Powerplay Overhead: Formulas and a discussion

[aspiringexpatriate]

Ever since Cycle 2, Power Play has used an Overhead formula, which the renowned veterans like John Casey spent weeks dissecting and evaluating. Originally, Overhead had one calculation which essentially instigated a brick wall for every Power around 700 exploited systems. At that point, the Overhead costs would exceed almost all probable incomes of Command Capital. Densely populated regions of the galaxy could squeak out more income than others, thus pushing the brick wall for Powers like Hudson (Sol) to about 800 or 900 exploited systems.

In July, the powers that be revised the Overhead calculation so that it no longer used the exact number of exploited systems, but leveled an average exploited system count of 13 systems per control system.

The other changes from July were possibly more impactful.

• There were two calculations, one gave smaller powers lower overhead, while one applied to powers exceeding 55 control systems, reducing their Overhead to manageable levels.
• If an Expansion would take a Power into deficit, that expansion would automatically fail, whether or not its expansion goals were met. (This specific 'fix' took several months to firmly take hold, with occasional bugs/inconsistencies popping up as recently as May.)

A month or so later, the average was reduced to 11.5 systems, and the 'max' formula multiplier reduced to 5.4.

I've lost the original Overhead formula, but because it didn't have a 'max' option, and Sandro himself likes the idea of impossibly large bubbles, it had to go. The new formulas, with their 'average exploited system' count, leave much to be desired. At this point, every Control System, whether it be Sol (with over 20 exploited systems) or Peraseii (with 4 exploited systems) cost exactly the same in Overhead.

If Overhead is presumably the cost of maintaining an exploited or contested system, then simplifying it to an 'average' which appears more arbitrary than mathematical winds up making the entire system of Power Play over-simplified, abstract, and essentially pointless. Expansion strategy becomes over-simplified, and the innate imbalances of galactic population become the driving force behind which Powers take the lead.

In order to facilitate a discussion, I'm going to run the numbers for Overhead using both formulas, but substituting the averaged exploited system count with the exact exploited system count. I'm going to use the count from every Power's Dominion, as that includes Contested Systems as well as every Exploited System.

This will be known as Averaged Formula 2, and the tweak with 13 changed to 11.5 and 5.8 changed to 5.4 will be Averaged Formula 3. Averaged Formula 3 is the Current Overhead Formula. Since each formula is two formulas, both results will be shown, but know that only the lowest number would be the result of the calculation.

Arissa Lavigny-Duval controls 65 systems with income coming in from 723 exploited systems, but a total of 890 exploited systems, and an Overhead calculated at 4036cc. That puts ALD control systems with an average of 13.69 exploited systems each, but only an average of 11.12 exploited systems contributing income.

Averaged Formula 2	Averaged Formula 3	Exact Formula 2	Exact Formula 3
8143, 4901	5637, 4036.5	9515, 5162	9515, 4806

I used Arissa Lavigny-Duval as a test case, because I'm overly familiar with her development as a Power, and our changes in strategy brought about by understanding the Overhead changes. This test, and the first round of calculations tells me that we haven't been paying Overhead for Contested Systems since August. Interesting. Still, the purpose of this test was to show how using the 'averages' is increasing the standing deficit for Powers who prepare control systems without many exploited systems. To solidify that, I'll only run 'Formula 3' with averaged, total exploited, and uncontested exploited system counts.

Averaged	Total Exploited	Uncontested Exploited
5637, 4036.5	9515, 4806	5101, 3904

Next up, I'll use Mahon and Hudson, those large Powers with the highest standing surpluses, and Aisling, a large Power with the deepest standing deficit.

Edmund Mahon controls 107 systems with income coming in from 1223 exploited systems, but a total of 1447 exploited systems, and an Overhead calculated at 6644cc. That puts Mahon control systems with an average of 13.52 exploited systems each, but only an average of 11.42 exploited systems contributing income.

Averaged	Total Exploited	Uncontested Exploited
25147, 6644.7	40893, 7813	24690, 6604

Zachary Hudson controls 82 systems with income coming in from 918 exploited systems, but a total of 1134 exploited systems, and an Overhead calculated at 5092cc. That puts Hudson control systems with an average of 13.83 exploited systems each, but only an average of 11.1 exploited systems contributing income.

Averaged	Total Exploited	Uncontested Exploited
11318, 5092.2	19683, 6123	10441, 4957

Aisling Duval controls 61 systems with income coming in from 649 exploited systems, but a total of 748 exploited systems, and an Overhead calculated at 3788cc. That puts Aisling control systems with an average of 12.26 exploited systems each, but only an average of 10.64 exploited systems contributing income.

Averaged	Total Exploited	Uncontested Exploited
4659, 3788.1	5648, 4039	3689, 3504

Now, since Antal is way out in the sticks and has successfully controlled Maia, let's see what happens with his numbers. Pranav Antal controls 53 systems with income coming in from 567 exploited systems, but a total of 631 exploited systems, and an Overhead calculated at 3056cc. That puts Antal control systems with an average of 11.91 exploited systems each, but only an average of 10.69 exploited systems contributing income.

Averaged	Total Exploited	Uncontested Exploited
3056.1, 3291.3	3391, 3407	2460, 3061

So, what can we see from this case study of half of the Powers?

The Overhead tweak FDev pushed through changing the average from 13 to 11.5 exploited systems per control system appears to have been a sly way for them to remove Overhead from Contested Systems. It also seems to be accurate for about half of the Powers, and starkly inaccurate for others.

The differences between 'Uncontested Exploited' and 'Averaged' Overhead calculations is around 200cc, but is remarkably less once a Power dips under 55 Control Systems.

Personally, I like the idea of shifting the Overhead calculation again, if only so that it means something, rather than being an abstract 'cost' that doesn't appear to convey any sort of reality.

Thoughts?

 

[Ant_Solo]

I've lost the original Overhead formula, but because it didn't have a 'max' option, and Sandro himself likes the idea of impossibly large bubbles, it had to go.

This was the estimation of the original formula:

overhead = number of systems³ / 74000

Source: https://forums.frontier.co.uk/showt...n-is-Doomed-(and-Lavigny-Duval-could-be-next)

 

[Martin Schou]

Here's what would happen if that was implemented now:

Power	Exploited Systems	Overheads	Income	Default
Mahon	1,447	40,942	9,776	-31,166
Hudson	1,134	19,706	7,379	-12,327
Torval	895	9,688	6,765	-2,923
ALD	890	9,527	5,525	-4,002
Winters	968	12,257	6,186	-6,071
Aisling	748	5,656	4,800	-856
Li Yong-Rui	791	6,688	5,434	-1,254
Antal	631	3,395	4,342	947
Patreus	679	4,230	4,584	354
Delaine	607	3,022	3,970	948

 

[Ant_Solo]

Here's what would happen if that was implemented now:

snip

That looks like fun, I say lets do it!

 

[Rubbernuke]

So Archon wins by 1CC, and Utopia is 2nd? That would make a fun cycle summary...

 

[Martin Schou]

So Archon wins by 1CC, and Utopia is 2nd? That would make a fun cycle summary...

It does depend a bit on what is included in the overheads. If it includes contested systems, this is the result. If you don't pay overheads for contested systems, economical warfare stops being effective.

 

[aspiringexpatriate]

It does depend a bit on what is included in the overheads. If it includes contested systems, this is the result. If you don't pay overheads for contested systems, economical warfare stops being effective.

Well, by using the 11.5 average, FDev essentially stopped including Contested Systems in the Overhead.

My main point in this thread was to show that simply by using an average count for systems, Overhead ceases to have any actual meaning whatsoever, and is just an arbitrary extra cost that you don't tell anyone about.

(I was hoping ALD's average would be drastically lower than Mahon's and Hudson's, but we have spent about 4-6 months 'culling' our under performing systems from the bubble.)

The original formula was always problematic, because it was a brick wall of limitation. But thanks for crunching the numbers for me.

 

[Martin Schou]

It's also problematic, because you never get to find out what the value is of a system. It looks good, but is that because it has a few very high population systems or is it actually horrible because it has three dozen low population systems which would tank your overheads?

And even if the overheads were included somehow, you'd then get a constant stream of "why is A better than B, when B has a much higher radius income - that makes no sense!"

 

[aspiringexpatriate]

But you can find out the CC value of a system. You look at its population.

If every potential expansion system had a Radius Income, Upkeep, and Overhead Figure before the Profit figure, it would be fine.

Of course, using the smaller formula, you're going to have to have a variable Overhead calculation. You could do something like 'Potential Overhead' just before 'Potential Profit'.

I've embraced the streams of 'I don't get it' questions for 12 months. That's why we exist, to answer those questions and hopefully encourage more useful participation.

 

[fergal]

My main point in this thread was to show that simply by using an average count for systems, Overhead ceases to have any actual meaning whatsoever, and is just an arbitrary extra cost that you don't tell anyone about.

Thats exactly what it is.
Its just a number they made up to ensure expansions could keep happening for the larger powers, while still allowing the smaller powers to be crippled.

There is such a large advantage for every power has who was able to reach the 55 system amount while maintaining a surplus, or very close to a surplus.
It means they are able to continue to play the expansion game, when "profitable" systems are prepared.

Now the galaxy is full, the other 8 powers are where Delaine and Antal have been at for 6-9 months, where winning expansions just causes even more fortification to be needed.

I think the original overhead calculation was silly in how quickly it maxed out (week 4 for ALD) but to replace it with a system that rewards larger powers, and powers in the "better" parts of space to the extent that it did, has made PP far more boring.

Here is where the powers where in week 11, the week that most of them were at or already over the 55 system calculation:

Arissa Lavigny-Duval 67
Edmund Mahon 62
Aisling Duval 59
Li Yong-Rui 58
Felicia Winters 55
Zachary Hudson 54
Denton Patreus 48
Zemina Torval 45
Pranav Antal 30
Archon Delaine 27

Hudson is 1 system off at this point, but was running a surplus and had no problems getting to 55 systems.
That left 4 powers with the harsher calculation, in the next 40 weeks Torval has managed to get past 55 systems, while facing no opposition nearly every week.
Patreus and Antal have broken their starting balance to get there.

When I first raised the problem, when the new overhead formula was first introduced, the general argument against what I was saying was that I was crazy and if you have less than 55 systems your overheads are lower per control system so the formula is an advantage for powers with less than 55 systems.

Unfortunately this just isn't true, and the main reason is the prep list.

When a Power has 32 systems, their overhead goes up by 61 (very close to the 62 averaging at 55) and every system expanded to between 31 and 55 makes the cost go up, to a maximum of 183.

And you need an average profit of 62 per system to balance the overhead cost at 55 systems, so why is this a problem?
You need to maintain a large CC surplus during the lower Overhead costs, to offset to higher costs near 55 systems.

At 32 systems (with all at 62 profit) you have overheads of 672, and a profit of 62*32 = 1984.
So you need a surplus of 1312cc when at 32 systems.
At 42 systems all at 62 profit, overheads go up to 1520 and profit is 42*62 = 2604, so a surplus of 1084.

That means the prep list would have 10 systems on it during those weeks (19 systems is when a surplus over 1000 starts with all 62 profit systems).
Which for anyone who has actually played the game knows, its impossible to have 10 systems on the list with all of them having a profit over 62.
And any system under this value will probably get no opposition and be expanded to, meaning expanding to systems with an average profit over 62 is impossible.

 

[Rubbernuke]

If anyone is left playing PP, the bottom 3 positions are going to be meat grinders as eventually they will all go bust as they choke on low CC systems.

I don't know if this intentional, but who in the future is going to invest time in powers who could have a life expectancy of a few cycles?

 

[aspiringexpatriate]

When a Power has 32 systems, their overhead goes up by 61 (very close to the 62 averaging at 55) and every system expanded to between 31 and 55 makes the cost go up, to a maximum of 183.

And you need an average profit of 62 per system to balance the overhead cost at 55 systems, so why is this a problem?
You need to maintain a large CC surplus during the lower Overhead costs, to offset to higher costs near 55 systems.

At 32 systems (with all at 62 profit) you have overheads of 672, and a profit of 62*32 = 1984.
So you need a surplus of 1312cc when at 32 systems.
At 42 systems all at 62 profit, overheads go up to 1520 and profit is 42*62 = 2604, so a surplus of 1084.

That means the prep list would have 10 systems on it during those weeks (19 systems is when a surplus over 1000 starts with all 62 profit systems).
Which for anyone who has actually played the game knows, its impossible to have 10 systems on the list with all of them having a profit over 62.
And any system under this value will probably get no opposition and be expanded to, meaning expanding to systems with an average profit over 62 is impossible.

You can combat this by having neighbouring Powers undermine you all to hell and so while your starting surplus is 1042cc, your week end surplus is more like 300cc. Isn't that how it worked out anyway for Delaine, Hudson, and Winters for most of the time? Except for those weeks where the strategy was to overblow your prep list.

You raise good points, and thanks for refreshing our memories about the situation.

There was a point where we were beginning to target systems of high potential profit with few exploited systems. So those couple of weeks where we did that strategy really screwed us later when the Overhead calculation changed. At least we've finally SCRAP'd most of those systems.

 

[Martin Schou]

There is really only two ways of improving it - get rid of overheads or make overheads flat. But it sort of boils down to one of the things that could do with a rework in terms of PowerPlay.

It's one of those things like ships - trying to make just one okay ends up making everything else look even more unbalanced :-/

 

[fergal]

You can combat this by having neighbouring Powers undermine you all to hell and so while your starting surplus is 1042cc, your week end surplus is more like 300cc. Isn't that how it worked out anyway for Delaine, Hudson, and Winters for most of the time? Except for those weeks where the strategy was to overblow your prep list.

That is exactly what we were able to do at Delaine, and we currently have an average cc profit of 59, but the other issue is there being no systems left.
Ever since we got more than 32 systems we have been worsening our position, and increasing our fortification needs. There hasn't been one expansion (that we won or failed to win) that would have improved our position, which isn't great for player retention.

You raise good points, and thanks for refreshing our memories about the situation.

There was a point where we were beginning to target systems of high potential profit with few exploited systems. So those couple of weeks where we did that strategy really screwed us later when the Overhead calculation changed. At least we've finally SCRAP'd most of those systems.

Yeah, that was a pain to count the individual profits to get the average profit per exploited system, rather than the useless number the map showed.

There is really only two ways of improving it - get rid of overheads or make overheads flat. But it sort of boils down to one of the things that could do with a rework in terms of PowerPlay.

It's one of those things like ships - trying to make just one okay ends up making everything else look even more unbalanced :-/

Any rework of overheads will have some powers better off, and others worse off.

I don't think there was anything wrong with the overheads constantly going up, just the ridiculous rate (having it cubed) needed to change.

The first thing that needs to change is the maps usage of the term "profit" when the largest cost (at least 62cc) isn't subtracted. Its just a lie that misleads every player who doesn't go hunting around on the reddits.
This isn't a change to the mechanics, just subtracting a number from the map display.
Even just subtracting 62 for everyone would be better, but making it subtract the actual overhead cost for the next expansion is ridiculously simple.

 

[freedom4556]

Even just subtracting 62 for everyone would be better, but making it subtract the actual overhead cost for the next expansion is ridiculously simple.

The problem Sandy always has with that is that multiple expansions can (and do) succeed at once, making the value untrue for each expansion after the first.

But I do agree with you, any display of the overhead cost is better than completely hiding it.

 

[aspiringexpatriate]

There is really only two ways of improving it - get rid of overheads or make overheads flat. But it sort of boils down to one of the things that could do with a rework in terms of PowerPlay.

It's one of those things like ships - trying to make just one okay ends up making everything else look even more unbalanced :-/

I can't help but disagree entirely.

Overhead as a representation of exploited systems, which you get access to only because of their proximity to control systems, is one factor of the calculation that makes Power Play more than just a bland game of risk. It's what adds reality to the strategy of conquering/influence/whatever the      abstraction Power Play aims to represent. Making Overhead flat is nonsensical and arbitrary, and completely doing away with them simplifies Power Play to the detriment of any point whatsoever.

Any rework of overheads will have some powers better off, and others worse off.

I don't think there was anything wrong with the overheads constantly going up, just the ridiculous rate (having it cubed) needed to change.

The first thing that needs to change is the maps usage of the term "profit" when the largest cost (at least 62cc) isn't subtracted. Its just a lie that misleads every player who doesn't go hunting around on the reddits.
This isn't a change to the mechanics, just subtracting a number from the map display.
Even just subtracting 62 for everyone would be better, but making it subtract the actual overhead cost for the next expansion is ridiculously simple.

Agreed. A display of Overhead would be wonderful. Then every player would see that there are no profitable systems left. Thus their constant expansion driven game would utterly breakdown. Still, we need at least a potential overhead display just for sanity's sake.