Pacing Specialists, part 1

Now that I’ve looked at how focused fire affects combats, I’d like to look at offense and defense specialists. After all, some players may prefer the fast paced but riskier offensive style while others prefer a more controlled defensive style.

1 on 1

In simple 1 on 1 match ups, it’s relatively easy to balance the styles out. Just work from “time to defeat = health / rate of damage taken” and make time to defeat equal for both sides. If we throw in a balanced unit as the baseline, that gives us:

Time to Defeat balanced [TtDb] = Time to Defeat specialist [TtDs]
balanced health [Hb] / balanced rate of damage taken [DTRb] = specialist health [Hs] / specialist rate of damage taken [DTRs]

Since all damage taken is from a single opponent, we get:
Hb / specialist damage rate [DRs] = Hs / balanced damage rate [DRb]
Hb * DRb = Hs * DRb

That means that health must be the inverse of damage rate and vice versa. For example, doubling health will only match the balances rates if we halve the damage. By the same token, if we double the damage of a given character we should halve the heath.

The numbers work well enough in one on one matches. However, things get more complicated with groups.

Scatter Fire Groups

If you’ve got a group where everyone favors the same pacing, conflicts without focused fire work out much like one on one battles. You can even get similar results if both sides share a similar distribution of specialists. Where things get messy is where you look at a group of mixed specialists vs a group of balanced character.

The problem breaks down as follows.

  • Your offense specialist will be the first to go due to their lower health.
  • In an all offense group this wouldn’t be an issue as you damage would be high enough to drop your opponents by the time your attackers start dropping. However, in a mixed group, you damage rate will be lower due to more defensive members.
  • This means by the time you offensive specialists start dropping, the enemy will still have some health left.
  • The only ones left to take out that last bit of health will be defense specialist, who will already be damaged and fewer in number than those they’re trying to take out.

2 on 2 test case

Let’s say we’ve got a pair of 2 man teams with similar stats. Now let’s give our first team an offensive specialist who trades double damage for half health.

The added damage of the offense specialist raises it’s team’s damage rate to 3 (1 balanced + 2 from specialist), but that specialist will drop in half of a tic (enemy damage rate of 2 total becomes 1 per member, half health / 1 damage per tic = half tick life expectancy). Meanwhile it would take 2/3rds of a tic for the mixed team to drop their more uniform counterparts.

So at half a tic, the mixed team is down to member at half health. Meanwhile, the uniform team has both members, but each is down to (3 damage rate * 0.5 tics = 1.5 damage inflicted, divided over 2 targets for 0.75 damage each).

Both sides actually have just as much health left total (0.5 on 1 vs 2 at 0.25). However, the uniform team still has 2 members while the mixed team only has 1. That leaves them with half their remaining health (1/8th) by the time the last mixed team member drops.

This doesn’t seem to get any better for larger offensive values. In fact, it looks like the damage inflicted before the offensive addition comes into play scales as follows:
damage inflicted [DI] = team damage rate [DRt] * time to offensive defeat [TtDo]
DI = (1 + offensive damage rate [DRo]) * offensive health [Ho] / rate offensive specialist takes damage [DTRo]
DI = (1 + DRo) * (1 / DRo) / (enemy team damage rate [DRet] / number of allies [Na])
DI = (1 + DRo) / (DRo * number of enemies [Ne] / Na)
DI = (1 + DRo) / (DRo * 2 / 2)
DI = (1 + DRo) / DRo

So the stronger the offense’s damage rate, the less the team can actually inflict before their heavy hitters drop. At that point, damage inflicted changes to:
damage inflicted [DI] = team damage rate [DRt] * time to offensive defeat [TtDo]
DI = 1 * (team health [Ht] / enemy team damage rate [DRet])
DI = number of allies [Na] * average ally health [Ha] / number of enemies [Ne]

Since damage was evenly distributed the health loss of survivor will equal the total health of the members who just dropped.
DI = 1 * (balanced health [Hb] – offense health [Ho]) / 2
DI = (1 – Ho) / 2
DI = (1 – 1 / offense damage rate [DRo]) / 2
DI = 1/2 – 1 / (2 * DRo)

Combining these gives us:
DI = damage in first phase [DI1] + damage in second phase [DI2]
DI = ((1 + DRo) / DRo) + (1/2 – 1 / (2 * DRo))
DI = 0.5 + (1 + DRo) / DRo – 1 / (2 * DRo)

That means as the offense’s damage rate approaches infinity:
DI = 0.5 + (1 + Inf) / Inf – 1 / (2 * Inf)
DI = 0.5 + 1 + 0
DI = 1.5

That works out to 75% the health loss inflicted by a balanced group.

In short, the same balancing that works for one on one conflicts does not work so well for mixed group battles. The powerful but fragile “glass cannon” types drop out too quickly and leave the enemy with a numerical advantage.

Published in: on June 8, 2011 at 9:21 pm  Leave a Comment  
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