Joey's Rattata

This is only slightly a Pokemon topic - Joey's Rattata meets probability.

If you haven't played HG/SS, you might not know about his Rattata. "It's like my Rattata is in the top percentage of Rattata." He calls you often, to talk about important things...like his Rattata. Even after it's evolved to Raticate, he'll still have many many thoughts to share about his Rattata.

It got me to thinking - what IS a top percentage Rattata? How difficult would it be to just stumble across one?

First, we need to start with what a top Rattata would have for stats. As we're in the Egg Moves blog, let's assume Joey is talking about IVs - anyone can train a good Rattata with EV training.

Second, each of the 6 stats range from 0-31. My ideal Rattata would have some specific IVs in certain stats, but let's just assume for quick math, we just care about the best ones we could expect out of 100 Rattata, if they were all naturally occurring. Amongst my friends who are serious about IVs, ideally, they get all 31s. They'll settle for 28+, honestly...so we'll work from that point.

Probability is a longer topic, but it breaks down to some quick math if you have Excel handy - just use BINOMDIST function. (There's a 4/31 chance of getting a 28 or higher which would count as a success. Figure out the number of successes out of 6, and you're there.)

If we believe in getting a 28 or higher qualifies - 3 IVs gets us to top 2%. Sadly, it takes us 4 to make that top 1%. It almost takes us to the top Rattata in a thousand!

If you like 30+ IV stats, a top Rattata would only need 2 IVs of that range to make the top 2%. Sadly, that top percent is elusive...it would take 3 to break into it - making it a one in a thousand kind of Rattata.

Breeding that kind of Rattata takes dedication, checking the right parents and re-breeding as the children develop into stronger genes than their folks. With judicial use of EV training items mentioned in the previous post, it's more likely in less time. Good luck!

P.S. As an odd heads-up, I was breeding Rattata for stats, using two EV training items instead of item+everstone. I assumed that each stat would get locked in from the item, but in a couple of circumstances, only one make it in! I'm guessing the third stat donated from the parents can overwrite the "lock-in" stat. Interesting!