User blog:BunsenH/Ghazt Stats Phase 3: Wishing Torches - Final Report

So. After a lot of work breeding Entbrat + T-Rox to get Ghazts, using different numbers of Wishing Torches, we have:

Which means..?

The really quick answer is that the base probability of success is (1.01 ± 0.24)%, and each torch boosts that by (1.033 ± 0.041)%. Please remember that these numbers apply only to that specific breeding combination. We don't know about the odds of breeding other Ethereals, and we don't know about other combinations being used to breed Ghazts.

If you'd like to know how we got those numbers, keep reading.

We can plot those numbers on a graph, and get something like:



We have the number of torches across the bottom of the chart, which is often referred to as the x axis. And the success rate going up the side, often referred to as the y axis. The general idea is that you can look across the x axis to find a value that you like, and then look up the chart to find the value that corresponds to it -- that is, that the y value depends on the x value.

The five data points are drawn in blue. Each data point also has a kind of capital-'I' shape drawn on it in black. They are referred to as "error bars". They show the uncertainty of each point, from the table above. The first two points have very small error bars; the other points' bars are somewhat larger.

There is also a straight line that (more or less) goes through those points. There's a bit of a problem, as you can see: those points aren't quite in a straight line. Choosing the best line, the one that most closely matches the points, can be tricky. There are many ways of calculating such a line, and the "best" version depends on the purpose of the chart. I'll go with the basic "linear regression" line (I'll give the equations later), which gives me:

Success Rate = 1.033% * (# torches) + 1.01%

The slope of the line means about what you might expect. A line with a small slope runs nearly horizontally; a line with a high slope value runs at a steep angle from the horizontal. There's a mathematical definition too: the slope is calculated from the amount a line changes vertically divided by the amount it changes horizontally. In this case, that means a change in the success rate divided by a change in the number of torches. Here, the slope is 1.033 -- that is, for each additional torch, the success rate increases by 1.033%.

Another term that's used in graphs is the intercept. That's the y value of the line at the point where it crosses the y axis... that is, where x (the number of torches) = 0. Here, the intercept is 1.01%.

As for describing how well the line fits the data points, there are lots of ways. I'm going to go with the one that I learned in my chemistry classes, which gives uncertainties in the slope and intercept. The calculations are a bit ugly but I'll give them later. They give me: slope = (1.033 ± 0.041), intercept = (1.01 ± 0.24). The uncertainties are relatively small, a tribute to a large data set. And to the work of the "minions", without whom none of this would have been possible.