"[Research] The effect of the colored ring size and "Nice", "Great", "Excellent" throws on capture rate"

#PokemonGO: So I've been lurking here for quite some time and have gained a lot of knowledge from the fine research that's taking place. About time I contributed some my self :). Afaik no-one ever really tackled the "what's the meaning of the size of that colored circle?" question. So here's my attempt! What we know for sure is Niantics famous quote "You have the greatest chance of capturing the Pokémon while the colored ring is at its smallest diameter." There has been some work done like this post and some claimes made with bot data like in this analyses, but I wanted to more detailed answers to those questions without breaking the TOS and use data generated by real people. I'm by no means a statistician, but I gave it my best shot. Questions:Does the size of the colored circle influence the capture rate?Does Scoring a "Nice", "Great" or "Excellent" influence the capture rate? Gathering the data:Get 200 capture attempts and measure:Theoretical Capture RateColored ring radius size (as a percentage of the white ring radius size)If a "Nice", "Great" or "Excellent" was obtainedIf the capture attempt was successfulI used jdero awesome 24h 1M xp attempt (He would have made it if he didn't get softbanned, I'm sure!) to obtain my samples. With each throw I took a screenshot and measured in paint.net the radius of both the white and colored circle and sampled the color of the colored circle. Thanks to the nice work in this post we know the correlation between circle color and Theoretical Capture Rate (TCR). After sampling the ring color, I maxed the "value" in the HSV color model (hue, saturation, and value) and used the Red and Green channels from the obtained color code to calculate the TCR.So I didn’t measure curve-balls. I really wanted to, but I didn't find any good way of measuring a curve-ball on a failed capture attempt. I also didn’t keep track of berries used because only a couple were used which is not enough to draw any conclusions.Now at this point you might ask why I didn’t keep track of which capture ball was used, but switching capture balls influences the circle color, so that’s already done for me :) Validating the Data:First I checked my radius measurements. I did this by checking if every “Nice” had a radius > 0,7, “Excellent” had a radius < 0,3 and “Great” had a radius in between those two. Only 1 measurement was of by 1%, so I’m pretty confident there’s not too much noise in those measurements.Next I checked if the captures that are supposed to be difficult are actually being captures less than the easy ones.-Group 1Group 2Group 3Group 4Group 5Group 6Group 7Group 8Group 9Group 10Theoretical Capture Rate0-10%10-20%20-30%30-40%40-50%50-60%60-70%70-80%80-90%90-100%Observed Capture RateN/A20%42%51%67%56%87%100%100%100%Sample Size0531794016152210Ok, some inconsistencies, but most likely due to small sample size. Yes, the Observed Capture Rate (OCR) is higher than the TCR, but that’s a good thing :)Finally I checked what would happen with the average OCR if I would randomly divide the samples in two groups. I did this a couple of times and found that a difference of 5% can easily be attributed to randomness.-Random split 1Random split 2Random split 3OCR group 156%56%60%OCR group 261%61%56%All in all, the data looks fine. Sure, not every scenario is represented equally, but good enough to continue. ResultsPhew… now that all the boring stuff is out of the way, we can finally look at some results! First let’s have a look at the radius. To do that I divided the samples into 5 groups based on radius. So sort all samples on radius, take the first 40, put them in group 1, put the next 40 in group 2, etc. You end up with 5 data point that I plotted on the graph (blue series) which shows the relation between the radius and the Observed Capture Rate (OCR).Now this influence of the radius on the OCR might be different for hard to catch mons. So first I calculated the average Theoretical Capture Rate (TCR) for all 200 samples which turned out to be 43%. To see if it’s different for other TCR’s, I first took the 100 samples with the highest TCR and divided them in 3 groups (red series) the same way I divided the blue series. And then took the the 100 samples with the lowest TCR and also divided them in 3 groups (yellow series). There average TCR is 54% and 31% respectively.effect of radius on different OCR & TCRThen to try and answer my second question I compared all bonus samples with samples that don’t have a bonus (A bonus is “Nice”, “Great” or “Excellent”).-BonusNo BonusSample size89111OCR62%56%To visualize a radius trend in the two groups I again divided both the Bonus and the No Bonus samples up in 3 groups each. So in the first bonus group there would be about ⅓ of the bonus samples with the smallest radius, etc.effect of radius on bonus and no bonus attemptsFinally I also dabbled a bit in statistics by calculating the correlation between radius and OCR from the No Bonus group, which turns out to be -0,16 DiscussionSo what does it mean? Let’s first look at the radius question. Radius:After splitting up the data many ways, one trend is clear, the smaller the radius, the bigger the Observed Capture Rate (OCR). It kinda looks like having a radius of 1 will give you no bonus (With the OCR being equal to the TCR) and a linear bonus for when the circle gets smaller. It also looks like the increase in % is smaller for a high TCR than a low TCR. This points in the direction of a multiplication modifier and not a constant that is being added. My best guess for the multiplication modifier would be about 2.0. So a linear progression between X1.0 and X2.0 for the radius being 1 and 0 respectively. This is definitely in line with what Niantic has said, with the addition that you don’t need to throw in the circle (no bonus required) to obtain the modifier. “Nice”,”Great”,”Excellent”:There might not be a higher OCR when getting a bonus and if there was, it's not very high. Although it would make sense from a game design point of view, with these samples the difference in OCR between getting a bonus and not is only 5%. And that 5% could very well be random noise. More data is needed, so I'm not sure. Future workIt would be nice to get some more data so we can get a better read on the exact increase in OCR for different radius sizes. But as you can imagine it’s fairly labor intensive work, so a collab seems to be the best solution. Here is a link to all my data that is stored in the famous “What the heck am I looking at” format. If more people like to contribute, send me (a link of) your data and I’ll combine it and make a nicer looking sheet. :)Also, figuring out how to measure curve-balls with non successful attempt would be a boon. ConclusionA smaller radius has a significant effect on your capture chanceThe smaller your radius, the bigger your capture chanceYou don’t need to get a “Nice”, “Great” or “Excellent” to get the increased capture chance (from the radius)There doesn’t seem to be any increase in capture chance from getting a “Nice”, “Great” or “Excellent”, and if there is, it’s a small increaseSpeculation: You might have a X2.0 modifier on your capture chance with the smallest possible circle as opposed to no modifier with the biggest possible circle. via /r/TheSilphRoad http://ift.tt/2bRNfpj