Tuesday, June 29, 2010

Truth and Beauty

Read this blog from the first post up or it won't make much sense.

It's said that Maxwell knew his equations for light were correct when they were mathematically beautiful--and that he knew something was wrong when they were ugly and kludgy. While I love the sentiment I'm not sure it applies to reality and I'm not optimistic enough to think it'll always apply to game design (of all things). However, today, the Truth = Beauty theory is doing pretty well. Here's why:

Attack Strategies
As you've seen from previous entries we are looking at questions of how a character with a X AP attack might add a Y AP attack that has an unusual rate of fire. An example would like like this:

  • 20 AP Standard Power Blast (25 IMP Damage). Fires twice a Round every Round.
  • 4 AP Charge-Up Power Blast (30 IMP Damage). Fires twice a Round but only on odd numbered Rounds.
The "most obvious" way to do that was to declare that a 4 AP investment in a Charge-Up-Blast would yield 30 points of damage. Unfortunately, that was not the case. Mathematically, using the simulator, we have determined that a 4 AP investment in a Charge-Up-Blast is worth more like 13 IMP damage, not 30: if the character designer said "Screw the standard blast, I'm puttin' all my points into a charge up blast!" it would deal something like 180 IMP damage and the character would be way, way too good.

So we had a problem: we liked the way that some unusual rates of fire interacted with standard attacks but we could not come up with a "cost per point of damage" that worked out.

Until last night.

Staring At The Numbers
Before I can go to the solution, let me explain how the cost-per-point-of-damage thing is actually working out. It's more complex than you'd probably think. In order to determine how much "one point" of ranged, standard-fire, Impact Damage was worth I took 3 Herds (16 AP, 32 AP, and 64 AP) and spent half the AP of my test characters on a ranged blast.

I then increased or decreased the amount of damage it did (from what it was "supposed to do" based on our testing with the 'Balanced Herds') until I had my group of 4 test characters winning an average of 50% of their battles with the same Power Blast. This gave me this result:

These are the numbers that came in around 50%: when I took an average of the damages vs. the costs (the AP cost for each blast was half the Herd Cost) it came out to 1 AP = 1.40 Ranged, Standard Impact Damage. This was handy. It was also wrong.

Using that (average) value and plugging in the actual AP's, for example, the 8 AP blast (the 16 AP Herd) would do 8 x 1.40  = 11.2 (rounds to 11) Impact Damage. That's 3pts under what tested at 50%. In the simulator a 16 AP Blaster armed with an 11 IMP damage Blast won under 40% of the time. If a player went with that strategy they'd be screwed. On the other end of the spectrum the 64 AP character (32 AP invested in the attack) wound up doing 44 Impact Damage (32 AP x 1.40 = 44 Impact Damage) instead of the slightly-too-high-anyway 36 Impact. That meant that at the upper end of the point scale Power Blast was a freakin' great deal.

I wasn't happy with that (never mind that at the middle of the road the 32 AP character would wind up blasting for 22 IMP damage instead of 21 which was close enough). But there didn't seem to be much of a solution. I did, however, wonder what the heck was up with that.

What Was Up With That?
Some examination and some thinking led me to this: a JAGS character is a combination of "normal guy" built with Character Points (CP) and a suite of "special" abilities bought with Archetype Points (AP). The 16 AP character gets a normal guy's worth of toughness (he starts at 14 Damage Points and a 12 Constitution--our guestimate as to what a PC-build would be like) for 0 AP.

Now, all of the other Herd characters get that too--but at the lower-AP levels the in-the-door investment has to overcome the 0 AP's worth of toughness the basic character has. That means that in order for the 16 AP guy to win 50% of his battles with a blast weapon he has to be doing at least enough damage to fairly hurt a normal man who also has some extra armor or a force field or whatever on top of that.

This "free normal guy" effect means that the first few points spent on Power Blast have to give you more damage "for the money" than every AP spent thereafter (once you are dominating the "normal guy"). This is why the damage-per-AP investment tapers off after a while and if you still keep paying the average price (1 AP = 1.40 IMP Damage) it eventually becomes a really, really great investment: that cost is factored partially (1/3 of its value) from that starting point).

So What's The Solution
I decided that a potential--and reasonably palatable--solution was to simply give you more damage for the first 8 AP invested and then give you a flat rate for each 8 AP after that. How'd I decide that? Well, 8 AP is a "magical" value in JAGS. It's how we think of "levels" of character (so a 32 AP character is, to our thinking, Level 4). We've costed things in terms of 8 AP and it's worked elegantly for us.

I did some analysis and came up with this chart:

This is complex but bear with me a moment. Down the left are different "types" of Power Blast. The first one is the Standard Blast (fire every round for 5 REA). Looking down you can see things like Cool-1 (that means it can fire every other round, starting with the first round) and Charge Up-1 (meaning it can fire every other round starting with the second round). There's other stuff too and that gets even more complex (Breath is what we factor for Fantasy-beast breath weapons).

The Orange Level 1 column is what our 8 AP tested at: that's how much damage the 16 AP character (with 8 of those AP invested in Power Blast) needed to win about 50% of their battles with the 16 AP Herd.

The Orange +1 Level Column is how much extra damage was added to bring the character to about 50% victory against the 32 AP Herd. 

The Orange Delta 64 Column is what happened when I added the +1 Level amount of damage twice more and compared that total-damage to the 50% win value against the 64 AP Herd.

So for Blast (Standard) the 8 AP investment scored an awesome 14 IMP, the next 8 AP would bring it up to 21 IMP damage, and two more levels (16 more AP) invested would give us 35 Impact Damage where as the value my tests said was good came out to 36. That was just about perfect!

I then proceeded to test everything else I'd run and I got the purple column: I adjusted the +1 Level number slightly so that when I added it 3 more times to the Level 1 number I got as close to the 36 AP number as possible. I was able to get very close. Elegant!

So Then What?
Well, I'd sort of figured this out yesterday and was still testing it when I re-examined the idea of having an "extra damage" blast like the one discussed at the start of this entry. I realized that the extra damage (even if it was 1x every other round) was effectively ADDING to the standard blast you already brought.

What, I thought, if I just let you buy +1 Level for some other type of Power Blast. This would mean that a character with 32 AP to  spend on an attack could go to that list above (using the Purple Numbers) and go: "Hmmm ... I'll spend 24 AP on a Standard Blast. That'll get me 14 (Level 1) + 7 + 7 = 28 Impact Damage every round as many times as I have REA to fire it (usually twice) and THEN I can spend my remaining 8 AP on ... let's see ... a Charge Up-2 Blast. That 'power-blast' will take me two Rounds to 'charge up' before I can fire it but it'll hit for (checks table) an extra 14 Impact Damage! Hey, I'll take that."

Testing proved this to be workable ("m still testing but it looks good).

That's elegant.

Beauty & Truth!


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