Capture Mechanics

[Malorn]

This is my attempt to model the capture mechanics described by Higby from the AMAA, the PAX East Q&A, and bits of information going back to last July.

Before I comment on the mechanics I want to lay out current understanding of how it works and give a somewhat close approximation to the system. I am not proposing anything in this original post - I am only trying to model & explain the capture mechanics as we know them.

Quite a lot of math here, so if you don't like that move along to the next thread.



Ticket System & Adjacent Territory Bonus

From what we know, the capture system is like Battlefield conquest maps only inverted, so instead of losing tickets we are accumulating tickets until we reach a point where the base is captured. Adjacent territory augments the ticket pool by granting bonus starting tickets.

Originally Posted by Higby

The way base capture works right now in our internal play tests is capturing a base is almost like winning a conquest map in a Battle Field type game; there are several control nodes you have to hold, and holding the majority of them means you're gaining control of the base.

If you own a lot of adjacent territory then you have a bonus to the beginning your bar of how much you need before you fully capture that thing.

Higby also said this back in July, which is why I made 950 base tickets and calibrated against a 30-minute hack time:

Originally Posted by Higby

The capturing system - and this is going really deep into some of the gameplay stuff - but the way it works is based on your adjacent territory that your empire owns you get bonuses to being able to capture the territory that is connected to that. We have a system of adjacency, so the front line is constantly shifting and constantly evolving based on territory that's being captured. And you will be able to capture any piece of territory on the map but you get significant bonuses to capturing ones that are adjacent to the territory that you already control. So back-hacking is still something someone could go do. If I want to I can go to the middle of your territory and capture this piece of territory. It might take me 30 minutes to capture this one region and then when your empire goes back there and re-captures it might only take them 30 seconds.

Assuming 1000 tickets to capture a base as higby indicated (number doesn't actually matter, it'll scale). You get bonus tickets (and the other empires get the same), based on adjacent territory.

B = Maximum bonus amount. I'll assume 950 because it fits the estimates we've seen Higby make for extreme cases.
A = Adjacent edges on the territory that are friendly
T = Total capturable edges on the territory
S = Starting tickets

S = B * A / T

For B = 950 the formula becomes

S = 950 * A / T

(most bases have 18 edges, so using that for T)

Extreme cases:
For A = 0, S = 0 (capture of a facility that you have no territory around)
For A = 18, S = 950 (recap of facility deep behind your lines that someone capped)

Even case:
For A = 9, S = 475 (this is if control is split 50/50, like a border territory)

Moderately Uneven case:
For A = 5, S = 264 (this would be if you had a small amount of territory)
For A = 13, S = 686 (this is the inverse of the one above it)

Higby mentioned that it might take up to 30 minutes to capture a base without any adjacent territory, so based on the estimate that 0 -> 1000 takes approximately 30 minutes if you hold all capture points you can calculate a tickets/second capture rate. To keep the math simple, I'm going to round to .6 tickets / second, which translates to 36 tickets a minute, or 27.78 minutes to capture a facility, assuming you hold all 7 tickets and have 0 starting tickets. The rate of capture is approximately .6 tickets / second, for all 7 capture points, or .0857 tickets / second per capture point, assuming 7 capture points (rate might be faster for smaller numbers of capture points to keep this capture mechanic consistent).

We can thus calculate capture scenarios, which I detail below. Note that this scales to any size territory, not just facilities. Smaller territories have fewer edges, but the formulas above still work and can make for consistent capture experiences, though they may have fewer control nodes making the captures go more smoothly.



Back Hack Scenario

For the Back-hack scenario, the attacker has 0 adjacent territory edges, and the defender has all 18. Higby said this scenario played out like...

Originally Posted by Higby

Well not preventing back-hacking, but kinda disincentivizing them, you could go capture it but the enemy is gonna come back and re-secure super fast cause they still own all the adjacent territory.

Attacker starts at S = 0
Defender starts at S = 950

The defender only needs to gain 50 tickets to stop the capture attempt, while the attacker must gain many times that, so by simple calculation it will be difficult to capture the base because the attackers must not allow any control points to defenders

At S = 0, as established above, the time for the attackers to capture the facility is 27.78 minutes, assuming they have all control points.

At S = 950, it only takes defenders 1.38 minutes to capture the facility if they have all points. So a ghost-hack is easy to stop.

This is consistent with Higby's statement:

Originally Posted by Higby

So if I'm a defender at a base I only really have to hold maybe two control nodes if I own the adjacent territory because I have such a big head start that you can’t really keep up, unless you just wipe us out completely and hold every single control node then eventually you'll do it.

The attackers must also maintain all control points for most of the hack attempt. Losing even one for a prolonged period of time will allow the defender tickets to reach 1000 and stop the capture. Not catching all the points simultaneously can also cause attackers to lose the base without any defenders even being there, since we can assume the tickets will start accumulating after the first node is captured.

This is also roughly the number that Higby gave for this scenario back in July, which was 30 minutes to capture a behind-the-lines territory and 30 seconds to take it back. I'm a little off from there but I think that's within reasonable rounding. That's the worst, case, now lets look at a hotly contested base where both sides have the same amount of territory.



Hotly Contested Facility

For a hotly contested facility, A = 9, which is half of the 18. This is true for both sides. This is a scenario of an essentially even match-up, territory-wise.

A = 9, S = 475, so each side must accumulate 525 tickets.

In the best-case scenario, when one side controls all 7 control nodes, the capture will take 875 seconds, or 14.6 minutes.

But in a hotly contested base, it is unlikely that you would control 7 nodes, so lets look at the worst-case scenario when you only have 4/7 control points. That woudl be a capture rate of .3428 tickets/sec, which means the capture takes 1531 seconds, or 25.5 minutes.

(Note: this is is not strictly the worst-case scenario, as the worst-case would be not having any control points for a time and then regaining them which could extend the capture beyond 25 minutes, but I think as a hotly contested base scenario goes this is fairly close).

This is roughly the same amount of time that it took to capture a hot base in PS1 when you factor in the pre-hack time + 15 minute hack, although this method assumes the base is hotly contested the entire capture time, which is unlikely.

A typical base capture therefore might take about 15-20 minutes with this model, with a lower bound of 14.6 and an upper bound of 25.5, depending on level of resistance. This is consistent with Higby's model statement here:

Originally Posted by Higby

And this is a process that takes 15-20 minutes from start to finish unless you have every single adjacent territory and you capture the control nodes immediately

I modeled the "every single adjacent territory" case above in the Back Hack scenario.

You can then look at other in-between scenarios using the same math, but I don't quite find those as interesting. The interesting cases are the even-territory scenario and the horribly lopsided territory scenario.

For normal territories, we can just assume only one control point, with that one control point generating .6 tickets / second. If we assume same rules apply as facility captures, we can see territory will have roughly the same capture times.

I don't expect this model is exact by any means, but I think it's close and fits the data we have thus far been given.


Commentary

Things which I like about this system

• Easy to balance.
  There's only a few numbers to tweak to get the desired behavior. Just as I defined a target time to capture a base at S = 0, the devs can do the same. They can use this sort of modeling to get the exact capture times they want to see, just by solving simple equations.
  
  
• Easy to Understand.
  Simplicity is good for capture mechanics so new players / all players can understand what they need to do to optimize a capture. If it is complex then it might be mysterious to many players who might then make really poor strategic choices thinking they are doing the right thing.
  
  
• Easily Extensible.
  They can add more factors in quite easily, such as the starting ticket formula could be augmented by a variety of other factors without throwing the rest of the capture mechanic out of balance. They could also augment the capture rate by number of held control nodes. It doesn't have to be linear, but I think it's best to keep it linear in order to keep the capture predictible and easy to understand. Another extensibility point is that they could dynamically adjust the bonuses while the capture is underway if territory changes hands during the capture.
  
  
• Every capture/resecure is discrete.
  Just like PS1 everything gets "hacked" and it takes positive action by the defenders to go take it back and stop it. This makes it easy to assign capture & resecure XP/Resources.

Things I don't like about the system

• Hack strength does not appear to be proportional to hack time.
  So triggering a hack on a base that is well under control still might force defenders to sit around for a long time if the neighboring territory isn't owned. Clearly defenders have a lot of time to respond to a behind-the-lines capture attempt and will have an easy time re-capturing, but for the hotly contested base sceanrio it seems like it would be easy to quagmire a base by constantly triggering a ghost-hack capture attempt on a front-line territory. This would force defenders to stick around for the full duration of the resecure, while in PS1 the resecure would be a quick hack.
  
  
• Doesn't appear to be dynamic to surrounding territory changes
  This might not be a real concern and it could be adjusted, but since the starting tickets are determined by adjacent territories it leaves the question open about how changes to adjacent territories affect an in-progress hack. As mentioned in the pros sections it would be fairly easy for them to adjust the starting ticket count appropriately if neighboring territories changed hands while the capture was underway.
  
  
• What constitutes a successful capture is arbitrary.
  What I mean by this is that if we are in a hot base contested by multiple teams, we might gradually gain control and at some mysterious point our control bar fills and we capture the base, but the enemy is still there and still in control of one or more control points. It seems likely that the hack process would start all over again, possibly leading to multiple re-secures before we finally boot the enemy out. That might be OK in that situation as people attending the fight would get periodic reward boosts from the cap rather than one big long fight with a reward at the very end. It seems like an awkward scenario to me. Could also be due to not having all the details of the system, so I won't press too hard on this.

Hopefully as we learn more some of the concerns might vanish and the model's accuracy can be further improved.

I'd really like to know how captures are initiated, it might help mitigate one of my concerns. In the absence of confirmation I assume that captures are initiated simply by someone capturing at least one control node in a territory/facility.

Edit: Higby confirmed via Twitter earlier that capturing any node initiates the capture, as assumed above. Unfortunately I believe this means I still have all of the listed concerns for the system.

I also have some ideas and formulas for a Tug-of-War model that I may post later in this thread.