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So when going through various postings and commentary on PROC (Programmed Random OCcurrences) and their rates, it seems that there is not necessarily a clear idea or sense of what is meant by "rate" and when % are thrown around in theory, it makes those of us who are theoretical scientists stop and think (to be fair, [i]everything[/i] makes us theoretical types stop and think ;)

Not following? Do a though experiment with me. A card could have a 100% PROGRAMMED rate of "proc-ing" (having it's ability go off in a battle) [no card does have that high of a rate, but this is a thought experiment, not a practical one, do keep up]. If that's the PROC rate built into the program card, how often will it APPEAR to "proc" to an end user?

Depends where it is in the deck.

Why? A few reasons: 

  1. The center card is always checked first
  2. There is a limit of 3 activations per battle
  3. (if we weren't doing a 100% scenario, we'd also have to account for the center card's programmed double rate!)

So, with that obviously, the center card will show a rate of 100%. So far, so good. BUT, the remaining 4 cards (the wings) while each having a PROGRAMMED rate of 100% can't all go off, in fact, only 2 of the 4 will go off (a 50% rate). A 50% chance of going off IS THE MAX for the APPARENT or DISPLAYED rate for a wing card. If we test this a thousand times we will get the same exact results, and, if we didn't know about the difference between center cards and wing cards, we might average it all together and say that that card (remember, the end user never knows the Programmed Rate they only get to see the displayed/apparent rate) "has a proc rate of 60%" ["5 display rate"] which, in my opinion, would be a terrible way to describe what's happening here.

So, I built a simulator that can take in any hypothesized PROC rate and will spit out the expected/theoretical displayed rate (assuming we're not terribly misunderstanding something, which of course, is possible). This simulator is a way to "double check" our hypothesis and assumptions based on our observations. I've plugged a bunch of numbers in and will show the results below and let the community discuss if any of the hypothesized PROC rates are in-line with their observed battle activations. At any rate, it should give us some ideas for testing skill 10 v skill 1, etc.

Expected Observations of Hypothesized Programmed Rates
Prog. Rate 5 Display Rate Wing Rate 3 procs 2 procs 1 procs 0 procs
100% 60% 50% 100% 0% 0% 0%
75% 58% 49% 95% 5% 0% 0%
60% 52% 45% 82% 15% 3% 0%
50% 46% 41% 69% 25% 6% 0%
45% 42% 39% 57% 31% 11% 1%
40% 37% 36% 46% 35% 17% 3%
35% 32% 32% 34% 36% 24% 5%
33% 30% 31% 30% 36% 27% 7%
30% 27% 29% 24% 35% 31% 10%
25% 22% 24% 16% 32% 37% 16%


Enjoy

PS:

Here's Yusoki's data, I believe that first column is an estimate and the activation/battle is his data

Yusoki on Ability Activation by Rarity
proc rates Rarity 3 2 1 0
75% high 90% 8% 2% 0%
66% rel hi 79% 16% 4% >1%
50% ave 50% 31% 16% 3%

and here's the numbers my simulator puts out that match that ballpark closest:

proc rates Wing dis. 3 2 1 0
68% 47% 90% 9% 1% 0%
58% 44% 80% 17% 3% 0%
42% 37% 50% 33% 15% 2%


For more accurate suggested PROC rates, visit my other blog entries and see Shinji's helpful posts

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