WltKDs, again?

[Doc Tsiolkovski]

Seems like the corruption wizards are no longer available...

Question:

How exactly does the WltKD work? (in c3c)

Everything including Alexman's articles and the discussion there assumes WltkD would act like another CH (in other words, -10%, increase of OCN for that city), but affecting only waste, not corruption.

However, this is not true....

Observations:

1. The effect of WltKD for a city can vary from nothing to like -30% corruption, depending on that city's rank. A Court/Police will always result in maximum 80% waste.
2. CH and PS (and the FP/SPHQ) are simply adding up. Both in a city -> -20% waste.
   WltKD works completely different. Once the city has two corruption reducing improvements (in other words, PS & CH), WltK will reduce waste for a further 20-30% .

In fact, you can set up a city with a rank @~2x OCN.
Only WltK - zero effect.
CH/PS - reduce for 10% each, cumulative.
CH/PS/WltK - 20% from the structures, another 20-30% from the celebrations.

To make the equitation even harder to understand: If you found new cities/ disband existing ones between the cpaital and that city - the WltKD effect will be affected.
The higher the city rank, the less noticable the WltKD effect...

Anyone with a deeper mathematical understanding? What's happening here?

 

[MRick]

I've no idea on how it works, but I would be happy if someone finds out !

...so... UP !

 

[Ansar]

I've no idea on how it works, but I would be happy if someone finds out !

...so... UP !

Same here.
I still wonder because i have never seen WltKDC actually work.
but its cool seeing it happen the fireworks

 

[Theoden]

I thought it increased OCN by 25% just as the COM trait does. With your observations however it seems like it ought to have another effect. Maybe the effect is added after the court/police has lowered the max corruption?

 

[Doc Tsiolkovski]

Something along that line is my impression as well. But that still doesn't really explain why the effect depends on the city rank.
And, it is really that strange:
You can set up a city at about 2x OCN (no FP so far). So, about 80% corrupt.
WltKD, zero effect.
CH, as you'd expect.
CH+WltKD, not the slightest difference to CH alone.
CH+PS, as you'd expect.
CH+PS+WltKD - suddenly, city is only about 40% corrupt (for waste)...

 

[SJ Frank]

Doc, I think the behavior you observed can still be explained by Alexman's article.

Near the end of the article, there is this equation:

MAXIMUM CORRUPTION

The sum of the distance and rank components of corruption can be greater than 100%. The game sets an upper limit for the total corruption in a city to be equal to 90% minus 10% for each city improvement and minus 70% for each Wonder in the city with the “reduces corruption” ability:

     Cmax = max(0.9 – (0.1 * Ni + 0.7 * Nwc), 0)

Corruption buildings do lower the max corruption of a city, but WLtKD does not.

When you build a city at ~=2*OCN, the combined Crank and Cdist should take the city way over 100% corruption, so the Cmax rule applies here. When you put this city in WLtKD, is was not enough to lower total waste below 90%, so there was no change. However, when you build the courthouse, since courthouse does lower Cmax, you did see change in corruption.

When you add CH, PS and WLtKD together, I guess it was enough to lower the city's total waste to below 70% (distance factor is 1/8th, Nopt increased by 75%, it might just be enough), so that Cmax rule does not apply anymore, and you get the see WLtKD finally working.

 

[SJ Frank]

I made a spreadsheet that calculated the expected value of corruption under the simplest circumstances.

I was surprised by how much CH, PS and WLtKD help against Distance Corruption. With those 3 factors acting together, any cities within 3-4 rings have negligible Distance Corruption.

The chart also shows when the city’s rank is around 2*OCN, it hits the Cmax cap with just a CH and PS, but gets to around 60% corruption with CH + PS + WLtKD.

 

[Doc Tsiolkovski]

Thanks for your insights, SJ_Frank!

I did run a couple of tests (and, less time-consuming, excel charts), and my final verdict is:

The corruption formula does not allow to exactly predict the waste reducing effects of WltKDs.
However, those inaccuracies can be neglected for the game; so, it is safe to say:

WltKD is the same as a free Courthouse in every city - as long as is less than 90% corrupt.

In other words, the effect is huge.

Considering it often requires only 10% more Lux to get the mid-size, mid-ranked cities into that mode (especially when a CH is already in place), I really wonder why so few players seem to use that powerful tool...

About the inaccuracies in the formula:

1) The predicted WltKD effect in cities without CH/PS and a corruption in the 85%+ range is substantially too high; in reality, you see almost no effect here. Now, while it may be 3x stronger than observed - it doesn't matter in-game, since we're talking about 1 or 2 shields/turn here.

2) In general, the WltKD effect slightly differs from that of another corruption reducing structure in the last ~10% before hitting the max-corruption cap. This is the only part where the curves (before the cap) of WltKD/CH are not identical.

Example: A city in the 80-85% corruption range can end with 80% corruption with a CH, but 75% with WltKD.
Or, city with CH+WltKD is at 67%, with CH + PS at 70%.

While this sounds a bit surprising for the math freaks, it again doesn't really matter in the game.
Alexman's formula treats WltKDs exactly like CHs, so it is obviously slightly wrong here.

However, the observation that confused me the most initially (those 30% boost effects) are not related to WltKDs. In a certain, small range of ranks an 80% city with CH will drop ~50% corruption with either a PS or WltKD, and the same effect happens with a higher ranked city after benefiting from all three - that's not something mysterious, but simply the effect of the switch between the two different corruption formulas @ R < Nopt.