Admiralty System's Critical Multiplier and Critical Rating Calculation is Slightly Bugged

intrinsical

Greetings everyone,

I'm the author of the Admiralty Optimizer program and today I was I working on figuring out why the Admiralty Optimizer's calculations for Critical Rating is occasionally different from Cryptic's. It took me quite a while to puzzle it out, but I think finally figure out why... I think Cryptic's formula for calculating Critical Rating is off in a very specific situation. In order to explain it, I first need to explain the Critical Rating formula. It is actually quite simple:

Critical_Rating = (Event_Crit_Rating * Event_Crit_Multiplier) + (Surplus_ENG * ENG_Crit_Multiplier) + (Surplus_TAC * TAC_Crit_Multiplier) + (Surplus_SCI * SCI_Crit_Multiplier)

When the ships you selected have a combined ENG/TAC/SCI score exceeding the assignment's ENG/TAC/SCI requirement, that's considered the surplus. So if my combined ships have a ENG score of 100 but the assignment only requires 75 ENG, you have 25 Surplus_ENG. Event/ENG/TAC/SCI Crit_Multiplier values are usually set to the value of 1 unless one or more of the selected ships has the special ability "(n)x Critical Multiplier from (Eng|Tac|Sci|All Stats|Events)". This special ability is commonly found in shuttles so for example, the Yellowstone Runabout and Captain's Yacht both have "5x Critical Multiplier to All Stats".

I used an assignment given to my character, "Check Status of Isolated Colony" with the "Astrometric Data Exchange" event. For testing purposes, I selected the U.S.S. Rhode Island which comes with 3x Critical Multiplier to All Stats. The assignment+event's requirements are 15 ENG, 15 TAC and 25 SCI. U.S.S. Rhode Island has 30 ENG, 27 TAC and 78 SCI, so plugging in the numbers,

Event_Crit_Rating = 5
ENG_Crit_Multiplier = 3
TAC_Crit_Multiplier = 3
SCI_Crit_Multiplier = 3
Surplus_ENG = 30 - 15 = 15
Surplus_TAC = 27 - 15 = 12
Surplus_SCI = 78 - 25 = 53
Critical Rating = (5 * 1) + (15 * 3) + (12 * 3) + (53 * 3) = 245

And in-game the Crit Rating is exactly 245. So far so good. The problem starts when you have two or more ships that both have the Critical Multiplier special ability. So let's get my Captain's Yacht, which has "5x Critical Multiplier from All Stats" to accompany U.S.S Rhode Island on the assignment, which changes the numbers to:

Event_Crit_Rating = 5
ENG_Crit_Multiplier = 3 + 5 = 8 (in-game, it's 7)
TAC_Crit_Multiplier = 3 + 5 = 8 (in-game, it's 7)
SCI_Crit_Multiplier = 3 + 5 = 8 (in-game, it's 7)
Surplus_ENG = 34 - 15 = 19
Surplus_TAC = 30 - 15 = 15
Surplus_SCI = 81 - 25 = 53
Critical Rating = (5 * 1) + (19 * 8) + (15 * 8) + (56 * 8) = 5 + 152 + 120 + 448 = 725
In-Game Critical Rating = (5 * 1) + (19 * 7) + (15 * 7) + (56 * 7) = 5 + 133 + 105 + 392 = 635

According to my formula, the Crit Rating should be 725. Unfortunately in-game the Admiralty UI shows a Crit Rating of 635, which you can get if the ENG, TAC and SCI Crit Mulitipliers are all set to 7 instead of 8.

Things get worse when I add the Yellowstone Runabout, which should make all three Critical Multiplier be 13 and should give a Critical Rating of 1305. Instead the in-game Critical Multiplier seems to be 11 and results in a Critical Rating of 1105. That's a whopping difference of 200.

Event_Crit_Rating = 5
ENG_Crit_Multiplier = 3 + 5 + 5 = 13 (in-game, it's 11)
TAC_Crit_Multiplier = 3 + 5 + 5 = 13 (in-game, it's 11)
SCI_Crit_Multiplier = 3 + 5 + 5 = 13 (in-game, it's 11)
Surplus_ENG = 37 - 15 = 22
Surplus_TAC = 34 - 15 = 19
Surplus_SCI = 84 - 25 = 59
Critical Rating = (5 * 1) + (22 * 13) + (19 * 13) + (59 * 13) = 5 + 286 + 247 + 767 = 1,305
In-Game Critical Rating = (5 * 1) + (22 * 11) + (19 * 11) + (59 * 11) = 5 + 242 + 209 + 649 = 1,105

So in summary when you select two or more ships that give bonuses to Critical Multiplier, the total Critical Multiplier is reduced by 1 per ship and the resulting the calculation of Critical Rating short changes you.

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mustrumridcully0

ruinthefun wrote: »

Actually, the Cryptic solution is, in fact, correct. Consider the hypothetical case of a ship whose power is "1x Critical Modifier". In other words, it's about as useful as boot full of warm TRIBBLE. It is clear that the addition of such a ship to the task force should not result in a 3x modifier turning into a 4x modifier, and that it should, in fact, remain 3. Therefore, your solution is actually incorrect and what we see in-game is correct.

Consider it this way: 2x Critical Modifier = +100% Now you see where your -1 per ship is from.

Yes, that makes sense to me. One has to consider bascially that every ship has an inherent 1x modifier unless noted otherwise.

intrinsical

I can accept that explanation, but how does the math work?

I'm asking because the current programming solution I see is inelegant and involves having to check how many ships have the Crit Multiplier ability and deducting that number from the Crit Multiplier stat, except for the special case where there is only ship in which case don't deduct. Or is there an easier way that I am currently not seeing?

jarvisandalfred

intrinsical wrote: »

I can accept that explanation, but how does the math work?

I'm asking because the current programming solution I see is inelegant and involves having to check how many ships have the Crit Multiplier ability and deducting that number from the Crit Multiplier stat, except for the special case where there is only ship in which case don't deduct. Or is there an easier way that I am currently not seeing?

It's like probably most things in STO, 1+%, where a 3x crit multiplier is a +200% (for 1+200%, or 300%). So if you change all of your 3x cards to +2x and all of your 5x cards to +4x, and then run 1+SumX as a constant crit multiplier, it should work fine.

intrinsical

jarvisandalfred wrote: »

intrinsical wrote: »

I can accept that explanation, but how does the math work?

I'm asking because the current programming solution I see is inelegant and involves having to check how many ships have the Crit Multiplier ability and deducting that number from the Crit Multiplier stat, except for the special case where there is only ship in which case don't deduct. Or is there an easier way that I am currently not seeing?

It's like probably most things in STO, 1+%, where a 3x crit multiplier is a +200% (for 1+200%, or 300%). So if you change all of your 3x cards to +2x and all of your 5x cards to +4x, and then run 1+SumX as a constant crit multiplier, it should work fine.

Yeah I soon realized it after a bit of thinking. Serves me right to make a post just after waking up.