Thanks for playing.
The drops in power are a little complex to explain. Basically each time you make a choice that defines your character (such has "has venom" or "does not have teeth"), the sum total of what is known about your character is compared against a list of possible creatures. If you've then eliminated all possibilities for other slots, that information gets set also. Your remaining power is the number of unknown slots.
So, for example, since few creatures have electricity in nature, identifying yourself as having electricity will:
1. Set electricity to true
2. Eliminate all creatures without electricity (a lot of them)
3. Scale down your unknowns based on the creatures that are left (I believe lungs is set to false in this case because no creatures with electricity also have lungs)
You then have to strike a balance between killing investigators and choosing traits that define you. Ultimately, each time you finish a run through you get rewarded with a few characters of the secret name you can enter at the name screen. There are 10 in total. Once you know them all, you'll get a play through with infinite power.