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Silph Study: #039

Published:
12.27.2020

Lucky Trades: Revisiting Older Pokémon Rates

Lucky trades have now been a part of Pokemon GO for over two years (since July, 2018) and are one of the most frequently discussed features on the Road. Since the Research Group’s last article on lucky trade rates, researchers have been aging and trading their Pokémon in order to refine our understanding about how age affects lucky trade probabilities. Some of these Pokémon have even reached the four-year milestone!

Today, we’re going to take a look at the results found from more than 70,000 (socially distanced!) trades. These findings are timely with Niantic’s testing of an expanded trade radius for limited-time events over the past few weeks. A few reminders of what we already know about lucky trades might be helpful before we dive into newer discoveries.

Recap of Previous Research

Our previous research showed that friendship level, trade distance, and Gentleman and Pilot medals have no impact on lucky trade rates. In addition, lucky rates are determined by the whole-year age of the Pokémon: i.e., any Pokémon ages 0 days through 364 days (“new” Pokémon) will all have the same lucky rate, while all Pokémon ages 366-729 days (1 year old) have a higher rate.¹

Later research on lucky rates determined the mechanics of guaranteed lucky trades: July-August 2016 Pokémon are guaranteed to turn lucky if the sender has been in fewer than 10 trades (as sender or recipient) where at least one party was guaranteed. In this article, we’ve specifically excluded any trades that meet this criteria.

With these findings in mind, let’s take a look at what we’ve discovered!

Key Findings

  1. Special trades have no impact on lucky rates.
  2. There is approximately a 5% increase in the lucky rate for every year the older Pokémon has aged when trading a new Pokémon for an older Pokémon.
  3. The ages of both Pokémon impact the chances of a lucky trade.

Special Trades

One of the main questions remaining from our original lucky trade research was whether or not special trades have higher lucky rates than non-special trades. The lucky rate for trades involving two non-special Pokémon younger than 365 days (“new”) remains consistent with our previous findings at 5.02% [95% CI 4.8%-5.2%].

Silph researchers have since completed 1,201 special trades where both Pokémon were less than a year old. Of those, 68 trades were lucky, giving a lucky rate of 5.66% [95% CI 4.1%-7.5%]. From these data, it seems highly likely that special trades are subject to the same lucky rates as regular trades. That means your Pidgey trade appears as likely to go lucky as your shiny Meltan trade!

Trading One Old Pokémon

The lucky rate for trades involving two new Pokémon (i.e. any Pokémon younger than 365 days) remains consistent with our previous findings at 5.02% [95% CI 4.8% -5.2%]. As has been observed on other parts of the Road, our data supports the conclusion that in trades involving one new and one older Pokémon, the chances of having a lucky trade increases by about 5% for every year of the oldest Pokémon’s age.

New Traded With: Total Number of Trades Lucky Trades Lucky Trade % 95% CI
New 69,209 3,472 5.02 [4.8, 5.2]
1 Year Old 1,779 192 10.79 [9.0, 12.8]
2 Year Old 935 152 16.26 [13.3, 19.5]
3 Year Old 1,290 269 20.85 [18.0, 23.8]

Trading Two Old Pokémon

What happens when both of the traded Pokémon are one year old or older? In 515 trades over the past year (excluding trades during the 2020 Lunar New Year event), results indicate that the lucky trade rate for two Pokémon that are both one year old (366-729 days old) is 15.95% [95% CI 12.1%-20.4%]. This is a significantly better rate than the ~10% rate observed for trades where only one of the traded Pokémon was one year old (p-value=0.0015). We can therefore conclude with some confidence that the ages of both Pokémon are taken into consideration when determining the lucky trade rate.

Looking Forward: A Synthesized Model

Tantalizingly, the lucky trade rate when swapping two Pokémon that are both one year old is remarkably similar to the lucky rate for trades involving one new and one two-year-old Pokémon (~15%). Could it be that the base lucky trade rate for two new Pokémon is approximately 5%, and that the lucky trade rate increases by around 5% for each full year either Pokémon spent in their original trainer’s storage? This is perhaps the simplest possible model fitting our observation about trades of two one-year-old Pokémon, and is shown in red on the graph below (the uppermost of the three dashed plots on the graph). The black dots on the graph show the lucky rate in our data as a function of the combined age of the traded Pokémon; the vertical error bars represent a 95% confidence interval.

However, there are two problems.

Firstly, in trades involving a two-year-old Pokémon swapped for a three-year-old Pokémon (total age of five years), just 33 of the 164 trades (20.12%) have been lucky [ 95% CI 14.0%-26.3%]. Although this is a small sample size, this is nevertheless an unlikely event (with a probability of just 0.07%) if the true rate for these trades were 30%. This indicates that lucky rates likely do not simply increase at 5% per combined year of age. Secondly, although it will be a long time before trainers have 10-year-old Pokémon to swap for one another, it nevertheless seems plausible to us that Niantic chose a formula that does not require readjustment once lucky trade rates start to exceed 100%.

We raise two alternatives. One possibility is that lucky trade rates are already capped, perhaps at 20%. This is shown in blue on the graph above (the horizontal dashed line). As we accumulate more data from trades with a combined age of five to six years, we expect to gain a clearer understanding of whether or not this potential model fits best.

Another possibility is a model in which the probability that a trade is not lucky decays exponentially with age; in other words, where the probability that a trade is not lucky is multiplied by 95% for each combined year of the traded Pokémon’s ages. The advantage of such a model is the probability that a trade is lucky never reaches 100% (that is, the probability that a trade is not lucky never reaches 0%). The same sort of formula is used in the catch mechanic. This possibility is shown in green on the graph (the middle of the three dashed plots), and is not unreasonable relative to the confidence interval for our 5-year data. The benefit of this type of formula is that it does not require Niantic to make readjustments as older Pokémon become available for trade.

More research will be required to determine a synthesized model of lucky trade rates. We will continue to investigate, and we welcome anyone interested in contributing to our research to join us in the Lab!

Parting Words

We hope that you’ve enjoyed this update on lucky trade mechanics. Lucky Pokémon will continue to be one of the best ways for travelers to obtain species with cheaper power-up costs for the foreseeable future. So dig through your storage to find any unneeded geriatric Pokémon hiding there, and complete some trades with your friends! See you on the Road!


Acknowledgements

Authors: Scientists Cham1nade and Titleist,  Lead Researchers NSM and Paleshadow
Analysis: Scientists PiFlavour and Titleist, and Lead Researcher Paleshadow
Graphics and data presentation: Scientists Titleist and WoodWoseWulf
Editing: Scientist skyeofthetyger
Project Leaders: NSM, Cham1nade, Paleshadow, and aniwol
Data collection: 179 Researchers

Footnotes

¹ We excluded Pokémon exactly on the cusp of the year change from our analysis, since we are unsure of precisely where Niantic puts the breakpoint, and it would be prohibitively difficult to collect enough data from Pokémon precisely 365 or 730 days old.