Hello ! If you want the detail of the analysis, read below, else feel free to scroll down to the TL;DR at the end !
A few days ago, I read a post on this sub written by u/Jepemega, in which OP tried to identify the new lucky interaction rates. This immediately prompted me to start recording my own data to see if I could confirm what OP found.
OP recorded 200 interactions, including 6 lucky ones. I've added to that a total of 717 interactions over the few days, including 24 lucky ones. The full dataset can be found here for anyone curious. Every day, at the end of the day, I identified people with which I interacted using "!interactable & friendlevel4" in my friendlist. I've only interacted using gift sending and opening, there is no battle or trade involved, as we know the lucky interaction rate is variable by type of interaction. I've also stratified the interactions by the level of my friend : each day, I've counted interactions with friends with a level strictly below 70 and above or equal to 70. Indeed, the recent update introduced an increase in the lucky interaction rate starting at level 70 – thus this post. I believe I've gathered sufficient data to figure out the new interaction rate, and the impact of the friend level (if you're already 70, as I am).
So, if you read above, we have a total of 30 lucky interactions out of 917 : using this dataset, we have a rate of 3.27 % when you're level 70. For reference, a previous TSR analysis of 41,445 interactions through gifts opened identified a lucky rate of 1.12 %, with a 95 % confidence interval (CI) of [1.02-1.23%]. This suggests that the recent updated tripled the lucky interaction rate for trainers with a level ≥70.
Now, this is the estimate, what about the CI ? For that purpose, and to verify the certainty of the estimate, I've performed a proportion test (prop.test in R), with as arguments a base probability of 2.24 % (the null hypothesis is that the lucky interaction "only" doubled), a confidence level of 0.95, and as alternative hypothesis "greater" (we suspect that the probability has more than doubled). The script used can be found here.
With a null probability of 2.24 %, the estimate is indeed 3.27 %, with a 95 % CI of [2.39-100%]. The p-value is 0.02279 : this means that there is a probability of 2.279 % to observe our dataset or a more extreme one (30 lucky out of 917 interactions) under the null hypothesis, that is, with a probability of 2.24 %. This p-value is sufficiently small to reasonably exclude the null hypothesis. In addition, the 95 % CI is strictly above the null probability of 2.24. Altogether, these results suggest that the lucky interaction rate has more than doubled, probably tripled, for trainers with a level ≥70. For what it is worth, my personal experience reflects the announced lucky rate increase : I now have trades planned for the next three weeks, whereas before the update it was a matter of only a few days.
All right, at this point we're happy, many lucky Pokémon ahead, but there is still a question : is the probability of lucky interactions even more increased when the two players are level 70 and above ?
To answer that, I've used a linear mixed model including as a fixed binomial variable the friend level (70 and more, or below 70), and as a random categorical variable the account (OOP's and mine two, MikeRobiote and Protozorreur). Again, the script can be found here. This mixed model outputs a very low estimate (0.19), alongside a very high p-value (p = 0.626), for that fixed binomial variable. This means that there is probably no effect of the friend level on the lucky interaction outcome.
All right, what does it mean practically ? Here is some translation of this statistical talk : if we admit that 3.27 % is the new lucky interaction rate, using a binomial law, we can calculate how many interactions are needed for at least one lucky interaction. We can use 50%, 95% and 99%, which roughly translates into "How many interactions are needed for having at least one lucky interaction for [50%/95%/99%] of people ?". The respective numbers are 21, 91 and 140. This means that only the unluckiest 1 % of players won't be lucky with their friend after 140 interactions (say 5 months if daily interaction), while it takes on average 21 interactions to get at least one lucky one.
I think that this analysis is sufficient to infer, with reasonable certainty, three key points. This will be the TL;DR below.
TL;DR :
1. The recent update probably tripled the lucky interaction rate, increasing from 1.12 % to 3.27 % for trainers above level 69 according to this analysis.
2. There is apparently no further boost for having the two interacting trainers above level 69, only one is enough.
3. It now takes on average 21 interactions to have at least a lucky one, and most (99 %) people will have at least one lucky interaction after 140 interactions – if at least one player is 70+ !
Some limitations in that approach : it would have been better to have some data coming from accounts below level 70. All three accounts used here were indeed level 70+. In addition, we only used gift-based interactions : the lucky interaction rate may be different for other kind of interactions. Finally, one can argue that 917 interactions is still low, and I can only agree : feel free to reach me so we can increase the sample size !
Feel free to comment, correct, or discuss this analysis ! Personally, I'm becoming overwhelmed with all these lucky friends, and I look forward to next season, when I hope the number of special trades per day will double !
by Kangouwou