Pokemon Level Report
Objective
Evolution within the Pokemon franchise has been a staple part of the games. With more innovation within the games, the methods of evolution broaden. However, an evolution method that stays the same each iteration is via level up. This study will identify whether later generation games have higher averages to evolve Pokemon. Applications to this study will be part of the baseline when discussing difficulty changes between each game.
Methodology
The data for this analysis comes from Bulbapedia, denoting every evolution-method Pokemon with the level they evolve. The Pokedex number for the pre-evolution form will be the number for assigning which generation the Pokemon belongs to.
Specifically, the cutoff Pokedex numbers for each generation will be as follows:
| Generation Number | Ending Pokedex Number |
|---|---|
| 1 | 151 |
| 2 | 251 |
| 3 | 386 |
| 4 | 493 |
| 5 | 649 |
| 6 | 721 |
| 7 | 809 |
| 8 | 905 |
| 9 | 1025 |
A new vector is created regarding these cutoffs in order to categorize each observed Pokemon into their respective generations to model the data separately.
Distribution of Each Generation
Below are the distributions of each generation’s Pokemon evolution levels. It should be noted that many distributions have shapes that are symmetrical or skewed positively. The only exception is Generation 6, which is skewed negatively.
Average Evolution Level in Each Generation
To track the average evolution level of each generation, the previous categorization is taken another step further to which the mean is taken for the Level vector. Below are the averages for each generation rounded to the nearest thousandth place:
| Generation Number | Average Evolution Level |
|---|---|
| 1 | 27.387 |
| 2 | 25.684 |
| 3 | 28.140 |
| 4 | 27.324 |
| 5 | 35.839 |
| 6 | 32.033 |
| 7 | 29.933 |
| 8 | 29.200 |
| 9 | 28.935 |
Because the generations are sequential, a time series can be plotted with each generation being a different point of time. We can see a positive relationship below with our original regression:
Average Leveli = β1 + β2 * Generationi + ei
Creating a Robust Model
Finding Issues in the Model
By itself, the generation does not have a significant effect on the evolution level at the 95% significance level. The full results are presented below:
===============================================
Dependent variable:
---------------------------
`Average Level`
-----------------------------------------------
Generation 0.417
(0.385)
Constant 27.300***
(2.166)
-----------------------------------------------
Observations 9
R2 0.144
Adjusted R2 0.021
Residual Std. Error 2.982 (df = 7)
F Statistic 1.175 (df = 1; 7)
===============================================
Note: *p<0.1; **p<0.05; ***p<0.01As such, more variables will need to be added in order to explain the model further.
However, before adding more variables, other tests need to be conducted to pinpoint any of the following issues: functional form and heteroscedasticity. The original model appears to be sufficient at the 95% significance level with its lin-lin form and its satisfactory variance, passing both the RESET and Breusch Pagan Test, as shown below:
RESET test
data: model1
RESET = 1.5384, df1 = 2, df2 = 5, p-value = 0.3015
studentized Breusch-Pagan test
data: model1
BP = 0.006581, df = 1, p-value = 0.9353Fixing Issues in the Model
To create a more accurate regression model, another variable will be added. Over years of innovation, more Pokemon evolution methods have been created, lessening the dominance of strictly level-up evolutions. As such, this robust model will include the amount of Pokemon in each generation that evolve via level-up. After implementing this new variable, Amount, the effect that both of the independents have become different to become significant in the model at the 10% significance level. The new regression and results are shown below, now including the test for multicollinearity:
Average Leveli = β1 + β2 * Generationi + β3 * Amounti + ei
===============================================
Dependent variable:
---------------------------
`Average Level`
-----------------------------------------------
Generation 0.984*
(0.420)
Amount 0.165*
(0.080)
Constant 17.615**
(5.026)
-----------------------------------------------
Observations 9
R2 0.499
Adjusted R2 0.332
Residual Std. Error 2.464 (df = 6)
F Statistic 2.986 (df = 2; 6)
===============================================
Note: *p<0.1; **p<0.05; ***p<0.01
RESET test
data: model2
RESET = 3.1571, df1 = 2, df2 = 4, p-value = 0.1504
studentized Breusch-Pagan test
data: model2
BP = 2.0924, df = 2, p-value = 0.3513df$Generation df$Amount
1.745311 1.745311 Findings
While the generation and amount of Pokemon that evolve via level-up both show clear positive relationships with the average level of evolution at the 10% significance level, they are still not enough to explain the majority of the model. Several aspects of game design and creative freedom as a whole are likely more reasonable factors to why there are differences between levels that Pokemon evolve at. With only two variables, 49% of the variation is actually explained, suggesting that more complicated variables are needed for the regression.
Conclusion
Pokemon games are diverse when it comes to raising digital creatures. In terms of changing forms through evolution, having a high enough level to evolve is a staple to the franchise. As time passes, more evolution methods are introduced as well as different numbers of Pokemon being introduced. This causes the focus to be less towards level-up evolutions. As such, the more time that passes and the more Pokemon introduced that evolve in this way, the higher the levels that dictate when these Pokemon change forms.
Looking towards other variables that might have causal impact, typings of the Pokemon in question may seem to be a good alternative, as Dragon types typically have high levels of evolution. But because of different type combinations and other story factors within the games, this would be too complex to implement.
References
List of Pokémon that evolve at or above a certain level. (2026, June 13). Bulbapedia, the community-driven Pokémon encyclopedia. Retrieved 22:33, July 13, 2026 from https://bulbapedia.bulbagarden.net/w/index.php?title=List_of_Pok%C3%A9mon_that_evolve_at_or_above_a_certain_level&oldid=4571461.