When the medal bonus was first announced, we went out and took screenshots of Pokemon and to see if we could estimate the amount of the bonus from the color of the capture ring. Unfortunately, we found that the color of the capture ring is not affected by medals. This result is in line with other research on reddit.

Because of this, we decided that the next easiest thing to do would be to hand collect data using the Pokemon GO Plus. This ensures that no other factors would contribute to the data, since the GO Plus only throws Poke Balls with no other multipliers. About half of the data points come from redditor /u/Spidertotz (thank you!), while the other half was collected by GamePress researchers. We have 1147 data points in total, 1053 of which are for the 3-medal bonus.

Before using this data to test the effect of medal bonuses, we first needed to verify that medals affect the catch rate of the Pokemon GO Plus. To do this, we calculated the expected catch rate using a Pokemon GO Plus prior to the medals update:

$$x=\frac{BCR}{2*CPM} $$

Then, we restricted the data to only those where the 3-medal bonus applies. For all catch rates that had a sample over 15, we calculated the difference in the actual probability of capture and the predicted probability of capture without modifiers. As you can see from the scatter plot below, for most of the capture rates, the observed probability of capture was higher than the predicted probability.

To test if this was statistically significant, we ran a series of one tailed binomial tests. For 8 out of 29 of these tests, the observed probability of capture was statistically higher than the calculated rate without modifiers. This leads us to conclude that medal bonuses do in fact increase catch rate on the Pokemon GO Plus.

Once we established that the GO Plus data does indeed include medals, we tried to estimate the value of the gold medal multiplier. Our fitted data shows the gold medal multiplier as

$$Medal = 1.339 \pm 0.031$$

Like in the curveball analysis, the independent variable was chosen to be the simple Poke Ball capture rate, $$x=\frac{BCR}{2*CPM} $$

where x cannot exceed 1 (and is otherwise rounded down to 1).

1.3 is quite a reasonable guess for the actual bonus, which has always been a single-decimal number for the flat bonuses we've found in the past. Note that the +/- shows the 1-sigma interval caused by lack of sample size, so the actual number need not be in the interval. There is rounding error because our Poke Ball catch probability only had two decimal places, which is not incorporated into the graph or best fit value.

Let's see how this hypothesis fits the curve: if it is correct, the black line (GUCT theory with Medal = 1.3) should match with the red dots (actual catch percent for that bin) within error about 68% of the time, since the bars show one standard deviation = sqrt(nCatchSuccesses):