I wanted to get back to this one; sorry it took so long.
>From: "Bryan" <bethexton_at_...>
>
>If there is a difference X between their scores, and there is no
>mastery advantage between them, then deltaW=((X^2)/4) % So if they
>both had a 13, and one augments by 2 to 15, then X=2, and deltaW=1%.
>That is right, this time, when it is for the honour of your sister,
>you'll win 1% more of the time than before.
You're double counting. That is, you're counting both the one side going up, and the other side going down. Meaning that as the disparity between ability levels grow, and more you're going to see a difference in the second order derivative (Delta Delta, if you will).
That said, there is a disparity in the effect, true. But...
>Of course, if it was previously 17 to 6, and the 6 goes to 8, the
>deltaW for the 17 goes from 30% to 20%, so it can have a substantial
>effect.
...the difference in the augmentor's percent chance to win, for example, is only about 4% higher for the second case just above than the first.
But let's continue on using your method, just to illustrate something else important.
>What if there is a mastery difference? I no longer have the file
>where I worked out hte exact equation, but it is something like
>(X-1)(x-2) +(x-2)(x-3). Which still pretty much scales in proportion
>to X^2.
Actually the curve goes back and forth in terms of that second order derivative. That is, the change sometimes goes up in size, and sometimes down, depending on the precise levels being compared.
>In other words, an augment actually matters less when your scores are
>close than when they are far apart.
Well, for the first margin, yes. But what about your second augment? Rather, what if instead of augmenting just that +2, you augment +10? Now that +2 is just pushing other augments farther out on the scale. And what you'll find is that, again, the margins for each number keep on changing. Meaning that you can get an average separation for all of the augments, but that each of them is providing a variable amount of delta. Meaning that the +2 could be part of a package that ends up actually increasing the delta by a higher percentage for close scores than for scores far apart. This is imminently apparent if you take the example of the 6 vs 17 augmenting +11 vs the 13 vs 13 augmenting 11. Here's the deltas:
6 v 17 = Delta 30.25%
17 v 17 = Delta 0%
Delta Delta = 30.25%
13 v 13 = Delta 0%
4W v 13 = Delta 37.5%
Delta Delta = 37.5%
The augment in that case makes more difference when the abilities are close together. What's more, the effects that these will have relate to where they are in terms of the mastery cycle (and whether a mastery is passed with the augments).
But, know what? This is all moot.
>Somehow that just doesn't feel right for the source material.
I could actually argue that, in fact, it is the right feel for the source material. That small things that the underdog does have large effects on their chances to win, but that when things are close, small things mean small effects. More importantly, actually, the key thing is that all of these marginal differences are actuall pretty small. Increasing your chance to win by less than a percent for a +2 is still statistically insignificant if it's raised to a 4.75%. That is, the player won't "feel" anything at all, either way, in rolling. Especially since they're only going to roll once for the contest. They wouldn't feel it even if they rolled 1000 times. But rolling once? They'll only "feel" it, in fact if they go, "Hey, look at that, the +2 made it a victory."
But even more tellingly, most people besides you and I, Bryan, aren't going to do the math to figure out the odds of success, much less the "Delta" for an augment. Players know the important thing... that if you augment it increases your chances of success. In fact, the fact that they can't really feel a whole lot of effect for small augments is a good thing. If they did, then large augments (where one can really feel the difference) would be unmanageable. Basically this makes large augments viable in play.
Which, I dunno, is something that I seek. I want loads of augments.
The system incentivizes the right things, and produces the correct results. The curve on the dice is funky, yeah. But the only effect I've ever seen that have is people posting about how funky it is in fora and mailing lists. Hasn't had any effect on play at all that I've seen.
In fact, in other discussions on this topic, if you really study the curves, you'll find this interesting effect where the chances of success actually vary by differing amounts for different levels of ability disparity based on where the abilities are in the Mastery cycle. Meaning, essentially, that those who are new to a level of mastery have a more wildly varying level of differences than those who are high in the mastery. That is a "newcomer" to the "journeyman" level of 1W has greater variability in their chances to win against an opponent a fixed number of levels above than does somebody with 20M.
I have fun interpreting this as the person who has achieved a level of mastery being suddenly introduced to a whole new level of techniques and such... information that makes them more likely to succeed, generally, but which, since not "mastered" yet, makes their performance more variable. Wheras somebody who's been in the mastery level a long time has not learned anythuing new, but has mastered those techniques, so their performance is very consistent.
But that's, again, not something you can "feel" in play. Just my own observations about the curve. What I mean to impart is that any such "feel" is really just in our heads, and you can change that "feel" simply by changing your perspective a little.
When I started playing HQ, I noticed that funky curve, and even changed how resolution works for a while thinking that I could "fix" it. Turns out that I just didn't appreciate the system and how it works. I recall me having a conversation with Ron Edwards, which I'll paraphrase:
Mike: "I fixed HQ. Before a small difference in abilities made little
difference to the chances of success. By making the system oppositionally
roll-over, the ability differences are more substantial."
Ron: "How is that an improvement?"
Mike: "Well, players can feel the differences more. They'll feel like their
abilities matter more."
Ron: "So then players will be able to assume that a lower marginal
difference in ability scores means a more certain liklihood of success than
with the original system?"
Mike (It dawns on him): "Oh, yeah. I forgot. That encourages players to play
gamey, because they feel that increasing their odds is about finding
advantage for their characters, and not really about just altering the odds
slightly as a reward for good play. Augmenting in this case, being fun
display of character. Like in Sorcerer where the odds are always heavily
skewed towards the center. That's a positive effect for the sort of game I
want to run, isn't it."
Ron: "Yup."
Mike: "I guess my fix is a break."
I totally sympathize with folks who find the HQ curve a tad odd. But all I can say is that, given some time, you may find that it's a work of genius, too. No, it's not like other curves... it's a lot better.
Mike
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