[quote=Vyrlokar]I’m grinding an overgoat too, and I’ve found that the most lucrative thing to do right now is this little story. Check my sig for my numbers. I’m currently at 18 brilliant Souls, having spent 1415 actions, and 1307 echoes worth of goods, for a total benefit/action of 3.05159010600707 echoes/action (2.19035176403603 echoes action once you take into account the actions needed to grind the materials, instead of their cost) [The link at my sig is constantly updated thanks to Google Docs magic]. With my percentages, it’s worth following the story until the end.
Current success percentages:
Tale of Terror->Sense of Deja Vu: 72.5738396624472%
Sense of Deja Vu->Glimpse of something larger: 72.6726726726727%
Glimpse of something larger->Deal with a Devil: 74.8936170212766%
Deal with a Devil->A Room Number at the Royal Beth: 61.9318181818182%
A Room Number at the Royal Beth->The Last Hope of a Fidgeting Writer: 50.4587155963303%
The Last Hope of a Fidgeting Writer->A Lens of Black Glass: 60%
A Lens of Black Glass-> Coruscating Soul: 54.5454545454545%
Given the data on my sig, could any armchair statistician calculate the confidence intervals and standard deviation for these percentages? Been a while for me.
edited by Vyrlokar on 4/8/2012[/quote]
My numbers for 1200 Tales are somewhere on Page 3. In short, I’m gonna combine the combined numbers in your sig, with mine, and I’ll figure out the 95% confidence intervals for individual conversions. In English, that means I’m gonna do some magic, and tell you 95% of the time, your probability of success (given enough attempts) should fall somewhere in this range.
If you want the sum of conversions, multiply the probabilities together. If you want the confidence intervals for the sum of conversions, a quick way would be to find the sum of all the relative uncertainties (the uncertainty, divided by the value itself), and multiply it by the actual sum. I’m not sure whether that’s the best way of doing it, so I’m using basic error propagation techniques I learnt in the science labs.
Tales → Senses: 72.182±0.95%
Senses → Glimpses: 71.246±1.13%
Glimpses → Deals: 70.882±1.46%
Deals → Numbers: 62.038±1.85%
Numbers → Hopes: 53.771±2.41%
Hopes → Lenses: 53.907±3.29%
Lenses → Coruscating Souls: 57.263±4.45%
The total probability, from Tales to Souls is the product of all the raw probabilities, which is 3.754%. The total fractional uncertainty is 26.3%, which means that 95% of the time, the number of Coruscating Souls you should get is 3.754±0.987% of the number of Tales of Terror you started with.