ship with Inferno rockets cannot gain any benefit from Cluster warheads or hull bonuses at all, since its computed reload time will be 0.75 * (1-75%) = 0.19 seconds.

I took another video with Hellstrikes:

And I found that yes, the minimum reload time is 0.2 seconds.

So on a Hellstrike, with 140% rocket reload bonus included in the hull:
Blueprint reload time: 0.75 seconds
Reload Time after Hull Bonus: 0.312 seconds
Reload Time at 37% rank: 0.197 seconds (limited to 0.2 seconds)

This means that Cluster Warheads on an Inferno-armed Hellstrike are useless after reaching 37% rank bonus (Hunter 4 or 4 stars).  Remember that rocket build I posted in the Hellstrike vs. Jugg X article?  Use Siege Battery or High Explosive Shells instead of the Cluster Warhead special.

SALVO DELAY 
The conventional wisdom is that the salvo delay for most weapons is 0.1 seconds.  However, my video above showed that the salvo delay for the Torrent Missile was 0.2 seconds.  Cryo weapons were published on bp-information as having the 0.2 second salvo delay baked into their statistics.

Androm on the Kixeye forums seems to think that many weapons have AT LEAST a 0.2 second (minimum) salvo time per shot as well - he looked at Chainguns, Mortars, and Assault Missiles:
https://www.kixeye.com/forum/discussion/430202

One of the weapons not analyzed in that post or video is the Impulse Launcher, which apparently has a PUBLISHED salvo time of 0.1 seconds.  I'll break out my F launcher armed Greta Nukes and take a video: 


Well well well, 0.2 second Salvo Time on those launchers too.  I think that nothing will fire anything faster than 0.2 seconds.  (I haven't looked in a base attack though.. Cerbs might be one more thing to check)

I suspect there is something inherent to the battle server architecture, that they run on a 0.2 second (5 Hz) cycle/frame/tick, and nothing can happen more frequently than that.  Essentially from a software perspective, it could be programmed it so that on every tick, the server decides if each weapon ought to fire, based on where it is in its reload/salvo cycle.

Before you all go freaking out about this, a faster tick results in more time fidelity, but also more bandwidth required and more potential for lag, so Kixeye had to select a time that found the right balance.  It may even be possible that BP used to run on a 0.1 second tick (which is why we all thought the salvo time was 0.1 seconds), but that value was revised to 0.2 at one point in order to improve game performance.

SUMMARY:
Well I think this article has dispelled up some myths (including ones that I believed) related to the reload and salvo time of weapons.  I'm working towards releasing that new DPS/Survival Time calculator that will be useful for both attacking and defending.

EDIT: Dennis (in his comments below) posted that he updated the Launcher Comparison calculator & posted it here:  https://docs.google.com/spreadsheets/d/1pZDTgAtvX7GtaOSLKIkPtoxNzCREkGTRKRE_LgIrpYg/edit?usp=sharing
Hopefully that will keep you guys sated until I can get the big one out there. Nice work!

My next article is going to be related to armor resistances and reductions.

I hope you all have a Happy New Year that is filled with Uranium and Instant Repairs!

R10 Hellstrike vs. R5 Juggernaut X

First a note about rank & reload....
I've been using the old school 1 / (1 + rank bonus) formula to calculate reloads for a long time, but I've been convinced that is wrong.

See threads at: https://www.kixeye.com/forum/discussion/comment/4292981
and: https://www.kixeye.com/forum/discussion/503010

It looks like rank is actually different from reload bonuses, so applied as reload time * (1 - rank %) / (1 + sum of reload bonus %).  This changes a lot of stuff, particularly the "N vs. S" launcher question.  Rank becomes much more valuable, and so do weapons with low salvo numbers.  I think I owe you all an update, and it is coming.

Now on to Hellstrikes:
The R10 Hellstrike got a bit of an extra boost (or a boost that was supposed to be there all along, and just hidden by poor QA) when Kixeye added a +30% Armor Ability improvement to R10 in the shipyard.  In fact, I thought 200,000 Uranium was a bit steep for only a +40% radioactive defense, and my initial thoughts on the Hellstrike retrofit were that the players that still used them will like them a little better, but there was no fundamental difference in capability.  The extra armor ability may make the difference in how these ships can be used, so I'll take another look and see if a high evade blitz fleet or a tank (both of which can be done successfully with JuggX) is more viable.

LIGHT TANK:
I'll start with the "light" tank I've been using in the last couple raids, and build a Hellstrike on the same concept:

http://www.dahippo.com/bp/ship/#!50II50V0V0V0V0V0V0V0V0C1S5B1A1A1A1A090JUA0V0V0V0V0V0V0C1S5B5P1A1A1A1A091A1A0ZZ0ZZ0ZZdA

To see the ships, just follow the Huggy's link, but as a description, I loaded each ship with D3-E armor, 1 Diplomat 1, Phalanx 2, Speed System 3, Scrambler 3, D5X, and Evade upgrade (Hellstrike only).

A comparison of the stats: 

Statistic	Juggernaut X R5	Hellstrike R10
Weight	4,181	4,189
Armor	13,835	13,050
Combat Speed	19.2	22.4
Turn Speed	44.0	26.4
Evade	83.2%	82.5%
Ballistic Defense	67%	60%
Explosive Defense	50%	67%
Penetrative Defense	56%	66%
Concussive Defense	0%	0%
Radioactive Defense	40%	40%
Build Time w/off	9d20h22m	11d22h01m
Repair Modifier	100%	150%

The JuggX has slightly better Evade and build time, but the Hellstrike has better speed and conventional resistances.  This comparison came out a lot closer than I thought.  One other tweak for this Hellstrike build could be replacing the D5X with Heavy Plating 3, which would further improve the conventional resistances at the expense of speed and weight.  However, the speed would stay higher than a fleet with base combat speed 11 and speed system 3, allowing it to stay useful as a tank.  The repair modifier of 150% on the Hellstrike is also a drawback, especially for a ship designed to soak damage.  Also remember that the JuggX will need a lot less uranium to retrofit than the Hellstrike R10 (which will need 5 warehouses to hold enough U).

As a tank, I think I'd give the edge to the Jugg X... with a little more evade, less repair time and less build time.

LAUNCHER FLEET:
The other big use of the Jugg X is as a high evade blitz fleet, equipped with launchers of course.  Some players refit their Hellstrikes with launchers and also were able to use them effectively.  I'll outfit a 3 ship fleet of each with Cryo launchers for comparison:

 First the Jugg X:

And the Hellstrike:

Both builds are at: 
http://www.dahippo.com/bp/ship/#!50II51R1R1R1Q1R1R1R1Q5H681V4X4X4X4X4W0ZZ0JUA1R1R1R1Q1R1R5H681V0O4X4X4X4X4W4W4W0ZZ0ZZdB

I decided to mix S and N cryo launchers - as I said in my article analyzing them, I wanted to be sure that my initial salvo would trigger a cryo overload, and a fleet with 15 S launchers would be one hit short.  

For the extra two weapon slots in the Hellstrike, I decided to add more N launchers for better anti-ship capability, but there would be plenty of options to use those slots differently, including Cryo S launchers, Phalanx, or even (light) rockets.  I added the Ion Thrusters in the 4th special slot of the Hellstrike for both the evade and the turn capabilities - when comparing Ion Thrusters to Evade Upgrade, the weight is the same, and the Evade bonus is close - 12% vs. 15%.

Stats comparison: 

Statistic	Jugg X R5	Hellstrike R10
Weight	9,636	10,427
Armor	21,985	20,400
Combat Speed	19.2	22.4
Turn Speed	20.0	31.9
Evade	79.8%	79.5%
Ballistic Defense	73%	67%
Explosive Defense	25%	50%
Penetrative Defense	56%	62%
Concussive Defense	0%	0%
Radioactive Defense	67%	60%
Build Time w/off	26d2h4m	25d22h22m
Repair Modifier	100%	150%
Fleet S Launchers	12	12
Fleet N Launchers	3	9

Which one do I like better?  I'm not sure...  The Jugg X has an edge on defense, with more armor, more radioactive resist, and a bit more evade.  The Hellstrike has more punch, more turn, more speed, and more missile defense.  If the evade is a big deal, using the Evade Upgrade on the Hellstrike tilts the evade edge in that direction.  If going from scratch, probably the lower Uranium cost to retrofit and lower repair time would tilt my preference for the Jugg X, but I think those Hellstrikes would be pretty fearsome as well.  The Hellstrike's extra N launchers and extra turn & speed would be really useful for FvF, especially as we expect Reavers to make a comeback.

HELLSTRIKE ROCKET BUILD:
Although not strictly a comparison with the JuggX, as one more option for the R10 Hellstrikes, I looked at a refit of my old Dock 10 design to take advantage of the extra weight, and stick with the Inferno Rockets.  One very specific thing I didn't mention in the first go around on the Hellstrike retrofit is that the increased range at R9 gives a solid advantage - by increasing Inferno Rocket range to 71, Hellstrike at R9 will outrange the Cerberus or Gargoyle defense turrets with their range of 64.  Gargoyles with their concussive damage have been considered an effective Hellstrike defense, but good drivers will now be able to stop outside their attack range.  Whether that is a good idea depends on the rest of the base defense.

The ship design for a 3 ship fleet (along with one ship from the old design) is here: 

http://www.dahippo.com/bp/ship/#!50JUA0U1R1R0U0U1Q5N2L1S5B19A0A040A040400JUA0U1R1R0U0U1Q5N2L1S5B19A0A040A040400JUA0U1R1R0U0U1Q5N2L1S5B19A0A040A040400ZZ0JU50U1E1K0U0U1E5N2L1S5B19A0A000A00000dB

It would be a straightforward refit to add the D5E/D4R pieces over the Forsaken plate and add the additional rockets (to take advantage of Dock 11 weight).  Armor builds slow, so each ship would take about 5 days 16 hours to refit.  Replacing Agility System with Radioactive Coating would be another optimization, but it would take an additional 2 days 11 hours per ship.

Compare stats:

Statistic	Dock 10 Hellstrike R5	Dock 11 Hellstrike R10
Weight	8,900	9,994
Armor	14,250	15,250
Combat Speed	20.8	22.4
Turn Speed	26.4	26.4
Evade	61.4%	76.3%
Ballistic Defense	66%	66%
Explosive Defense	71%	71%
Penetrative Defense	60%	60%
Concussive Defense	0%	0%
Radioactive Defense	0%	48%
Build Time w/off	22d3h37m	23d22h47m
Repair Modifier	150%	150%

The bumps in Evade and Radioactive defense will make a big difference in hitting bases nowadays... if really serious about it, changing the AG3 to RC3 would improve the radioactive defense to 60%. 

SUMMARY:
Well, my initial take on the R10 Hellstrike (before announcement of the armor bonus) was that Hellstrike users would like it, but it wouldn't prompt a bunch of people to start building them all of a sudden.

I still think that, but I'm a bit less sure.  A refit of my old Hellstrikes looks a lot more tempting... although since the launcher refit would take almost as long as a new build, the rocket refit would be more likely.  If I were a player who had nothing to start with, I think I'd still go with a Jugg X build for most situations, but I wouldn't fault someone who preferred the Hellstrike.

Many high end base hitting fleets these days are using two "tank" ships along with two Mastodons.  Although none of the builds in this article would be quite right for a Hellstrike in that role, I could see an R10 Hellstrike being a part of one of those fleets as well (along with the Savage, Grim, Frosty, Berzerker or Jug X ships I've seen).

UPCOMING:
The one year anniversary of this blog is coming up, and I plan to take a look back at some of the articles I wrote, and determine if my opinions were any good or if they were full of sh*t.

I also have a plan to revisit the "noobs" series since my "low" level base hit level 50 recently,  and I want to do a ship armor roundup (as suggested by a reader), since I haven't done one since March.  But apparently I need to do an update to all the DPS stuff first, so that one's at the top of my list.

New Mission Items - D104-S, Cryo Turret, Turret Armor D4-M

Three new blueprints have been announced for the Forsaken mission: the Cryo launcher D104-S, The base Cryo Turret, and the Zynthonite Reinforcements (Turret Armor D4-M).  I'll analyze each of them in this article.

Also - looking over the prizes in each Tier, I think these are the best groups of prizes we've seen in a while:

Tier 1: The high DPS/weight Negotiator 1 is here, along with Level 1 Hail & Phalanx.  The BC has always been a great hull for low level players, and the R10 upgrades make it even more useful.

Tier 2: OK, maybe not that much too great here besides the next level of Negotiator...

Tier 3: Impulse Launcher D92-U shows up in the Forsaken Mission for the first time, which is nice for players that don't have them yet, and I think that one is more generally useful than the D92-S launcher from Tier 4.  Speed 3 and Strike 3 are here.  The Harpoon for base defense isn't quite as hard hitting as the Javelin, but close.  The Negotiator 3 is also a useful medium-weight mortar.  Countermeasure Equipment 3 is very useful... the enhanced BC & Mercury hulls make nice countermeasure platforms.

Tier 4: The new items show up here, and I don't really think any of the Tier 4 items this week are total duds, although I don't think the Fuel-Air Munitions field is that great, and winning the Atlas Carrier wouldn't be too great if you don't have a UAV weapon to put on it.  Of course, if you chose to spend 9 Million points last week on the Atlas over something else... man that sucks.

And now on to the new stuff...

Cryo Launcher D104-S

The Cryo Launcher D104-S is in a similar niche as the Impulse Launcher D92-S - it has a higher damage, larger supercharge boost, lower accuracy, and longer reload time than the baseline "prize" launchers.  For the impulse launchers, unless you have both a high rank AND a high reload bonus, the F Launchers are better than the S.  I'll compare these as well.

	Cryo Launcher S	Cryo Launcher N	Siege Missile Z w SFB3	Impulse Launcher F	Impulse Launcher S
Max Range	91.0	91.0	88.4	91.0	91.0
Damage	1220	980	1,088	648	900
Bldg Damage	1830	490	2,176	972	1,350
Bonus Damage	0	0	359	0	0
Salvo	1	8	1	9	1
Reload Time	6.0	2.5	5.0	2.5	6.0
Accuracy	50%	70%	70%	70%	50%
Weight (Shipyard 2)	700	600	1,120	970	700
Bonus Armor	200	350	600	300	150
Fleet DPS	101.7	175.9	202.6	137.5	75.0
Fleet DPS/hton	14.5	29.3	18.1	14.2	10.7
Building DPS	305.0	125.6	507.0	294.5	225.0
Building DPS/hton	43.6	20.9	45.3	30.4	32.1
Hits to Overload	16	80	0	120	15
Salvos to Overload	5.0	10.0	0	13.3	15.0
Reference Overload Time (sec)	192.0	55.7	0	62.9	180.0
Overload Effect	4296 Cryo Field	4296 Cryo Field	0	7864 shock	7864 shock
Overload DPS/hton	3.2	12.9	0	12.9	6.2
Build Time (w Off)	1d 2h 16m	13h 46m 30s	13h 46m 30s	1d 2h 16m	1d 2h 16m
Build Time / ton (minutes)	2.25	1.38	0.74	1.62	2.25

The S version of the Cryo Launcher doesn't have the weak building damage of the N version, and with 16 hits needed for an overload, I could imagine plenty of fleet builds having enough launchers for an overload in a single salvo.  

The biggest use of the Impulse Launcher S seemed to be on Enforcers (with high rank) for base defense.  I think with the high ship DPS of the D104-N, I wouldn't go refitting D104-S over D104-N launchers on Enforcers.  What I have seen is a few players trying to hit bases or dredges with Cryo launcher fleets, and the low building damage seems to be a big weakness for that role.  I would suggest a mix of S and N Cryo launchers to try to mitigate that weakness. A key trait of a fleet mixing the launchers would be that it should be able to create a cryo field against buildings with its "alpha strike" (initial salvo)... so the fleet should make sure to have enough launchers such that (N launchers * 8 + S launchers * 5 >= 80).  That shouldn't be too tough.  

Maybe something like: 

http://www.dahippo.com/bp/ship/#!50MO00V0V0V0V5H1V0O684S4S00004W1A4W4W0MO00V0V0V0V5H1V0O684S4S00004W1A4W4W0MO00V0V0V0V5H1V0O684S4S00004W1A4W4W0MO00V0V0V0V5H1V0O684S4S00004W1A4W4W0MO00V0V0V0V5H1V0O684S4S00004W1A4W4WdB

15 N launchers and 10 S launchers should give a lot of punch across ship and building targets.

(Huggy didn't add the D104S yet, so I used D92S (same weight & build time) instead)

Cryo Turret

This new base turret brings the potential for Cryo Launchers to anyone's base who can reach Tier 4, not just those who chose to shell out 25 Million points for the Wendigo in Avalanche.  Will this turret make those of us who spent the points, spent the uranium to upgrade a turret base, and then started a 19+ day build to change a Brimstone to a Wendigo have second thoughts?



I compared the damage output of this turret to some others.  Even with a Level 5 turret base, there is only 21% power margin (12% with Level 4), so there is no useful offensive special that could be added to this turret.

	Wendigo	Cryo Turret	Deadeye Executioner	Executioner with Thermo 3	Javelin with DUShells 3	Sent 5 with Scram 3
Range	131	120	30 - 199	50 - 146	80 - 149	30 - 135
Damage	5,042	5,042	1,886	2,359	2,754	1,144
Submerged Dam	0	0	0	0	0	0
Damage Type	Radioactive	Radioactive	Penetrative	Penetrative	Ballistic/Penetrative	Penetrative/Ballistic
Salvo	5	5	3	2	1	4
Cycle Time	7.9	7.9	10.2	10.1	12	5.3
Spread	NA	NA	NA	NA	NA	NA
Splash	NA	NA	NA	NA	NA	NA
Accuracy	100%	70%	100%	100%	140%	100%
Ship DPS	638.2	446.8	184.9	233.6	321.3	215.8
Power Consumed	3,920	3,292	3,654	3,420	3,693	1,209
Salvos to Overload	1	4	-	-	-	-
Reference Overload Time (sec)	7.9	45.1	-	-	-	-
Overload Effect	4296 Cryo Field	4296 Cryo Field	-	-	-	-
Overload DPS	543.8	95.2	-	-	-	-
Build Time (w Off)	17d9h29m	11d12h32m	12d18h56m	10d5h32m
Other	Charge stacks with other cryo launchers	Charge stacks with other cryo launchers	No CM, 50% Pen Bypass	No CM, 50% Pen Bypass	None	40% CM Evade

The DPS on the Cryo turret is pretty good, but the range isn't.  The Wendigo, with its higher accuracy, range, and ability to make shockwaves is still worth a premium over this Cryo turret, but with Radioactive resistance being generally lower on most ships than Penetrative or Ballistic, the Cryo turret is worth using, if you can find a base design that takes advantage of it.  (Since Victory Mortars have a similar range (125), you might want to look at some VM designs for inspiration). I'm not even including the shockwave potential here - if you can cluster a few of these turrets, use them to compliment a Wendigo, or use some ships with D104 launchers, you may be able to pop some cryo fields on attackers and really mess them up.

Zynthonite Reinforcements D4-M

I'm not surprised that Kixeye decided to release some blueprint turret armor - it seemed like that was their plan as soon as it was released. The confusingly named D4-M is the first winnable blueprint for turret armor.  This armor provides additional armor points as well as Missile Defense, independent of any special that may also provide resistance.  

	ZR D4M	DU3	DU2	DU1
Armor Points	16,040	22,000	17,000	12,000
Power	925	1252	968	683
AP/ Power	17.3	17.6	17.6	17.6
Other	Missile def + 25%
Build Time	1d13h53m	1d3h14m	18h56m	13h22m

With similar armor points and power draw as DU2, this armor might be worth considering.  The +25% doesn't seem to help much if you are only considering the benefit on the armor, but when also considering the benefit applies to the basic turret armor, then the benefit might show up.

A Level 4 turret with DU3 would have 32,800 armor points (against any weapon)
A Level 4 turret with D4M would have 26,840 armor points, but 33,550 effective armor points against Missiles (25% resistance).

On a Level 4 turret, you've saved a little power, but not given yourself much benefit.  Combining this with a missile defense special would give more benefit, but the relative benefit would be the same for both turrets.

How about a Level 5 turret?
A Level 5 Turret with 2 DU3 would have 58,400 armor points

A Level 5 Turret with 2 D4M would have 46,480 armor points, but 66,815 effective armor points against Missiles (43.75% resistance stacked).

This isn't astounding, but if also adding a missile defense special, I could imagine a missile fleet needing to stop to kill that Level 5 turret. If using two D4M with Reactive Panel 3 (25% power, 50% missile defense), any weapon drawing up to 1350 power could be used.  This would include a Napalm or Cerberus 5, but not a Gargoyle or a Coaxial turret.  Of course a fleet wouldn't stop for a Napalm, but getting a lot more shots out of a Napalm sure would be appreciated in most base defense scenarios.

Have a Merry Christmas... you keep playing, I'll keep posting!