Please reference Happiness & Efficiency for the fundamentals of this page.
Intro[]
Shocking your creatures is a great way to gain a boost to damage. If you intend to attack no more than once a day, then your optimal strategy is to simply shock your creature for as much as it can take. Since the Happiness recovery rate is 5% of your max Happiness per payday, creatures will always achieve max Happiness in at most 20 paydays (possibly up to 24 depending on rounding).
Any other shocking requires a little more thought if you want to get the most per Amp. In particular, shocking your Warlocks to gain a boost to your Research is a great technique to give your Dungeons that slight edge (similar calculations could be applied to creatures that are doing multiple attacks, but that is outside the scope of this article and probably not frequent enough to warrant the attention). Since shocking a Warlock multiple times increases the Efficiency boost, we want to maximize the total gain while minimizing the time it takes to recover the lost Happiness. Furthermore, we can examine what our gains are from investing in more Happiness.
One important idea is that you want to always shock your units at the beginning of the payday, since all of these changes happen at payday, regardless of when you shocked them.
Basics[]
Here are the fundamental rules that are applicable.
1) Creatures can be shocked only to maximum +100% Efficiency bonus (they can be shocked more, but the effect will only decrease Happiness). 2) Creatures regain 5% (rounded down) of your maximum Happiness every payday (that they are paid for). 3) Creatures lose 25% of their Efficiency bonus (minimum 5% points) every payday. 4) Each shock costs 10 points of Happiness
From these rules we can see how your Efficiency progresses (without additional shocking) as a function of payday. There are two cases, one with just Forced Labor and one with Merciless Labor. For this table, the column on the left represents the number of times the creature has been shocked (Merciless Labor in red). The row represents the creature's Efficiency bonus as a function of payday.
Forced Labor/Merciless Labor
| # of Shocks | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 0 | 0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% |
| 1 | +5% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% |
| 2/1 | +10% | +5% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% |
| 3 | +15% | +10% | +5% | +0% | +0% | +0% | +0% | +0% | +0% | +0% | +0% |
| 4/2 | +20% | +15% | +10% | +5% | +0% | +0% | +0% | +0% | +0% | +0% | +0% |
| 5 | +25% | +19% | +14% | +9% | +4% | +0% | +0% | +0% | +0% | +0% | +0% |
| 6/3 | +30% | +23% | +18% | +13% | +8% | +3% | +0% | +0% | +0% | +0% | +0% |
| 7 | +35% | +27% | +21% | +16% | +11% | +6% | +1% | +0% | +0% | +0% | +0% |
| 8/4 | +40% | +30% | +23% | +18% | +13% | +8% | +3% | +0% | +0% | +0% | +0% |
| 9 | +45% | +34% | +26% | +20% | +15% | +10% | +5% | +0% | +0% | +0% | +0% |
| 10/5 | +50% | +38% | +29% | +22% | +17% | +12% | +7% | +2% | +0% | +0% | +0% |
| 11 | +55% | +42% | +32% | +24% | +18% | +13% | +8% | +3% | +0% | +0% | +0% |
| 12/6 | +60% | +45% | +34% | +26% | +20% | +15% | +10% | +5% | +0% | +0% | +0% |
| 13 | +65% | +49% | +37% | +28% | +21% | +16% | +11% | +6% | +1% | +0% | +0% |
| 14/7 | +70% | +53% | +40% | +30% | +23% | +18% | +13% | +8% | +3% | +0% | +0% |
| 15 | +75% | +57% | +43% | +33% | +25% | +19% | +14% | +9% | +4% | +0% | +0% |
| 16/8 | +80% | +60% | +45% | +34% | +26% | +20% | +15% | +10% | +5% | +0% | +0% |
| 17 | +85% | +64% | +48% | +36% | +27% | +21% | +16% | +11% | +6% | +1% | +0% |
| 18/9 | +90% | +68% | +51% | +39% | +30% | +23% | +18% | +13% | +8% | +3% | +0% |
| 19 | +95% | +72% | +54% | +41% | +31% | +24% | +18% | +13% | +8% | +3% | +0% |
| 20/10 | +100% | +75% | +57% | +43% | +33% | +25% | +19% | +14% | +9% | +4% | +0% |
Similarly, we can work out how many paydays it takes to recover from a given Happiness deficit. For this table, the left column represents how much Happiness you are trying to recover as a function of your recovery rate (5% of max rounded down). Note that some of the values are blank because they are impossible to attain.
| Happiness | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 20 | 4 | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
| 30 | 6 | 5 | 5 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 |
| 40 | 8 | 7 | 6 | 5 | 5 | 4 | 4 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | 2 |
| 50 | 10 | 9 | 8 | 7 | 6 | 5 | 5 | 5 | 4 | 4 | 4 | 4 | 3 | 3 | 3 | 3 |
| 60 | 12 | 10 | 9 | 8 | 7 | 6 | 6 | 5 | 5 | 5 | 4 | 4 | 4 | 4 | 4 | 3 |
| 70 | 14 | 12 | 10 | 9 | 8 | 7 | 7 | 6 | 6 | 5 | 5 | 5 | 5 | 4 | 4 | 4 |
| 80 | 16 | 14 | 12 | 10 | 9 | 8 | 8 | 7 | 7 | 6 | 6 | 5 | 5 | 5 | 5 | 4 |
| 90 | 18 | 15 | 13 | 12 | 10 | 9 | 9 | 8 | 7 | 7 | 6 | 6 | 6 | 5 | 5 | 5 |
| 100 | 20 | 17 | 15 | 13 | 12 | 10 | 10 | 9 | 8 | 8 | 7 | 7 | 6 | 6 | 6 | 5 |
| 110 | 22 | 19 | 16 | 14 | 13 | 11 | 10 | 10 | 9 | 8 | 8 | 7 | 7 | 7 | 6 | 6 |
| 120 | - | 20 | 18 | 15 | 14 | 12 | 11 | 10 | 10 | 9 | 8 | 8 | 8 | 7 | 7 | 6 |
| 130 | - | 22 | 19 | 17 | 15 | 13 | 12 | 11 | 10 | 10 | 9 | 9 | 8 | 8 | 7 | 7 |
| 140 | - | - | 20 | 18 | 16 | 14 | 13 | 12 | 11 | 10 | 10 | 9 | 9 | 8 | 8 | 7 |
| 150 | - | - | 22 | 19 | 17 | 15 | 14 | 13 | 12 | 11 | 10 | 10 | 9 | 9 | 8 | 8 |
| 160 | - | - | - | 20 | 18 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 10 | 9 | 9 | 8 |
| 170 | - | - | - | 22 | 19 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 10 | 9 | 9 |
| 180 | - | - | - | - | 20 | 18 | 17 | 15 | 14 | 13 | 12 | 12 | 11 | 10 | 10 | 9 |
| 190 | - | - | - | - | 22 | 19 | 18 | 16 | 15 | 14 | 13 | 12 | 12 | 11 | 10 | 10 |
| 200 | - | - | - | - | - | 20 | 19 | 17 | 16 | 15 | 14 | 13 | 12 | 12 | 11 | 10 |
Greedy Algorithm[]
The first method up for discussion is the Greedy Algorithm. With this you shock up to a point and then shock once per payday. One common value to shock to is +20%, since you will lose 5% per payday, but each shock gains you 5%. Therefor, you will break even for as long as you have Happiness, and then you will quickly drop to +0% while you recover back to your full value. For example, if you are recovering 5 Happiness per payday, and you have Forced Labor, then 13 paydays at +20%, then one each at +15%, +10%, +5%, then 17 paydays at +0% until you return to where you began. This whole cycle takes 30 hours to complete, and will yield an average of +9.67% bonus. If you have Merciless Labor, you can instead keep steady at +40% bonus. Below is a chart indicating how long the cycle is and what your total bonus will be.
| Happiness Rate | 5 | 6 | 7 | 8 | 9 |
| Paydays per Cycle | 13 | 21 | 34 | 61 | 141 |
| Average Bonus (FL) | 9.67% | 11.84% | 13.96% | 16.03% | 18.04% |
| Average Bonus (ML) | 18.33% | 22.90% | 27.34% | 31.67% | 35.89% |
Note that once you are regaining 10 Happiness per payday, you can actually continue this indefinitely (for an average of +20% or +40%). Of course, for this method to work properly, you need to shock once per hour, every hour, and some of those cycles are far too long as most of us require (uninterrupted) sleep.
Minimum Method[]
I don't have a better name for this, but the idea is that you shock your creatures up to a certain amount, and then wait for them to fully recover. If you log in exactly when they achieve maximum Happiness again, then you can maximize the time without a bonus. Since most of the time (as we'll see in the graphs below) you'll want to spend all or almost all of your Happiness, and since the recovery rate for Happiness is 5% of your max Happiness, it will always take 20 (22) hours or less to completely recover. As such, if you log in at the same time every day, you're catching your units after 24 hours, which is pretty efficient, adding only 4 hours of bonusless research.
How to read the graphs[]
Below you will find two graphs: one for Forced Labor and one for Merciless Labor. The graph indicates the average % bonus you'll get over the entire duration, assuming that as soon as your creature returns to maximum Happiness you begin shocking again. The first column is how many Happiness points you shock them for. Each other column represents the recovery rate of your Happiness, which is your max Happiness * 0.05 rounded down (so 5% from 100-119, 6% from 120-139, etc.). The very last column gives you the average if you only shock them every 24 hours. For example, if I have a max Happiness of 160, then I have a recovery of 8 Happiness per Payday. If I were to shock my creatures for all 160 Happiness every 20 hours (from the table above), then I will average a research bonus of +14.75%, which is about three Bookshelf worth of bonus. If instead I simply shock once every 24 hours, I will get an average bonus of +12.29%.
Forced Labor[]
| Happiness | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 24 Hours |
| 0 | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% |
| 10 | +2.50% | +2.50% | +2.50% | +2.50% | +2.50% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +5.00% | +0.21% |
| 20 | +3.75% | +3.75% | +5.00% | +5.00% | +5.00% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +10.00% | +0.63% |
| 30 | +5.00% | +6.00% | +6.00% | +7.50% | +7.50% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +12.50% | +12.50% | +12.50% | +12.50% | +12.50% | +12.50% | +1.25% |
| 40 | +6.25% | +7.14% | +8.33% | +10.00% | +10.00% | +12.50% | +12.50% | +12.50% | +12.50% | +15.00% | +15.00% | +15.00% | +15.00% | +15.00% | +15.00% | +10.00% | +2.08% |
| 50 | +7.10% | +7.89% | +8.88% | +10.14% | +11.83% | +14.20% | +14.20% | +14.20% | +16.75% | +16.75% | +16.75% | +16.75% | +19.33% | +19.33% | +19.33% | +19.33% | +2.96% |
| 60 | +7.92% | +9.50% | +10.56% | +11.88% | +13.57% | +15.83% | +15.83% | +18.40% | +18.40% | +18.40% | +21.00% | +21.00% | +21.00% | +21.00% | +21.00% | +23.67% | +3.96% |
| 70 | +8.36% | +9.75% | +11.70% | +13.00% | +14.63% | +16.71% | +16.71% | +19.33% | +19.33% | +22.00% | +22.00% | +22.00% | +22.00% | +24.75% | +24.75% | +24.75% | +4.88% |
| 80 | +8.44% | +9.64% | +11.25% | +13.50% | +15.00% | +16.88% | +16.88% | +19.29% | +19.29% | +22.00% | +22.00% | +24.80% | +24.80% | +24.80% | +24.80% | +27.75% | +5.63% |
| 90 | +8.61% | +10.33% | +11.92% | +12.92% | +15.50% | +17.22% | +17.22% | +19.38% | +22.14% | +22.14% | +25.00% | +25.00% | +25.00% | +28.00% | +28.00% | +28.00% | +6.46% |
| 100 | +8.85% | +10.41% | +11.80% | +13.62% | +14.75% | +17.70% | +17.70% | +19.67% | +22.13% | +22.13% | +25.00% | +25.00% | +28.00% | +28.00% | +28.00% | +31.20% | +7.38% |
| 110 | +8.86% | +10.26% | +12.19% | +13.93% | +15.00% | +17.73% | +19.50% | +19.50% | +21.67% | +24.38% | +24.38% | +27.43% | +27.43% | +27.43% | +30.67% | +30.67% | +8.13% |
| 120 | - | +10.75% | +11.94% | +14.33% | +15.36% | +17.92% | +19.55% | +21.50% | +21.50% | +23.89% | +26.88% | +26.88% | +26.88% | +30.00% | +30.00% | +33.33% | +8.96% |
| 130 | - | +10.64% | +12.32% | +13.76% | +15.60% | +18.00% | +19.50% | +21.27% | +23.40% | +23.40% | +26.00% | +26.00% | +29.13% | +29.13% | +32.43% | +32.43% | +9.75% |
| 140 | - | - | +12.90% | +14.33% | +16.13% | +18.43% | +19.85% | +21.50% | +23.45% | +25.80% | +25.80% | +28.67% | +28.67% | +31.88% | +31.88% | +35.29% | +10.75% |
| 150 | - | - | +12.68% | +14.68% | +16.41% | +18.60% | +19.93% | +21.46% | +23.25% | +25.36% | +27.90% | +27.90% | +31.00% | +31.00% | +34.38% | +34.38% | +11.63% |
| 160 | - | - | - | +14.75% | +16.39% | +18.44% | +19.67% | +21.07% | +22.69% | +24.58% | +26.82% | +29.50% | +29.50% | +32.78% | +32.78% | +36.25% | +12.29% |
| 170 | - | - | - | +14.32% | +16.58% | +18.53% | +19.69% | +21.00% | +22.50% | +24.23% | +26.25% | +28.64% | +31.50% | +31.50% | +34.89% | +34.89% | +13.13% |
| 180 | - | - | - | - | +17.15% | +19.06% | +20.18% | +22.87% | +24.50% | +26.38% | +28.58% | +28.58% | +31.18% | +34.30% | +34.30% | +37.78% | +14.29% |
| 190 | - | - | - | - | +16.32% | +18.89% | +19.94% | +22.44% | +23.93% | +25.64% | +27.62% | +29.92% | +29.92% | +32.64% | +35.90% | +35.90% | +14.96% |
| 200 | - | - | - | - | - | +18.95% | +19.95% | +22.29% | +23.69% | +25.27% | +27.07% | +29.15% | +31.58% | +31.58% | +34.45% | +37.90% | +15.79% |
Note that for several Max Happiness values, the ideal amount to shock is one shock short of zero. This is likely due to the nature of the rounding and exact values that the sequence goes through, in combination with a slightly shorter reload time. It also only matters if you can catch it as soon as it's ready to go again, instead of waiting 24 hours.
Merciless Labor[]
| Happiness | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 24 Hours |
| 0 | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% | +0.00% |
| 1 | +7.50% | +7.50% | +7.50% | +7.50% | +7.50% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +10.00% | +0.63% |
| 2 | +12.50% | +12.50% | +15.00% | +15.00% | +15.00% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +17.50% | +20.00% | +2.08% |
| 3 | +15.83% | +18.40% | +18.40% | +21.00% | +21.00% | +23.67% | +23.67% | +23.67% | +23.67% | +23.67% | +26.50% | +26.50% | +26.50% | +26.50% | +26.50% | +26.50% | +3.96% |
| 4 | +16.88% | +19.29% | +22.00% | +24.80% | +24.80% | +27.75% | +27.75% | +27.75% | +27.75% | +31.00% | +31.00% | +31.00% | +31.00% | +31.00% | +31.00% | +20.00% | +5.63% |
| 5 | +17.70% | +19.67% | +22.13% | +25.00% | +28.00% | +31.20% | +31.20% | +31.20% | +34.75% | +34.75% | +34.75% | +34.75% | +39.00% | +39.00% | +39.00% | +39.00% | +7.38% |
| 6 | +17.92% | +21.50% | +23.89% | +26.88% | +30.00% | +33.33% | +33.33% | +37.00% | +37.00% | +37.00% | +41.25% | +41.25% | +41.25% | +41.25% | +41.25% | +46.33% | +8.96% |
| 7 | +18.43% | +21.50% | +25.80% | +28.67% | +31.88% | +35.29% | +35.29% | +39.00% | +39.00% | +43.20% | +43.20% | +43.20% | +43.20% | +48.25% | +48.25% | +48.25% | +10.75% |
| 8 | +18.44% | +21.07% | +24.58% | +29.50% | +32.78% | +36.25% | +36.25% | +40.00% | +40.00% | +44.17% | +44.17% | +49.00% | +49.00% | +49.00% | +49.00% | +54.75% | +12.29% |
| 9 | +19.06% | +22.87% | +26.38% | +28.58% | +34.30% | +37.78% | +37.78% | +41.50% | +45.57% | +45.57% | +50.17% | +50.17% | +50.17% | +55.60% | +55.60% | +55.60% | +14.29% |
| 10 | +18.95% | +22.29% | +25.27% | +29.15% | +31.58% | +37.90% | +37.90% | +41.67% | +45.75% | +45.75% | +50.29% | +50.29% | +55.50% | +55.50% | +55.50% | +61.60% | +15.79% |
One of the major strengths of this method is the ability to fire and forget. You don't have to be logged in 24/7 in order to get the most out of your researchers. Mostly, this tells you how much you can benefit by increasing your Den happiness.
Combination[]
Alternatively, you can attempt to combine the two methods. This is likely to be a stronger overall average than either of those two methods alone, but there is a lot of variation in this method and the analysis would be far too cumbersome to include in this already overloaded page.
Conclusions[]
If you want to absolutely maximize your research, you will want to shock the heck out of your warlocks. Even if you only shock them once a day, and you have no Happiness enhancements, you're getting more than a Bookcase worth out of them. Also, you want to increase your Den Happiness (through tiles and through furniture). Happy shocking!