Note: lots of stuff on this page old and wrong!
While most effects in Kittens Game increase linearly with their cause (such as Catnip production with Catnip Fields), there are some effects that experience diminishing returns. In other words, the effect size is less than directly proportional to the cause. This effect is present in many important aspects of the game, such as the Faith bonus and Paragon production bonus.
There are two types of diminishing returns in Kittens Game, limited and unlimited. Limited diminishing returns have a cap to their effect that is approached but never reached. Unlimited diminishing returns have no cap to their effect, but still increase slower as the effect grows.
Limited diminishing returns is the more common of the two types. In Kittens Game, an effect subject to this type of diminishing return has a cap, and the first 75% of that cap is linear. However, the remaining 25% has the effect size decreased to keep it from reaching the cap. The effect size as a percentage of the cap past 75% of the cap is given by the following set of equations:
If Effect is less than 75% of Limit
then the final impact is just the effect.
Otherwise,
Diminished Effect = (1 - (delta / (|effect| - undiminished + delta ) ) ) * delta + undiminished
This means, for example, if an effect is capped at 100% and your effect would be 100% if the effect was linear, your effect would actually be 87.5%.
The following is a table showing Undiminished Effect and the corresponding Diminished Effect as a percentage of the cap for select values past 75%:
| Undiminished Effect (Percentage of Cap) | Diminished Effect (Percentage of Cap) |
|---|---|
| 75% | 75.00% |
| 80% | 79.17% |
| 85% | 82.14% |
| 90% | 84.38% |
| 95% | 86.11% |
| 100% | 87.50% |
| 105% | 88.64% |
| 110% | 89.58% |
| 115% | 90.38% |
| 120% | 91.07% |
| 125% | 91.67% |
| 130% | 92.19% |
| 135% | 92.65% |
| 140% | 93.06% |
| 145% | 93.42% |
| 150% | 93.75% |
| 175% | 95.00% |
| 200% | 95.83% |
| 225% | 96.43% |
| 250% | 96.88% |
| 275% | 97.22% |
| 300% | 97.50% |
| 400% | 98.21% |
| 500% | 98.61% |
| 600% | 98.86% |
| 700% | 99.03% |
| 800% | 99.17% |
| 900% | 99.26% |
| 1000% | 99.34% |
| 2000% | 99.68% |
| 3000% | 99.79% |
| 4000% | 99.84% |
| 5000% | 99.87% |
| 10000% | 99.94% |
| 15000% | 99.96% |
| 20000% | 99.97% |
| 30000% | 99.98% |
| 50000% | 99.99% |
The following table shows which effects experience limited diminishing returns, what their cause is, what their limit is, and how the limit can be raised (if at all):
| Effect | Base (linear) effect | Limit | Limit Increase |
|---|---|---|---|
| Faith Production Bonus | (sqrt(1+8 * faith / 1000)-1)/2 (complicated, but hits 750% at ~281,625,000 praised faith) |
1000% | Atheism - 100% per Transcendence Tier Black Obelisk - 5% per Transcendence Tier |
| Paragon Production Bonus | 1% per Paragon | 200% | Sefirots – 10% each |
| Paragon Auto Production Bonus (Smelters, Calciners, and Accelerators) |
0.25% per Paragon | 50% | Sefirots – 2.5% each |
| Paragon Space Manufacturing Bonus (Hydraulic Fracturers) |
0.05% per Paragon | 10% | Sefirots – 0.5% each |
| Price Ratio Reduction (How much the cost of the N+1 instance of a building increases after building the Nth instance) |
Ironwood Huts – 0.5 (Huts only) Concrete Huts – 0.3 (Huts only) Unobtainium Huts – 0.25 (Huts only) Eludium Huts – 0.1 (Huts only) Enlightenment – 0.01 Golden Ratio -(1 + Math.sqrt(5)) / 200 Divine Proportion – 0.0177777778 Vitruvian Feline – 0.02 Renaissance – 0.0225 |
Base Price Ratio-1 If this limit was achieved, all buildings would cost the same as the 1st |
None |
| Space Oil Price Reduction | 5% per Space Elevator | 75% | None |
| Trade Ship Starchart Price Reduction (Initially 25 starcharts per ship) | 1.25% per Satellite with Satellite Navigation | 75% | None |
| Harbour Storage | 1% per Trade Ship with Cargo Ships | 225% | 5% per Reactor with Reactor Vessel |
| Happiness Penalty Mitigation (The 2% drop in Happiness for each kitten after the first 5) |
4.8% per Amphitheatre 75% per Broadcast Tower |
100% | None |
| Catnip Demand Reduction (Starts at 0.85 catnip consumed per kitten per tick) |
0.50% per Pasture 0.15% per Unicorn Pasture |
50% | None |
| Rare Resource Demand Reduction furs: 0.01 (consumed / kitten / tick) ivory: 0.007 (consumed / kitten / tick) spice: 0.001 (consumed / kitten / tick) |
4% per Tradepost | 100% | None |
| Bonus to Zebra Cap when Resetting | 0.0001 * Science spent in Science Tab | 100 | None |
| Extra Catpower from extra Zebras Only additional zebras are affected |
0.15 / tick for the first zebra 0.05 / tick for additional zebras |
2 per tick | None |
| Karma cost decrease of Cryochambers | (sqrt(1+8 * burned paragon / 500)-1)/2 | 100% | None |
| Embassy increase to chance of secondary resource | 1% per embassy | 75% | None |
Unlimited diminishing returns is the less common of the two types, mostly applying to faith related effects. In Kittens Game, an effect subject to this type of diminishing return has no cap. The effect size is given by
Diminished Effect = (sqrt(1+8*Undiminished Effect)-1)/2
It is very close to a simple square root function. For large effect sizes, it approaches a square root function, that is, quadrupling the undiminished effect approximately doubles the diminished effect.
The following is a table showing Undiminished Effect and the corresponding Diminished Effect for select values:
| Undiminished Effect | Diminished Effect |
|---|---|
| 0 | 0.00 |
| 1 | 1.00 |
| 2 | 1.56 |
| 3 | 2.00 |
| 4 | 2.37 |
| 5 | 2.70 |
| 10 | 4.00 |
| 20 | 5.84 |
| 30 | 7.26 |
| 40 | 8.46 |
| 50 | 9.51 |
| 100 | 13.7 |
| 1000 | 44.2 |
| 10000 | 140 |
| 1000000 | 1410 |
| 1000000000000 | 1410000 |
The following table shows which effects experience unlimited diminishing returns and what their cause is:
| Effect | Cause (basic 1:1 relationship) |
|---|---|
| Apocrypha Bonus | 10% per 99009.9 Faith sacrificed when Adoring the Galaxy 10% per 100000 Faith left when resetting |
| Order of the Void | 2.5% per 99009.9 Faith Sacrificed with Apocrypha |
| Max Culture | 1 per 0.01 Manuscripts (rounded down to whole manuscripts) |
| Karma | 0.2 per kitten over 35 when resetting 0.6 per kitten over 60 when resetting 0.8 per kitten over 100 when resetting 1 per kitten over 150 when resetting 2 per kitten over 300 when resetting |