Champions Online Developer Diary - Systems Balancing, Pt 2.

Coming back for a second week of numbers crunching in Champions Online, Brian Urbanek, Systems Designer takes last week's discussion a bit further. Brian delves into combat factors, including energy cost, damage scaling, and survival. Learn the numbers behind your heroes in Mr. Urbanek's Systems Balancing, Part 2.
Damage (per second) only has meaning with relation to a player's ability to endure that damage. 400 damage per second per attack on average is amazingly powerful if everyone has 10 hit points, and kinda pathetic if everyone has ten million. This leads us to the single most important factor you can ever consider when designing a game, the factor to which all others must bow: time.

by Brian Urbanek style="font-style: italic;">
Systems Designer style="font-style: italic;">
Cryptic Studios

Last time, I talked about the art of baselines, and the expectations of
player progression. Let's lunge sideways now over to combat factors.
Don't worry; it'll all come together eventually. At the top of the last
article, I said that twenty points of energy equals twenty five points
of damage. Well. That's all well and true and accurate, but as I'm
hoping you're starting to see, it becomes a lot more complicated than

First, energy costs. Your energy pool doesn't grow as you level up
(except for your first few levels), it grows as you get talents or gear
that raise your Endurance stat. Now, in general, that means that yes,
it is going to raise as you level, but not really at any rate that can
be easily predicted, and many players will never choose to raise it at
all. After all, we want the choice to raise your Endurance to be an
interesting one, and for a choice to be interesting, it needs to offer
exciting options, but not so good that it's obviously better than the
alternatives, but also not obviously worse than those other options.
The result of that is pretty simple: no power in the game can (or, at
least, none SHOULD...) have an energy cost over 100, and energy costs
don't increase as you level up.

That being said, we already established some other baseline assumptions
that we need to take into account; specifically, players should find
combat against lower level enemies very easy, and very dangerous
against higher level enemies. There are other ways to do this, but we
chose the tried and true method of more hit points and bigger damage

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hspace="3">First, damage. Damage scales in basically the same way as
player statistics; that is, an inflationary model with a 1% inflation
factor. There are other ways we could have done it, but by having
matching inflation factors, it makes a lot of other calculations much,
much easier and cleaner to work with. When you start having lots of
closely linked baselines growing and shrinking on different curves,
things can get very out of hand very quickly.

So, okay, now we have a raw damage base that scales from 25 to 250. I
picked 30% as the amount of bonus you can get from your super stats at
"target" value because it generated enough swing to be really visible
and meaningful, but not so much that if you were a bit above or below
the expected stat values you wouldn't be able to play. Two super stats
means 60% net bonus damage, which at level 40, works out to a nice
round happy 400.

Of course, damage (per second) only has meaning with relation to a
player's ability to endure that damage. 400 damage per second per
attack on average is amazingly powerful if everyone has 10 hit points,
and kinda pathetic if everyone has ten million. This leads us to the
single most important factor you can ever consider when designing a
game, the factor to which all others must bow: time.

In the case of Champions, the original vision was for "fast and
furious" combat. After much analysis and scientific inquiry, scenes of
people peering through microscopes, experiments with supercoliders,
orbital vehicles, and some time on the Hubble telescope, we eventually
said "how about twenty seconds?", and lo, we had a baseline.

So, twenty seconds of survival versus an enemy (or enemies) that
matched our average player in combat yields 8000 hp. Great! We're done!
Wasn't that easy?

Except it's nowhere near that easy.

First, we have to figure in critical hits. That adds a few percent to
the damage. Next is the fact that players can't do constant DPS in
Champions; they run out of energy and have to build it back up, which
reduces their overall DPS because energy building attacks only do about
30% of target DPS. Then there is the fact that we want players to have
a little bit of defense in their gear, which means they don't need
quite as many hit points. And, of course, there is the built in small
amount of dodge, factor in X, divide by Y, subtract the price of rice
in China...  and it all works out to about 5,787.656 hp as the
target value at level 40 by which our average player will survive for
exactly 20.0 seconds.

Well, that's a very precise number, and it's based on perfectly good
math. The problem is, the assumptions that fed into that math are
subject to error. A lot of error. An amazing amount of error. How much
defense will players have? Did they get a passive defense, or not? Have
they got any dodge value on their gear? What Role are they using...
etc, etc.

So, we have a number that we want to know with a high degree of
precision, and we have a lot of numbers feeding into itÂ… which we have
very, very low confidence in. But, because that's not quite complicated
enough, let's toss in Constitution. Constitution raises your hit points
(that makes sense, right?) and everybody has at least some.
Unfortunately, not everyone has the same amount; in fact players could
have as little as ten or as much as 200+. Further, the value of a hit
point isn't always the same. 100 more hit points is good; 100 more hit
points when you have 20% damage reduction is better. 100 hit points
when you have 80% damage reduction is really, REALLY good. In fact,
it's just about exactly as good as giving a guy with no damage
reduction at all 500 points. So, how much value do we want to really
give to Constitution?

Well, fortunately, there's another angle that needs to be considered
which actually simplifies the whole issue, which is stat equality. See,
I already decided that your stats should get you "about" 60% bonus
damage. Well, that's a percent, but it's also a flat number. Like I
said; it raises your damage per second from 250 to 400 at level 40. So,
it's not just 60%, it's also +150 points per second. Or, looked at
another way, it's roughly .4 points of damage per second per point of
stat (slightly different at every level, going up slightly as you level
up.) Well, .41 (amortized average) * 20 seconds * "defense is more
boring than offense" bonus / assumed armor = a bit over 9 hit points
per point of constitution, round up to 10.

Push that through the other equations, and we get a value where players
get between 15% - 35% of their hit points from their Constitution. Not
as much of the total as I'd really have liked, but it keeps Con very
nicely in line with all of the other stats as well as compensating for
the number of unknowns in how many hit points players actually have.

Well, I have about seventeen more chapters that I could write about all
of this, but I'm already about three times my target word count, so
I'll just cut it off here with a big TO BE CONTINUED!

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