The Case for the Sigmoid Curve

[DigitalRommel]

It appears to me that much of design of the Clausewitz engine uses linear functions to describe changes with respect to game objects. Clausewitz uses modifiers to slope or y-intercept to generate variation and complexity. I suggest that logistic functions offer more realistic outcomes.

For instance there are airfields. Cutting down trees to produce a dirt airstrip (level 1) is much easier in terms of time and cost than producing a major metropolitan airport (level 10). There is also infrastructure - farm land with dirt roads and smuggler paths to an industrialized city with a multilane autobahn. These changes are not proportional. Cost, time, and capability are not well defined by straight line paths.

It terms of multivariate problems a much more realistic output is also possible. As an example, the effect of both terrain and infrastructure on supply transport could be modeled much more realistically. As infrastructure reaches higher levels, the effect of a province's terrain becomes less meaningful.

Some might suggest that the additional processing would make this technique prohibitive. I suggest this isn't the case, because in most instances, these interactions can be pre-computed and saved in the same way pathfinding is pre-computed.

EDIT: corrected my use of terms.

 

[byzantium43]

I like the idea. And you said it real smart like.

 

[unmerged(149861)]

Basicly, infastructure should make the effects of a provinces terrain less vital and reduce build time, amiright?:wacko:

 

[Raineman111]

I believe the OP means that there should be an exponential increase in cost for province improvements. As well as an exponentially proportionate decrease in terrain penalties (both movement and throughput) based on increased infrastructue lvl.
I completely agree with OP's suggestions.

 

[Herbinator]

I think he means that build levels (airfields, ports, infrastructure, etc) should be non-linear. And also not simply exponentially more expensive.

Never heard of Sigmoid used as a curve, but certainly have as a flexture! :rofl:

Yes, I like the sophistication of 2-order polynomial builds: cheap initially, then increasingly more expensive, then becoming cheaper (per level) again. Seems more realistic.

(Computing cycles is not an issue in my view).

 

[DigitalRommel]

Never heard of Sigmoid used as a curve, but certainly have as a flexture! :rofl:

:rofl: ... I bet you heard that joke in a "physics for pre-meds" course.

As to some other posts, I'm not specifically trying to suggest to the designers what to model, but merely a more realistic way to model.

In terms of exponential distributions, the cumulative distribution function isn't exactly the same as those found in the logistic function. You notice that in early outputs there is a lower slope (steepness). For example, the change in utility provided from level 1 to level 2 would be less than exponentially larger. At the other extreme, say levels 9 to 10, the change in utility is also not as large as an exponential increase. When graphed it produces a "S" pattern.

That all said, I do certainly agree that some parts of the Clausewitz engine could benefit from an exponential distribution. My central point is that the linear functions used don't produce as realistic a model as could be achieved. The reason I prefer the s-curve is because most real world systems can't sustain exponential changes. There is always some regulating factor that eventually mitigates and softens the change.

 

[JakMezak]

As an economist by education, I whole heartedly have to agree with the OP. Increasing and then eventually diminishing returns is a realistic fact of life. I think it would be particularly helpful to force the player down a more balanced road if it were implemented in multiple facets of game play. For instance (just one example), allocating your entire educated population to research is not going to be efficient as opposed to distributing those educated people amongst various job types. This is because some people are more suited to being researchers and some more to being officers and some more to being diplomats, etc. Forcing everyone to be a researcher for the sake of tech rushing seems gamey because it is. No normal society would force all their talented people down one career path. Needless to say, this idea extends to production and most of the other game play ideas in HOI3.

 

[unmerged(171774)]

As an economist by education, I whole heartedly have to agree with the OP. Increasing and then eventually diminishing returns is a realistic fact of life. I think it would be particularly helpful to force the player down a more balanced road if it were implemented in multiple facets of game play. For instance (just one example), allocating your entire educated population to research is not going to be efficient as opposed to distributing those educated people amongst various job types. This is because some people are more suited to being researchers and some more to being officers and some more to being diplomats, etc. Forcing everyone to be a researcher for the sake of tech rushing seems gamey because it is. No normal society would force all their talented people down one career path. Needless to say, this idea extends to production and most of the other game play ideas in HOI3.

Well, if in RL like in HoI3 (a model of RL) allocating your entire population to research have such overwhelming benefits over diplomacy and spying, I assured you will do it. E.g. if even ineefective allresearch strat give more benefits over effective research/diplo/spy start, I prefer ineffective allresearch, because my goal is not effeciency per se, but different.

 

[JakMezak]

Well in some ways ==='s point above actually confirms mine. The fact that in game you can and would prefer to allocate almost nothing to diplomacy and espionage is sign and symptom of the problem. There should be a reward for the player doing a more realistic (balanced) allocation of their resources. For example, the first point you allocate from research to diplomacy nets you 3 diplomatic points at the cost of only 0.2 research points, the next change in that direction only gives you say 2.5 diplomatic points at a cost of say 0.3 research points. The reasoning is that the first batch of people you took out of research and put into diplomacy were bad researchers but really great diplomats. The next group you moved were slightly better researchers and slightly worse diplomats (i.e. they were more average).

The same principle works for factory allocation. Every factory in Germany could theorectically pump out Panzer IV's but some guy's little shop in Bavaria that used to make shoes is probably not going to be the most efficient place to pump out Panzer IV parts. It can be done, but not necessarily efficiently. It ultimately goes back to the argument people had on this forum during development about shipyards being used to make tanks. An S curve with increasing and then decreasing returns is more realistic in this case.

That being said, bug fixes and AI improvements seem to be and should be the main focus of the development group. However, this idea is one to keep on the back burner for any expansions or even future games in general.

(Edited to clarify my point.)