I read Rob's editorial. Anyone else read it? I much enjoyed it, esp. cuz I like me some math.http://www.rpgfan.com/news/2011/1653.html
1) the problem isn't numbers (whether too few or too many). The problem is *always* hidden numbers. Which, if you're really freaking bored, you can approximate for yourself by testing something over and over (making sure you know as many possible factors as you can, esp if against different enemies with different attributes).
2) this idea on reverse-engineering a true hit/miss approximation is something we can take back to sports and their "Fantasy" equivalents. I am reminded of the opening chapters of Stephen Johnson's "Everything Bad Is Good For You," wherein he compares D&D to some of his favorite sports approximation statistics-games. Also, this: http://xkcd.com/904/
(be sure to read alt-text)
3) This statement needs further scrutiny:
Suppose we have a 5% chance to miss. Firing four times, we have a chance of missing all four shots equal to:
0.05^(4) = 6.25 E -6
Needless to say, that's an exceptionally small number. And yet these odds can happen repeatedly in games like Diablo and the aforementioned Fallout 3.
Outside of the very possible "hidden numbers" problem, this observation on Rob's part needs to be weighed heavily against human nature: that is, our ability to blow out of proportion the frequency of times things don't "go our way" compared to how often they do. How *repeatedly* in those games? And is it really so statistically unlikely as what you're expressing? Be sure to listen to the Radiolab episode on Stochasticity (that is, Randomness):http://www.radiolab.org/2009/jun/15/
You flip a coin seven times and get eight heads in a row. OH MY GOSH! CRAZY! The likelihood of this (and, technically, any combination of eight that takes order into account) is 0.5 ^ 8, or 0.00390625. That's still about 200 times as likely as the scenario Rob lays out (.05^4). In any case, the eight in a row is a big deal if that happens on your first eight. You might think the coin is weighted. But out of 100 flips, how likely is it to get eight of the same thing in a row? How about out of 1000 flips?
And how many attack attempts do you make in any given game? 1000? 10000? 50000?
It's just important that we tend to focus on the frustrating aspects, when it feels like the numbers are "against" us.
I know people rant and rave on this when they have accuracy approximations in Strategy RPGs like FFT or Fire Emblem. But that's the thing about randomness: it's *random,* and unless you have a sufficient sample size, you can't very well go about disproving the odds displayed to you.
(I'm a HUGE fan of numbers!)