https://docs.google.com/spreadsheets/d/1VGvH8QGCfvGXPe2GwE_MbNSjD1UIROGsLXnrohdxP8Y/edit?usp=sharing

*Assumptions*

All of these scores can be understood with the same assumptions. A score of 100 is a decent benchmark for a "powerful" result, and larger numbers are better.

The sheet was created with gen 3 in mind, so there's no special/ physical split considerations, and fairy type is not included.

Some pokemon have abilities that influence their numbers; those changes have been included where possible, and the "better" of any available options has always been chosen (eg. Thick Fat Azumarill instead of Huge Power).

*Scores*

**Attack Score**, a weighted average of attack (weight 2) and speed (weight 1).

**Special Attack Score**, a weighted average of special attack (weight 2) and speed (weight 1).

**Defense Score**, a weighted average of defense (weight 2) and HP (weight 1).

**Special Defense Score**, a weighted average of special defense (weight 2) and HP (weight 1).

**Resistance/ Weakness Index**(R/W Index), a composite score that evaluates the ratio of type resistances to weaknesses. Several types are given additional weight (squared: ground, water, ice, and electric) because of the frequency of their use in attacks. Higher levels of weakness/ protection are accounted for using the same multipliers/ denominators as in-game battle calculations. Immunities are treated as the highest level of resistance available (x1/8) to avoid using zero/ infinity.

To find the value, each set of resistances and weaknesses are averaged, compared in a ratio, and then exponentiated (log base 2) and multiplied by 10 to better fit the goal of having 100 be a "good" value.

**Toughness Index**, a score that reveals the whole of a pokemon's defensive power. First either the Defense Score or Special Defense score is chosen based on which is higher, then that is averaged with the R/W Index.

**Net Ability**, a average of each of the above values. Each of the better of the two attacks and defenses are chosen.

*Benefits*

These scores are easy to evaluate and understand, because they remain in line with the magnitude of base stats. They take into account some practical assumptions about the environment they're used in, and thus are better suited for real-world use. Using a stats-based analysis can circumvent some biases.

*Drawbacks*

These aren't highly-tuned or sophisticated equations. A fair amount of the content of the equations are based on arbitrary decisions. Assumptions about the environment may not be accurate to all experiences. Equations were designed without taking into account the competitive metagame. Some fudging was done for averaging types -- there's 17 types, but R/W is averaged by dividing by 16. This was done both because normal type isn't a weakness, and because it makes the numbers cleaner.

*Potential Improvements*

With the inclusion of additional statistical analysis, weights could be made more accurate. A more in-depth calculation between defense and special defense that includes only the resistances/ weaknesses for those types might be more valuable as a tool than the current Toughness Index. These equations work well in gen 3 because there's no special/physical split; trying to use a similar method on newer-gen games would require very difference assumptions.

Please let me know what other sorts of improvements you think would be worthwhile.