From some of my personal experience ratting in a nyx for 3-5 hours some days I have noticed a huge drop in battleship commander spawns and npc capital spawns.
On the other hand ratting with a single or duo nightmare I get more battleship commander spawns ratting with multiple VNI mostly afk each in it’s own anomaly again no caps no commanders for hours.
Perhaps it’s just me but it seems both carrier and supercarrier usage reduces chance of a spawn aswel as low Imput builds like vni or Ishtars.
On the other hand decided to test out belt ratting a bit see what I get.-no battleship commanders yet lots of npc capitals if you keep cleaning the belts fast my best spawn rate was 3 dreadnaughts in same system just different belts in 25mins.
I am also not alone in this asumption as every capital ratter in my Corp that I asked shares same story for anomaly spawns
I suggest you alternate 10 havens with a VNI (in same system), then 10 havens with a nyx, then 10 havens in nm, and repeat this untill you get 10 commanders for each. Of course that means, for several days. This would also reduce the chance that other elements have an impact, eg the time of the day, the number of people in system, the number of commanders already killed in the last hour.
Record every time you get a commander.
Then you will have enough data to affirm if “the ship used impacts the spawn rate of commanders in havens”.
i cannot say something about the chance you may have in a captital, but me and other ppl reported that the chance for commander spawns was highly reduced by ccp as it seems. i do belt ratting in a machariel in NPC nullsec btw. so, yes, i can confirm your assumtion.
As far as belt spawns I am currently at around 70 capital/supercap/hauler spawns without encountering a single battleship commander spawn.
I took it upon myself to do some extensive belt ratting searching for officers and instead noticed battleship commanders don’t spawn anymore