I always consider that. But there are three points against that. The first is I've looked at what I said, and it's seems pretty clear. That's not conclusive, because I could have missed something. But for me to reconsider that, you'd have to demonstrate where I miscommunicated, not just make a vague claim. Secondly, they didn't misunderstand my arguments in the same way. You made one argument, and they made other arguments. And most importantly is the third: People really don't understand probability well, and it can be challenging to break down their preconceptions. That's the reason why I posted what I posted. I expected some pushback.
I think the problem is more possibly where you are placing emphasis rather than the points themselves.
Yes, a +1 is a big deal at the outliers. But its not a big deal as you drift away from those edges.
But to an optimizer that +1 is a bonus period and they NEEED IT!
Or when I was a playtester on AQW. We had some nuts flipping out over how "unballanced" one class was over the others because its attack was .01 second faster. Even after we pointed out No. It didnt. Those were vauguarities in personal or serverside processing. But no-no. This is game breaking! And on the flip side others were declaring a different class THE BEST WHY TAKE ANY OTHER??? because they believed is was .01 sec faster. And of course it was not either.
And all this and so much worse behaviors been around a long time in tabletop gaming. As said. Some perceive it as an "I WIN!" button.
But at the end of the day to the more obsessive optimizer a +1 is a bonus across the board and thats all that matters. Better if can pump it up to a +2, 3, 4, etc.
I didn't place the emphasis on that, I just used it as an example. Which I expanded upon in later posts, because the people initially responding to my post were misunderstanding the probabilities, and spelling out how 2/1 = 100% by listing the 3 numbers is easier than using 11/10 = 10%, and listing 21 numbers. Making things more confusing for the people I actually responding to because other people might come along and assume the example I used for illustration is the totality of what I'm saying doesn't seem like a good approach. Nor is repeating all of what I said in my first post, in every post. This really seems like a case where you read it superficially and drew the wrong conclusions, and where there wasn't a way for me to communicate it better.
You pretty much nailed my read of their argument... Pat was putting so much emphasis on the outlier effects while ignoring that almost NO modern game (i.e. the types where you're most likely to see "builds" and planned optimization) build their system to have lots of outliers because, frankly, extremely low/high probabilities of success aren't actually that interesting.
Same as above, plus note the 11/10 example I just used above is the middle of the range, and it still amounts to twice the +1 = +5%. That's good illustration that +1 = +5% is the wrong way of thinking.
Also, I think you're wrong about how frequently characters succeed in different games. It's not toward the middle. The study by WotC that Mishihari mentioned a couple posts back was in the back of my head when I wrote my first post, and that matches with my experience with a wide variety of games. Competent characters, which generally include the PCs, don't typically have a 20% chance of success, or even a 50%. Most tend to succeed in the 60-90% range. There's psychological reasons for this: People play games to have fun, and little victories like hitting fairly frequently become a system of positive feedback. Old school D&D tends to be a little bit of an outlier, because things like to hit rolls and saves can vary more, based on level. In low level games, the chance to hit or save can be anywhere from 5% to 50%. The reward here is a little different, with low level games feeling very hard or whiffy, but that gives a feeling of accomplishment to the players as characters advance and become more reliably successful at individual rolls. It's more of a delayed reward, which supports the themes of a game that focuses on leveling up rather than starting characters as full-fledged heroes.
Let's look at the full range, on the d20 spectrum, using some more broadly illustrative examples. (Incidentally, this is in line with where I hoped the discussion would go after my initial post, but the conversation got sidetracked a bit because people were misunderstanding how probability works, so I ended up repeating my example in a couple different ways, leading to the confusion you felt.)
Succeed on a / What a +1 bonus means to your chance of success
20: +100% (doubles it, since you now succeed on a 19 or 20, not just a 20)
16+: +20%
11+: +10%
6+: +7%
2+: +5% (chance of success increases from 2-20 to 1-20, or 20/19)
If we think of this in the long term, if you only succeed on a 20, a +1 bonus means you succeed twice as often, over the course of a campaign (well, as long as the conditions hold). Even a +1 bonus to hit when your chance to hit is 50% (11+) means you do an extra 10% damage, over time. The +5% in the last line of the table (2+) is rounded down (from 5.26%), so even when your starting chance of success is high, a +1 bonus means more than 5%, which should clearly show that +1 = +5% is always the wrong way of thinking about it.
And note this is focused on success. If we focus on failure and penalties, which is important when it's about avoiding a negative results (e.g. saves), then this is what happens:
Succeed on a (fail on a) / What a -1 penalty means to your chance of failure
20 (19-): +5% (chance of failure increases from 2-20 to 1-20, or 20/19)
16+ (15-): +7%
11+ (10-): +10%
6+ (5-): +20%
2+ (1): +100% (doubles it, since you now fail on a 1 or 2, not just a 1)
The table flips. That means there's always a way of looking at it where a +1 bonus is equal to +10% or more, and outliers become twice as common.
Though if you play in a game where the PCs have a high chance of positive results, and a low chance of negative results (to hit and saves, for instance), those will tend to fall in the 5% to 10% range. As I mentioned above, old school D&D is a notable exception. Another is getting hit by a monster, in most games (even if the PCs have a high chance to hit, the monsters tend to have a high chance to hit as well, which is a negative results for the PCs).