In Pokémon Red & Blue, right after choosing your starter (Bulbasaur, Charmander or Squirtle), your rival call you for a duel. This analysis will help you with some questions, namely:

Is it worth to use stats-reducing move?

If so, what is the optimal number of these moves?

What are my chance of winning?

Comparison of Pokémon

In the world of Pokémon, Pokémon have stats that are approximately calculated as follows:

except for the hit points, which is computed as follows:

In this combat, has a value of 0 (the Pokémon wasn’t trained yet) and the level is 5. To give Pokémon some variability in their stats, the value is a random value between 0 and 15.

Lastly, the stats are a good way to compare Pokémon as they can greatly affect the battles:

Charmander has arguably the best base stats for this battle: his high attack makes him do high damage scratches and his high speed increases his chance to do critical hits.

Alas, poor Bulbasaur has the worst stats: its high special is only used when he uses his grass dealing moves, which he will learn at higher levels.

Rival Pokémon

Your rival doesn’t have random values for his , they are fixed at 8, except for his attack at 9. This is slightly above average and gives him these stats:

Moves

In this battle, the trainer can choose between two moves: an attack or a stats reducing move.

Scratch is clearly a better move than tackle, with more damage and no chance of missing. This is a great advantage for Charmander.

Your rival will choose randomly between his two moves with equal chance.

Optimal number of stats reducing moves

One rookie mistake is to only use damage dealing moves. Let’s compare this strategy against the use of stats-reducing move in the beginning of the combat.

10000 simulations were done for each strategies. Strategies were tested for since stats can’t be reduced more than 6 times.

For all Pokémon, using the right amount of stats-reducing moves can greatly increase the chances of winning. It happens that 2 stats-reducing moves is optimal for the 3 starters.

This is mostly the case for Bulbasaur, who starts the game under 50% chance of winning, but increases his chance by 20% when using 2 growls before attacking.

Charmander has at first the highest chance of winning when using only his damage-dealing move. Then again, using 2 growls can raise this chance even higher.

With his tail whip, Squirtle can get the highest possible chance of winning, with over 95% chance of winning. Even with only one tail whip, he’d only lose 1 in 20 games in average.

Stats and chances of winning

Using already done simulations, we can use the logistic regression to compute the effect of every stats. Using a regular logit transformation as the link function, we have the following results:

For stats, higher values mean that it has a higher impact on the winning probability. For Bulbasaur, attack is the stat helping him the most against Charmander, defense helps the most Charmander against Squirtle and higher HP is what increase the most his chances against Bulbasaur.

Non-significant variables were dropped from this analysis. For example, since Bulbasaur can’t be faster than Charmander, higher speed did not statistically improve odds of winning and was therefore removed.

Conclusion

Well, this concludes this small analysis. In all cases, you could always use the potion previously taken from the PC if you’re about to lose. Still, you should remember that stats-reducing moves can be useful.