Star Trek Online - Hull repair rate and leadership trait

Through a combination of in-game testing and information from the following links, I now mostly understand how hull repair rates work. Much of the information from the first link is out of date, but some of it is still correct.

http://theenginescannaetakeit.wordpr...echanics/#hull
http://home.comcast.net/~amicus/Skil...%20Effects.htm

Introduction

The hull repair rate shown in the UI is what it appears, the percentage of your hull that is regenerated per minute. If two ships have the same hull repair rate but one ship has more hull than the other, then the ship with more hull will regain more hitpoints per minute than the ship with less hull. To see the hull repair rate of your ship, look under the "Defense" tab while in system space. Alternatively, hover your cursor over the crew icons in your HUD.

The hull repair rate is affected by crew. The game distinguishes between alive crew and able crew. As far as I can tell, the hull repair rate depends on able crew, not alive crew.

Method for Testing the Effect of Crew

I will briefly describe the method I used for testing the effect of crew on the hull repair rate:

1. Use two ships. Let's call them ship A and ship B.
2. Ship A fires torpedoes at ship B to reduce ship B's crew.
3. Ship A stops firing at ship B to allow ship B's crew to recover.
4. In ship B, hover the cursor over the crew icons in the HUD to see the number of able crew and the hull repair rate. Use the command /screenshot_ui_jpg to capture both these numbers simultaneously.
5. If ship B needs to remain in combat (i.e., red alert), then ship B should periodically fire at ship A or activate an ability like "Eject Warp Plasma".

Formula for Calculating the Hull Repair Rate

I will now discuss how the hull repair rate shown in the UI is calculated. To understand the formula, you must first understand the following variables.

HRR: the percentage your hull repaired per minute

base_HRR: the base hull repair rate of your ship determined by its class:

Cruiser, Carrier: 72%/min
Light Cruiser: 60%/min
Science Vessel: 60%/min (needs confirmation)
Bird-of-Prey: 60%/min
Escort: 50%/min (Raptors probably belong here, but I'm not sure.)

SHR: your skill in "Starship Hull Repair"

num_leadership: an integer from 0 to 6 equal to the number of officers on your ship with the leadership trait including the captain.

(Currently, only humans have the leadership trait.)

Borg_2pc:
35%/min if you have equipped at least 2 pieces of the Mk XI Borg set (not sure if the Mk X and Mk XII sets give different bonuses);
0%/min if you have not equipped at least 2 pieces of the Borg set of the same mark.

(The Mk XI set also gives +10 to "Starship Hull Repair"; this is counted separately in SHR.)

combat_factor: 1 if you are out of combat; 1/6 if you are in combat.

total_crew: the crew complement of your ship

able_crew: the number of able crew on your ship. This is different from the number of alive crew.

able_crew_frac: able_crew / total_crew

crew_factor: a scale factor that depends on your crew, computed as follows:

crew_factor =
1, if able_crew_frac >= 3/4,
(4/3) * able_crew_frac, if 3/16 <= able_crew_frac < 3/4,
1/4, if able_crew_frac < 3/16.

Finally, the hull repair rate is computed according to the following formula:

HRR = base_HRR * (1 + SHR/100) * (combat_factor * crew_factor + 0.2*num_leadership) + Borg_2pc

Note: This formula may not be exactly what the game uses, but it is a good approximation to data obtained from in-game testing. The formula does not include the Omega reputation passive "Hull-Repairing Nanites", because I have been unable to test it. I have also not tested the effect of the Autonomous Regeneration Sequencer.

The important thing to notice is that the bonus from the leadership trait is modified by "Starship Hull Repair", but not by combat status or crew. The Borg 2-piece bonus is also unaffected by combat status and crew.

Hull Regeneration Tick Rate

I will now discuss the hull regeneration tick rate, that is, how often an increase in hull is shown in the UI. The following numbers were estimated by a human counting the number of seconds in his head between increases in hull. Thus, they are rough estimates only. Out of combat, hull regeneration ticks once every second. (I suspect that even if it ticked faster than once per second, the UI would not refresh fast enough to catch it.) In combat, the tick rate depends on bonuses from passives and equipment:

1. With no bonuses from passives or equipment, hull regeneration ticks once every 7 seconds.
2. With 2 pieces of the Mk XI Borg set, hull regeneration ticks once every 3 seconds.
3. With 1 human officer, hull regeneration ticks once every 3 seconds.
4. With 1 human officer and 2 pieces of the Mk XI Borg set, hull regeneration ticks once every 2 seconds.
5. With 5 human officers, hull regeneration ticks once every 2 seconds.
6. With 5 human officers and 2 pieces of the Mk XI Borg set, hull regeneration ticks once every 1 second.

Note: The 7 seconds in the first item of the list may actually be 6 seconds, because the hull repair rate in combat is 1/6 that out of combat. I suspect that there may be a UI delay or human error in counting.

There are two explanations for the above observations: (1) there are multiple sources of hull regeneration that tick at different rates, or (2) there is a single source of hull generation whose tick rate is modified by bonuses. I do not know which is correct.

Crew Recovery Rate

Although strictly speaking, crew recovery rates are a different topic from hull repair rates, I would be remiss if I did not discuss crew recovery rates, because the hull repair rate depends on crew. If you have no bonuses from equipment or doffs, then the UI should report that you have a crew recovery rate of 50%/min out of combat and 5%/min in combat. It is not clear whether these rates refer to alive crew or able crew. As far as I can tell, they apply to neither. The following numbers were estimated by a human counting the number of seconds it took to regenerate 100 able crew and 100 alive crew. Thus, they are rough estimates only.

Ship: Assault Cruiser
Total Crew: 800
Able Crew (in combat): 100 crew in 98 seconds (61.2 crew/min or 7.65%/min)
Able Crew (out of combat): 100 crew in 12 seconds (500 crew/min or 62.5%/min)
Alive Crew (in combat): no change in over 2 minutes
Alive Crew (out of combat): 100 crew in 8 seconds (750 crew/min or 93.75%/min)

Ship: Light Cruiser
Total Crew: 200
Able Crew (in combat): 100 crew in 100 seconds (60 crew/min or 30%/min)
Able Crew (out of combat): 100 crew in 12 seconds (500 crew/min or 250%/min)
Alive Crew (in combat): no change in over 2 minutes
Alive Crew (out of combat): 100 crew in 26 seconds (230.77 crew/min or 115.38%/min)

My guess is that able crew regenerates at ~60 crew/min in combat and ~500 crew/min out of combat, regardless of ship. I also conjecture that alive crew regenerates at ~100%/min out of combat and never regenerates in combat, regardless of ship.

Examples from Testing

Below I give some examples from in-game tests. The following tests were performed at 100% crew. The hull repair rates reported by the UI agree with the formula above to within 0.1%/min. The difference is likely due to rounding.

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 99
Hull Repair Rate (out of combat): 143.3%/min
Hull Repair Rate (in combat): 23.9%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 35%/min
Leadership Trait: 0 humans
Starship Hull Repair: 109
Hull Repair Rate (out of combat): 185.5%/min
Hull Repair Rate (in combat): 60.1%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 1 human
Hull Repair Rate (out of combat): 171.9%/min
Hull Repair Rate (in combat): 52.5%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 35%/min
Leadership Trait: 1 human
Starship Hull Repair: 109
Hull Repair Rate (out of combat): 215.6%/min
Hull Repair Rate (in combat): 90.2%/min

Ship: Light Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 99
Hull Repair Rate (out of combat): 119.4%/min
Hull Repair Rate (in combat): 19.9%/min

Ship: Fleet Tactical Escort Retrofit
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 35%/min
Leadership Trait: 5 humans
Starship Hull Repair: 109
Hull Repair Rate (out of combat): 244%/min
Hull Repair Rate (in combat): 157%/min

Ship: Vo'Quv Carrier
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 109
Hull Repair Rate (out of combat): 150.5%/min
Hull Repair Rate (in combat): 25.1%/min

Ship: Ki'tang Bird-of-Prey
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 109
Hull Repair Rate (out of combat): 125.4%/min
Hull Repair Rate (in combat): 20.9%/min

The following tests show the effect of crew on the hull repair rate. The hull repair rates reported by the UI agree with the formula above to within 3%/min. Some of the error is likely due to rounding. I also suspect that the UI does not update the number of able crew and the hull repair rate simultaneously, so they may sometimes be out of sync.

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 99
Total Crew: 800
in combat: 0 crew, 6.0%/min
in combat: 50 crew, 6.0%/min
in combat: 100 crew, 6.0%/min
in combat: 148 crew, 6.0%/min
in combat: 150 crew, 6.0%/min
in combat: 152 crew, 6.1%/min
in combat: 200 crew, 8.0%/min
in combat: 300 crew, 12.0%/min
in combat: 400 crew, 15.9%/min
in combat: 500 crew, 19.9%/min
in combat: 598 crew, 23.8%/min
in combat: 600 crew, 23.9%/min
in combat: 602 crew, 23.9%/min
in combat: 700 crew, 23.9%/min
in combat: 800 crew, 23.9%/min
out of combat: 54 crew, 35.8%/min
out of combat: 106 crew, 35.8%/min
out of combat: 148 crew, 35.8%/min
out of combat: 155 crew, 36.4%/min
out of combat: 205 crew, 48.5%/min
out of combat: 307 crew, 72.8%/min
out of combat: 407 crew, 95.2%/min
out of combat: 506 crew, 119.5%/min
out of combat: 598 crew, 141.9%/min
out of combat: 608 crew, 143.3%/min
out of combat: 709 crew, 143.3%/min
out of combat: 800 crew, 143.3%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 35%/min
Leadership Trait: 0 humans
Starship Hull Repair: 109
Total Crew: 800
in combat: 0 crew, 41.3%/min
in combat: 50 crew, 41.3%/min
in combat: 100 crew, 41.3%/min
in combat: 148 crew, 41.3%/min
in combat: 150 crew, 41.3%/min
in combat: 152 crew, 41.4%/min
in combat: 200 crew, 43.4%/min
in combat: 300 crew, 47.6%/min
in combat: 400 crew, 51.7%/min
in combat: 500 crew, 55.9%/min
in combat: 598 crew, 60.0%/min
in combat: 600 crew, 60.1%/min
in combat: 602 crew, 60.1%/min
in combat: 700 crew, 60.1%/min
in combat: 800 crew, 60.1%/min
out of combat: 55 crew, 72.6%/min
out of combat: 105 crew, 72.6%/min
out of combat: 143 crew, 72.6%/min
out of combat: 154 crew, 72.8%/min
out of combat: 209 crew, 86.6%/min
out of combat: 301 crew, 109.6%/min
out of combat: 409 crew, 135.6%/min
out of combat: 508 crew, 160.8%/min
out of combat: 594 crew, 183.8%/min
out of combat: 608 crew, 185.5%/min
out of combat: 709 crew, 185.5%/min
out of combat: 800 crew, 185.5%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 1 human
Starship Hull Repair: 99
Total Crew: 800
in combat: 0 crew, 34.6%/min
in combat: 50 crew, 34.6%/min
in combat: 100 crew, 34.6%/min
in combat: 148 crew, 34.6%/min
in combat: 150 crew, 34.6%/min
in combat: 152 crew, 34.7%/min
in combat: 200 crew, 36.7%/min
in combat: 300 crew, 40.6%/min
in combat: 400 crew, 44.6%/min
in combat: 500 crew, 48.5%/min
in combat: 598 crew, 52.5%/min
in combat: 600 crew, 52.5%/min
in combat: 602 crew, 52.5%/min
in combat: 700 crew, 52.5%/min
in combat: 800 crew, 52.5%/min
out of combat: 58 crew, 64.5%/min
out of combat: 106 crew, 64.5%/min
out of combat: 149 crew, 64.5%/min
out of combat: 158 crew, 66.1%/min
out of combat: 207 crew, 77.5%/min
out of combat: 304 crew, 99.8%/min
out of combat: 408 crew, 124.2%/min
out of combat: 507 crew, 148.5%/min
out of combat: 598 crew, 171.2%/min
out of combat: 608 crew, 171.9%/min
out of combat: 709 crew, 171.9%/min
out of combat: 800 crew, 171.9%/min

Ship: Assault Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 35%/min
Leadership Trait: 1 human
Starship Hull Repair: 109
Total Crew: 800
in combat: 0 crew, 71.4%/min
in combat: 50 crew, 71.4%/min
in combat: 100 crew, 71.4%/min
in combat: 148 crew, 71.4%/min
in combat: 150 crew, 71.4%/min
in combat: 152 crew, 71.4%/min
in combat: 200 crew, 73.5%/min
in combat: 300 crew, 77.6%/min
in combat: 400 crew, 81.8%/min
in combat: 500 crew, 86.0%/min
in combat: 598 crew, 90.1%/min
in combat: 600 crew, 90.2%/min
in combat: 602 crew, 90.2%/min
in combat: 700 crew, 90.2%/min
in combat: 800 crew, 90.2%/min
out of combat: 51 crew, 102.7%/min
out of combat: 102 crew, 102.7%/min
out of combat: 145 crew, 102.7%/min
out of combat: 156 crew, 103.9%/min
out of combat: 207 crew, 116.2%/min
out of combat: 309 crew, 141.8%/min
out of combat: 409 crew, 167.0%/min
out of combat: 508 crew, 190.3%/min
out of combat: 597 crew, 214.3%/min
out of combat: 608 crew, 215.6%/min
out of combat: 709 crew, 215.6%/min
out of combat: 800 crew, 215.6%/min

Ship: Light Cruiser
Hull-Repairing Nanites: No
Borg 2-pc Bonus: 0%/min
Leadership Trait: 0 humans
Starship Hull Repair: 99
Total Crew: 200
in combat: 0 crew, 5.0%/min
in combat: 25 crew, 5.0%/min
in combat: 36 crew, 5.0%/min
in combat: 37 crew, 5.0%/min
in combat: 38 crew, 5.0%/min
in combat: 39 crew, 5.2%/min
in combat: 50 crew, 6.7%/min
in combat: 75 crew, 9.9%/min
in combat: 100 crew, 13.3%/min
in combat: 125 crew, 16.6%/min
in combat: 148 crew, 19.6%/min
in combat: 149 crew, 19.8%/min
in combat: 150 crew, 19.9%/min
in combat: 151 crew, 19.9%/min
in combat: 152 crew, 19.9%/min
in combat: 175 crew, 19.9%/min
in combat: 200 crew, 19.9%/min
out of combat: 29 crew, 29.9%/min
out of combat: 31 crew, 29.9%/min
out of combat: 44 crew, 34.4%/min
out of combat: 59 crew, 46.2%/min
out of combat: 75 crew, 58.8%/min
out of combat: 105 crew, 82.1%/min
out of combat: 121 crew, 94.9%/min
out of combat: 146 crew, 113.9%/min
out of combat: 158 crew, 119.4%/min
out of combat: 179 crew, 119.4%/min
out of combat: 200 crew, 119.4%/min

Acknowledgments: Thanks to @squonkman for helping me test.