Thursday, May 5, 2011

Getting a Larger Can ...

They say when you open a can of worms the only way to close it is to get a larger can. I started analysis of what was going on with the TAP stuff with respect to Fast Company and came across an unpleasant realization: the % of points an ability is worth usually varies as well.

Thus +8 REA balances at 10 AP for 16 AP characters, 16 AP for 32 AP characters, and 24 AP for 64 AP characters.

What I'd done was take the values and average them to produce a single double-digit decimal number (.51 for +8 REA). You'd multiply that by your Total AP and get the cost for that ability at whatever AP value your character was.

But that was only (clearly) an estimation.

When I tried looking at L3 and L4 Fast Co characters (evaluated at 64 and around 99 AP respectively) I discovered something: When I used the actual tested values the 64 AP character (L3 Fast Co) added up perfectly. The 99 AP character added up to 90 AP--about 10% off.

That was too close for comfort.

So what I'm doing now is going back and using the real tested values in the table so that the % of your Total AP that an ability costs shifts along with your Total AP (these abilities are a larger fraction of your AP when you are a 16 AP character than if you are a 64 AP character).

This technique seems to produce better numbers--of course time (and further testing) will tell--but here's a few things it does improve on and one place it could go very, very wrong:

  • Improvement: We always knew there was some kind of "minimum cost" for these abilities (+8 REA doesn't cost 1 AP if you are built with 4 APs no matter what the math says). While this doesn't completely fix that problem it does give almost all of these abilities a higher point cost earlier on. This mimics what we see with attack powers (in reverse, however) when they give you more damage in the first levels. Still, having the cost be more balanced for lower point totals is nice.
  • Averaging: I'm not going to run a test with every AP level from 1 to 64 (or infinity) so I have to pick my battles. I'm averaging the test values for the 8 AP Levels between 16, 32, and 64. This, of course, re-introduces a margin of error but I think it's a much smaller one.
The Potential Problem
Because the TAP multiplier goes down as your AP value goes up there is a possibility that a higher level will cost less than a lower level. If the math is right this, I think, should not happen--but if there's something wrong, it could. Thankfully: for the testing I've done that is not the case. Although the 64 AP multipliers are almost across the board less than the 16 AP multipliers for the same ability the gradient is always correct (there's one case--with a defect: SLOW where this isn't the case ... and I need to look at that more closely).

For now, though, this is producing sane numbers. It just means more work.


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