"Interpreting the Grand Unified Catch Theory by Gamepress"

#PokemonGO: TL;DR (1) Always do curveballs, (2) If you succeed at Excellent throws less than 64% of the time, you are better off trying to do Great throws instead, (3) If you succeed at Great throws less than 33% of the time, you are better off trying to do Nice throws instead.Following this initial thread by /u/q_e_dSSB discussing a new Gamepress post, I decided to transform what started as a comment into a post because it is starting to get huge.First of all, let me give you my interpretations of Gamepress' results if I accept them at face value. I compiled the throw bonuses in a table that makes all of this easier for me to interpret. A few take aways:Throwing a curve ball is super important. A curved pokeball is equally strong as a straight Ultra ball (both are equivalent to throwing 2 pokeballs at once).The difference between a "Great Curveball" and an "Excellent Curveball" is not that large (the latter is only 20% better).Suppose a scenario where you always try to hit an "Excellent Curveball", and you succeed a fraction of the time that we'll call "S". You are throwing the equivalent of 3.1 balls at once when you succeed, or 1.7 balls when you fail (that's what you get from the curveball alone). You end up on average with a bonus of S x 3.1 + (1-S) x 1.7. If you simply abandon this idea and just throw lazy "Nices", you will get a factor 2.0, probably most of the time. Now, the interesting part: Unless you have S > 21% (i.e., you succeed at least once out of 5 throws), you are better off always doing "Nice" throws.A similar calculation comparing "Excellent" to "Great" throws reveals that it is better to systematically throw "Great" bonuses (assuming you always succeed) than aiming for "Excellent" unless you succeed > 64% of your excellent throws.Now comparing "Great" to "Nice"; you are better off just aiming for "Nice" throws unless you succeed > 33% of your "Great" throws.I was surprised that Gamepress do not find an improvement with smaller color ring sizes unless the ball hits inside the colored ring. I was surprised and flattered to see that they compared their simulations to my figure based on RhyniD's data. I see it as a reasonable possibility that I found f = 1.7 when including all throws because of the curveball bonus, although I would have naively suspected to find a slightly smaller value unless most of RhyniD's data are curveballs (I don't this this information was included in the data set). That being said, 25/40 (63%) of the throws with a radius > 0.7 in RhyniD's dataset also had a "Nice" bonus, so if all the throws were curve balls we could have expected a value closer to 1.15 (Nice) x 1.7 (Curve) = 1.955. If I make the simplistic assumption that the average of all individual throws' "f" factors give rise to this value of ~1.7 for the plateau, it would be fully consistent with a fraction of ~78% curveballs (~156 out of the 200 throws) in RhyniD's data set. Taking all of this into account, the value of the plateau may well be fully consistent with their results.At first I had dismissed a "physical" interpretation to the plateau shape at R > 0.7 by interpreting this as a lack of data above R = 0.7, but that may have been simply wrong, as there are 40/200 (20%) of the throws above this threshold in RhyniD's data. It actually seems consistent with a lack of an improvement as a function of radius at R > 0.7. This may provide a hint that different radii without "Nice/Great/Excellent" bonuses have no effect on catch rate, and that different radii sizes may also have no effect within all possible "Nice" throws (i.e., fractional radius between 0.7 and 1.0). That being said, my plot may be consistent with these hypotheses, but it does not prove them to be true in a very efficient way; the 68% confidence level (blue region) at R > 0.7 is large enough that it could hide true variations anywhere between f~1.6 and ~1.8.There is also more comparison that can be made between their analysis and mine, using this second plot from my original post, which displays "No bonus" and "Nice/Great/Excellent" bonuses separately. If they are right that "No bonus" throws do not gain anything from different color circle radii, then the blue curve in this plot should be a horizontal line. The blue line seems to show some improvement at R < 0.7 even when the ball hit outside of the color circle, but the statistical evidence is very weak there, since the 68% confidence region is almost entirely consistent with a horizontal line (e.g. you could place a straight line at f ~ 1.8 and it would mostly be located inside the blue shaded region).The red curve in this plot is super wiggly as a function of radius, and this is probably due to the low amount of data (the 68% confidence level is super large), but counting all throws in the two separate (blue/red) samples would be consistent with an fractional improvement of 1.125 ± 0.23 (because f converges at 1.8 ± 0.3 for the red curve, and 1.6 ± 0.2 for the blue curve), and from the analysis of gamepress one would expect a factor 1.15. The differences in the red and blue curves are thus surprisingly consistent with what gamepress are finding despite the awfully weak statistical significance of my results (i.e., because it's based on only 200 throws).All in all, I was surprised to see some of these results by gamepress, but upon closer inspection I agree with them that there is nothing inconsistent there. The only claim that leaves me skeptical there is this one :While this may seem less certain than our analysis for previous multipliers, what we are quite confident of from our data is that ordinary throws where the ball hits outside of the ring always has a multiplier of 1.I would have liked to see how the data supports this, and how strong the statistical significance is. Especially since this is actually one of the most important conclusions from their analysis, as it directly impacts decision making when throwing balls. via /r/TheSilphRoad http://ift.tt/2evGR8t