[MH1] Mathematical analysis of ambient energy draw

[mlangsdorf]

Has anyone else tried to analyze the ambient energy draw rules mathematically?

I wrote an ugly little C program that clumsily randomly simulated a single attempt to draw ambient energy, and then reran that attempt 1000 times for a range of ambient energy draws and skill levels. Then I summed up and printed out the average number of tries to successfully draw that energy, the number of quirks, and the average number of critical fails.

Here's a summary of my results:
1. Given time, skilled casters (or casters with access to good grimoires) can pull large amounts of ambient energy safely. With an effective starting skill of 20+, the effective quirk rate is nearly 0 and the critical fail chance is less than 10%, even when drawing 150+ energy. Of course, that's a lot of time - 2 minutes for a caster using a grimoire and making 16+ attempts.

2. As long as effective skill (skill + grimoire - repeated attempt penalty) stays above 16, the average energy draw approximates starting skill + grimoire bonus - 11. That's not 100%, but it's a decent rule of thumb. So a skill-17 witch with a +4 grimoire can expect to draw 10 energy per attempt for her first 15 attempts.

3. The odds change dramatically if effective skill drops below 16. At skill 16, a caster can draw 45 energy without suffering a critical failure 90% of the time. At skill 15, the success rate is only 80% and the quirk rate triples. At skill 13, the success rate isn't much worse, but the energy will likely have 5 quirks attached to it.

Likewise, the skill 16 caster can draw 80 energy without a critfail about 80% of the time (I'd call that "within the odds of someone who has Luck available) and only have 1-2 quirks on it. The skill 14 caster will critfail 40% of the time, and even a successful casting has 13 quirks on the energy!

4. Those two facts taken together should imply something for maximum reliable safe energy draw, but I can't get a formula that matches the curve I'm getting from the data by analysis alone. Maybe I'll graph it and come back with a better answer.

5. Critical failure energy averages out to half the energy of the spell, which isn't particularly surprising. That's the mean, though, and I didn't collect histogram data so the actual distribution may be somewhat different. The key take away is that whether or not the odds favor casting a big spell, a critical failure for a big spell usually has a really big result.

Anyone else have comments or thoughts?

[PK]

It's complicated, especially considering the cumulative -1 penalty for every third attempt. That penalty is what makes the real difference between skill levels at higher levels -- e.g., not only can my skill-18 caster bring in a teeny bit more energy per attempt than your skill-16 one, but he can draw energy eight times before dropping below skill-16 as opposed to you dropping there after doing it twice.

But to answer your title question, yes, someone did -- while the RPM system was being developed, Thomas Weigel did a detailed analysis of the ambient energy potential vs. critical failure risk for each skill level. His results were far too complex to try working into a product, but I did use them for some quick-n-dirty rules that will show up in MH4, as they'll be especially useful for an application of one of the templates there.