>>56375395Here's a toy example using a type chart that only consists of Dark, Psychic, and Fighting. The first order average multipliers are in the columns labeled by a bold, underlined 1.
As you can see, the first order offensive multipliers are just the averages of each row. Fighting has the highest average, so it's in theory the best offensive type followed by Dark then Psychic.
To calculate defensive multipliers, I had to use a modified method. Bigger = better in the offensive case but in the defensive case it's the opposite. To make them agree, I took the average of each column then subtracted it from 2. So the "average" for the Dark is 7/6 instead of 5/6. Now bigger = better, so Dark is the best defensive type then Psychic then Fighting.
To get the second order averages, I took weighted averages of each row/column using the first order averages as weights (after normalizing them). So the second order offensive average multiplier for Dark is
[(7/6)*0.5 + (1)*2 + (5/6)*0.5] / [7/6 + 1 + 5/6] = 1
which is coincidentally the same as its first order average. You can see that the Psychic and Fighting ones are different however. Psychic's multiplier went down, reflecting the fact that its resisted by the best defensive type according to the first order analysis. Fighting is the opposite; its positive matchup against Dark caused its multiplier to go up.
The same ideas above can applied recursively to calculate third order and higher averages. Continued in the next post.
