# 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

Systems Designer

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 that.

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 numbers.

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!

Systems Designer

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 that.

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 numbers.

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!