I don't know as there is a way to explain... Here's the thread from which I copied Ducimus' "math" from (I already have a headache from that "math" word):
Of refits, new commands, rank, and retirements
It seems to be a cumulative number that is stored, and it is (re-)calculated after each patrol, and is called a "campaign rating". In other words, the game does not store past patrol scores, only the cumulative "Campaign Rating", and the total Renown. A "missing" component in the equation, is that nothing is mentioned of "order of operations", ie: if there is a use of parenthesis to control addition first, then multiplaction... Without the use of parenthesis to control the "order of operations", things would be really bad with a "bad", or low rating early in a career, but either way, you can see with Ducimus' calculations, that an early patrol that is low-scoring, can result in a hole that is nigh-on impossible for a player to crawl out of. In real math, a division by zero is undefined, aka: illegal. It always results in "zero". You would need at least a couple of "Excellent" patrols to recover, and those can be difficult to come by.
Submarine availability looms large when you look at conning tower availability. I might try to make another version of the "Submarine Equipment Upgrades.pdf", and have it include the sub availability and their conning tower dates. That way, if a skipper knows he wants to keep his boat, but wants to get an updated conning tower for the future fitting of a radar, he might be able come in "early" from patrol, and possibly get what he wants... As it stands now though, each sub is in its own "UpgradeClass", in an attempt at having a player "step" through the progression to get a higher class sub... but there again, that "campaign rating" might decide the boat anyway, based upon your renown score it seems, and looks to be a hard-coded, "invisible" calculation, buried somewhere in the game's code, that actually decides which boat you are offered. The game sure does like handing out early Balao boats...
