Estimated Evolution Levels

Contents

• Description of how evolution levels are estimated
• Tables with all estimated evolution levels by generation

Algorithmic estimation of evolution levels

For any level-up evolution (evolution that always happens at a specific level), the estimated evolution level equals the evolution level.

For any evolution that is not a level-up evolution, an evolution level is estimated from all level-up evolutions in the loaded ROM via the following algorithm.

Definitions

For a given level-up evolution “X → Y” at level lvl_XY, where X has a Base Stat Total (BST) X_bst and Y has a BST Y_bst, the level-up triplet of this evolution is defined as:

(X_bst, Y_bst, lvl_XY)

For example, in Generation 1, the level-up triplet for “Bulbasaur → Ivysaur” would be:

(253, 325, 16)

The set of all level-up triplets for all level-up evolutions is called samples.

For a non-level-up evolution, where the BST before the evolution is targetPreBST and the BST after the evolution is targetPostBST, an evolution level is estimated as follows:

Initialization

double p = 1;                  // distance weighting exponent: 1/d^p
double preFactor = 1.5;        // scaling factor for pre-evolution BST difference
double postFactor = 3;         // scaling factor for post-evolution BST difference
double largeWeightForZero = 1; // weight to use if distance is zero

Furthermore, let weightedSum = 0 and weightSum = 0.

Algorithm

For each level-up triplet (samplePre, samplePost, sampleLevel) in samples:

1. Compute the euclidian distance between the sample’s (samplePre, samplePost) pair and the target’s (targetPreBST, targetPostBST) pair. The smaller this distance, the more similar the evolution is to the target.

   double dx = targetPreBST - samplePre;
   double dy = targetPostBST - samplePost;
   double dist = Math.sqrt(dx * dx + dy * dy);
   

2. Assign a weight to the sample.

   • If the distance is zero, use largeWeightForZero.
   • Otherwise, use 1 / (distance ^ p) so that closer samples have higher weight.

3. Compute scaling factors scaledPre and scaledPost for how the target’s BSTs compare to the sample’s BSTs.

   • The preFactor and postFactor values control how much influence these differences have. postFactor is chosen larger than preFactor such that BST differences in the post-evolution species have a greater influence.

     double scaledPre = Math.pow((double) targetPreBST / samplePre, preFactor);
     double scaledPost = Math.pow((double) targetPostBST / samplePost, postFactor);
     

4. Adjust the sample’s evolution level by multiplying its level with the average of the two scaling factors.

5. Add the weighted contribution of this adjusted level to the totals:

   • Add (adjustedLevel * weight) to weightedSum.
   • Add weight to weightSum.

Final Computation

After all samples are processed, compute the estimated evolution level as the weighted average:

estimatedLevel = round(weightedSum / weightSum);

Summary

This algorithm performs a distance-weighted interpolation or extrapolation using all known level-up evolutions. It estimates the evolution level of non-level-up evolutions based on how their Base Stat Totals compare to those of known evolutions.

• Evolutions with BST pairs closer to the target have stronger influence.
• The post-evolution difference between the sample’s and the target’s BSTs has a stronger influence than the pre-evolution difference between the sample’s and the target’s BSTs.

Estimated Evolutions Levels

Following are the estimated evolution levels for each evolution in the respective generation.

• Generation 1 (Red/Blue/Yellow)
• Generation 2 (Gold/Silver/Crystal)
• Generation 3 (Ruby/Sapphire/Emerald/FireRed/LeafGreen)
• Generation 4 (Diamond/Pearl/Platinum/HeartGold/SoulSilver)
• Generation 5 (Black/White/Black2/White2)
• Generation 6 (X/Y/Omega Ruby/Alpha Sapphire)
• Generation 7 (Sun/Moon/Ultra Sun/Ultra Moon)

Generation 1 (Red/Blue/Yellow)

Generation 2 (Gold/Silver/Crystal)

Generation 3 (Ruby/Sapphire/Emerald/FireRed/LeafGreen)

Generation 4 (Diamond/Pearl/Platinum/HeartGold/SoulSilver)

Generation 5 (Black/White/Black2/White2)

Generation 6 (X/Y/Omega Ruby/Alpha Sapphire)

Generation 7 (Sun/Moon/Ultra Sun/Ultra Moon)