Here is a typical situation out of a book or film: protagonist and antognist are fairly evenly matched, or the antagonist is just slightly better. Then the protagonist gets either a little more inspiration or a shade more training, and suddenly has enough of an edge to win.
To translate into HQ, the protagonist finds another augment or spends an hp or two. Intuitevely, getting that small edge in a tight contest should be a big thing. THIS time the fight is defend your sister's honor, and that should make all the difference.
Now let's look at the numbers. If you calculate the percentage chance of A winning minus the percentage chance of B winning, you'll get what I call DeltaW (difference in wins). This is not looking at the quality of the wins, and obviously is only applicable to simple contests). If they are tied in rating, they each win 47.5% of the time (5% are ties), so deltaW = 47.5-47.5=0.
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.
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.
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.
In other words, an augment actually matters less when your scores are close than when they are far apart.
Somehow that just doesn't feel right for the source material.
Unfortunately I don't actually have a solution for it. So it is pretty much, anyone have any thoughts?
-Ed
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