Earlier this year, the brand new Buddy Adventure feature was released, giving you more ways to connect with your most beloved and strongest Pokémon. Buddies can now follow you around the game map, and a host of new perks can be unlocked. One of these perks is the ability to find items, delivered in the form of Presents, from Buddies who have reached the Great Buddy level. Diligent researchers have recorded the contents of over **2,500** Presents since the feature’s release, creating a one-of-a-kind dataset to put Present contents under the microscope. Let’s take a closer look at what we’ve discovered!

#### Available Items and Probabilities

Researchers were quickly able to determine that **5** types of items are available from Presents: Razz Berries, Nanab Berries, Pinap Berries, Revives, and Hyper Potions. The proportion of Presents that contained each of these items are shown in the table below.

Item | Proportion (n=2,552) |
Relative Weight |
---|---|---|

Razz Berries | 32.1% | 2 |

Nanab Berries | 17.9% | 1 |

Pinap Berries | 16.1% | 1 |

Revives | 16.9% | 1 |

Hyper Potions | 17.0% | 1 |

These data give strong support for a simple model that assigns a ratio of 2:1:1:1:1 for each item type’s probability (Chi-squared *p*-value = 0.35). The effects of Pokémon species and Buddy level on item type were also investigated, but no significant results were found.

#### Bundle Sizes

The second piece of the puzzle was the number of items a Present can yield. We found that Presents have a minimum number of items inside. Presents containing Berries have a minimum of 7 items¹, while Presents containing healing items have a minimum of 2. All item types have an equal probability of giving additional items on top of the minimum, which we’ll call the “Base” number of items. The table below shows the counts and probabilities of each bundle size relative to the Base items.

Size | Observed Counts |
Observed Probabilities |
Theoretical Probabilities |
---|---|---|---|

Base | 1,003 | 39.3% | 41.2% |

Base + 1 | 1,200 | 47.0% | 45.5% |

Base + 2 | 325 | 12.7% | 12.6% |

Base + 3 | 22 | 0.9% | 0.7% |

Base + 4 | 2 | <0.1% | <0.1% |

We first tried to fit the observed probabilities to weighting ratios (as was done above for item types), but no simple relationship fit the data. Next, we hypothesized that the distribution of bundle sizes might be drawn from a probability distribution, as the shape appears similar to many common probability density functions… let’s dig further.

After testing several functions², we found that a modified normal distribution does an excellent job at describing these data. Because the normal distribution is a continuous distribution, we reasoned that the server must be rounding the sampled values to the nearest whole number. After setting the value of “Base” to 0, we find that a normal distribution (with any negative values set to 0) with a mean of **2/3** and a standard deviation of **3/4** fit the data well (Chi-squared *p*-value = 0.22). Below is a graph to visually illustrate what this model describes. The area of each shaded regions corresponds to the probability of receiving additional items.

Along with the fit, the simplicity of these parameter values gives us confidence that this is indeed the correct model being used.

#### Parting Words

While the Present feature is a simple, fun way to interact with your Pokémon, we hope you found it interesting to take a peek behind the curtain and see what makes this feature tick. Our next article in this series will shed light on the Souvenirs that your Ultra Buddies bring you. Until then, travelers, stay safe on the Road!

###### Footnotes

¹The minimum number of Berries was previously 5, but was increased to 7 around March 12th.

²Poisson, gamma, and binomial distributions were also tested. None gave a sufficient fit to the data for any parameter values.