Shocking strategies

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, creatures will always achieve max Happiness in at most 20 hours.

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. There are initially two basic ways we could do this.

Apparently creatures can be shocked only to maximum +100% bonus.

Greedy Algorithm
The first method is the Greedy Algorithm. This basically means that every time I log in, I shock my Warlocks. I haven't yet worked it out explicitly, but a few examples done by hand should prove to you that this is less effective than the following method. In addition, it requires a lot more maintenance as you need to log in so many times throughout the day.

Efficient 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 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 first portion of the table indicates how much you've shocked your Warlock. The further down the chart you go, the more you've shocked it, and the greater the % bonus to Efficiency. The second portion of 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 very last column gives you the average if you only shock them every 24 hours.

Forced Labor
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.

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.