I love the new sprawl mechanics in the beta branch, and I've really been hoping that they stick around as-is (preferably without the 50 sprawl "grace period" that just makes the math messier in the name of making red numbers pop up ever so slightly later). I've been playing with a bunch of math because that's the kind of player I am, and I stumbled onto something that I think might help the presentation of sprawl a lot and make it feel closer to other mechanics people take fewer issues with.
You can actually calculate an "effective research production" using the numbers that already exist, and this is totally independent of technology cost. The same is true of unity and traditions, as the sprawl aspect is applied as a multiplier after adding together the base plus the extra for each tradition you've unlocked. Unity does have other things that are spent on, but I think those are solvable problems.
The equation isn't simple, but it's not that bad either:
Effective Research Output = Actual Research Output / (1 + Sprawl * Sprawl Coefficient)
Spoiler for more math, which you can skip if you just take my word on the derivation.
You could display this "effective production" in the top bar and in the tooltip, you can display the difference between the two numbers as an upkeep similar to all the other upkeeps and negative modifiers in the other resources. I think this would encourage people to think of sprawl as a mechanic similar to the upkeep we pay for buildings, districts, pops, fleets, etc. It would provoke less of that feeling "MUST ELIMINATE RED NUMBER!" because it will be right next to a positive number.
I think this also gives a better picture of our tech output in several ways.
This keeps essentially the same numbers while shifting the presentation from a penalty to an upkeep. Ideally, a shift from a penalty to a bonus a la WoW's rest system being hated when it was presented as a penalty but loved when the exact same mechanic (numbers and all) was presented as a bonus. I don't think there's a good way to do that here, though. I think a similar approach of shifting it from a negative that's all on its own to being right next to a positive and much larger number while also being put into the actual numeric terms of research/unity per month would achieve much the same thing.
You can actually calculate an "effective research production" using the numbers that already exist, and this is totally independent of technology cost. The same is true of unity and traditions, as the sprawl aspect is applied as a multiplier after adding together the base plus the extra for each tradition you've unlocked. Unity does have other things that are spent on, but I think those are solvable problems.
The equation isn't simple, but it's not that bad either:
Effective Research Output = Actual Research Output / (1 + Sprawl * Sprawl Coefficient)
Spoiler for more math, which you can skip if you just take my word on the derivation.
You can derive this by declaring the effective output as the amount of produced research needed to achieve the un-modified cost in the same period of time. This lets you combine the two basic "time equals cost divided by output" of the actual numbers and the hypothetical numbers like this:
Months to Research = Actual Tech Cost/Actual Research Output
Months to Research = Base Tech Cost/Effective Research Output
You can set the right side of the two above equations equal to each other and solve for Effective Research.
Effective Research Output = Base Tech Cost * (Actual Research Output / Actual Tech Cost)
You can then put "Actual tech cost" into terms of Base Tech Cost and the Sprawl modifier and factor out that Base Tech Cost:
Effective Research Output = (Base Tech Cost * Actual Research Output) / (Base Tech Cost * (1 + Sprawl Modifier)
Base Tech Cost divided by itself cancels out, leaving you with the final equation above, which can be either the Sprawl Modifier or Sprawl and the coefficient (0.001 for tech and 0.002 for traditions).
Months to Research = Actual Tech Cost/Actual Research Output
Months to Research = Base Tech Cost/Effective Research Output
You can set the right side of the two above equations equal to each other and solve for Effective Research.
Effective Research Output = Base Tech Cost * (Actual Research Output / Actual Tech Cost)
You can then put "Actual tech cost" into terms of Base Tech Cost and the Sprawl modifier and factor out that Base Tech Cost:
Effective Research Output = (Base Tech Cost * Actual Research Output) / (Base Tech Cost * (1 + Sprawl Modifier)
Base Tech Cost divided by itself cancels out, leaving you with the final equation above, which can be either the Sprawl Modifier or Sprawl and the coefficient (0.001 for tech and 0.002 for traditions).
You could display this "effective production" in the top bar and in the tooltip, you can display the difference between the two numbers as an upkeep similar to all the other upkeeps and negative modifiers in the other resources. I think this would encourage people to think of sprawl as a mechanic similar to the upkeep we pay for buildings, districts, pops, fleets, etc. It would provoke less of that feeling "MUST ELIMINATE RED NUMBER!" because it will be right next to a positive number.
I think this also gives a better picture of our tech output in several ways.
- The numbers are more intuitive, as a higher aggregate number will always mean faster progress through the tech tree.
- "If I go from 400 research to 800 research, I'll research techs in roughly half the time" is much closer to correct when looking at this effective research.
- The technologies themselves could present their base cost at the high level with extra details in the tooltips or something.
- Or you could just change the aggregate output just before applying research speed bonuses and drop the cost increase for techs all together.
- Either way, having those be consistent instead of all over the place does have some value.
- People will have a better idea of the real cost of sprawl. When they take a system and have moments like "Oh, my sprawl upkeep for research and unity only increased by 0.3 each? Clearly that system is worth taking even if it only has 2 science."
- This would help alleviate the exaggerated stress people feel about sprawl.
- (Also yes, the effective cost increase for systems and pops doesn't get much larger than 1 per system/pop in 90% of cases throughout early-mid game. It can get into the 1-2 range if you have enormous output compared to your sprawl, but you have to be going really heavy into tech/unity for that to happen.)
This keeps essentially the same numbers while shifting the presentation from a penalty to an upkeep. Ideally, a shift from a penalty to a bonus a la WoW's rest system being hated when it was presented as a penalty but loved when the exact same mechanic (numbers and all) was presented as a bonus. I don't think there's a good way to do that here, though. I think a similar approach of shifting it from a negative that's all on its own to being right next to a positive and much larger number while also being put into the actual numeric terms of research/unity per month would achieve much the same thing.
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