VeryAngryFelid wrote:It is really irrelevant in 90% cases, the formula is linear. You get attacked 10 times and 9 of those attacks don't care about your extra EV.
Okay, disclaimer I'm not a math whiz at all. I'm terrible about making calculation errors when I try to do longhand work myself. And no, I don't find it natural to muck around in all of Crawl's formulae. (The format makes me dizzy to begin with. I'd have to change the fonts and size to start with.) Heck, I couldn't even get an online file to dump to offline fsim the other day, if you recall.
But I'm going to try picking at this anyway, because I honestly do not believe I am conceptually that horrible at it... And if someone can show me it's a totally silly effort, then I'll simply shrug I tried to explore it to my satisfaction and probably laugh and walk away. Here goes. It depends of course what you want some EV to do, and you didn't talk about particular Crawl threshold points so far that I noticed (15 or 25 EV versus 9-12 or 30-40 for that matter). I have no idea what "some Felid" was working with to begin with... But taking what there was, that 1 in 10 attacks business sounds way too simplistic a figure for me.
From what little I recall of my high school probability lectures, I somehow suspected Tasonir has a bit of the reality there. In simple probability (or is that "in theory" where games go on for ages and nothing ever happens?) sure any one roll has those odds. And maybe that works out neatly in 100 or 1,000 trials but... We're actually talking about cumulative probability here because it's over the course of multiple trials. And btw I'd venture that except for oh Abyss/Pandemonium (maybe?), we're also probably going to decide life or death more by "Did I avoid a few extra hits while repositioning or did this push me over a nice Crawl EV threshold I didn't have otherwise" than "Did this item really prevent all sorts of ranged attacks all day?" Well, I am anyway.
Back to the point. So if I recall, to actually simulate the likely outcomes, some multiplicative and counterfactual math (odds of event actually not happening over multiple runs) are also involved. I'm not sure about the neat formula - if I could even write the neat thing out once I found it somewhere - but... After quite a bit of googling, I think if it might be something like whatever powers this
binomial calculator.
Here are the parameters that make me think so. In particular:
What is a binomial experiment?
A binomial experiment has the following characteristics:
The experiment involves repeated trials.
Each trial has only two possible outcomes - a success or a failure.
The probability that a particular outcome will occur on any given trial is constant.
All of the trials in the experiment are independent.
Now, if I'm right (or in the ballpark at least, I hope):
This calculator looks neat because it will tell you a range of probabilities over cumulative trials: You can see the chances of getting not/less, equal, or more than a given number of hits over however many rolls. I'm not sure what its boundaries are; at some point things break down with larger numbers and you get Error figures, but that's any calculator I guess.
If this is indeed an appropriate place to look, then you can plug in some numbers and see:
0.3 probability for hits. The probability of less than 3 hits given 10 shots? Around 38.3 % And of less than 2 hits? 14.9%
Probability for less than 3 hits in 10 attacks with probability of hit at 0.2 ? About 67.8% For less than 2 hits? 37.6%
That's some absolute shift in percentage terms, moving the dial for success by 20 (edit: 20-some to 30?) %. (See, maybe I can copy from calculators but I'm pretty lousy at consistent subtraction.
)
Assuming my goal is not to be absolutely untouchable but rather to avoid taking damage a notable chunk of the time. Unless one finds a totally awesome robe/skin, that's before we even get to a touch of armor help even on many elves, resistances and damage randomness (and see also Deflect Missiles). I think that's fairly substantial.
Of course, you can play this any way you like on interpretation. You can also plug in other numbers of trials, other numbers of hits you'd like to look at. But where my concern is, does adding EV matter (at least adding 8 EV by whatever combination of training and items), then it looks to me like I could say, well if my goal is to at least noticeably reduce the chance of being hit 2 or 3 times in as many as ten attacks (which I also wonder is perhaps rather a lot)... Then in that case, that added EV actually changed my chances of pulling it off by much more than 1 in 10 per attack. At least, that's the case within the limited data emphasized so far. For all I know, that Felid could be sitting just 2 points right or left of some benchmark where the curve is completely skewed within Crawl's system.
That is, if I'm doing and interpreting this right. I don't think it's a simple linear calculation, in any case.