No. No matter how you EV train you shouldn't have to fight 300 Patrats at all.

Now, for each pokemon there is an EV cap, this cap is 510 EVs, so that means, no matter what, a pokemon can never have 510 EVs total over all of it's stats. However, there is another cap, and that cap is max amount you can put into 1 stat. This value is 255 EVs, so you can put a max of 255 EVs into 1 stat and 255 into another.

Now for some of the (simple) maths behind it. At level 100, 4 EVs = 1 extra stat point. So, if you put 255 EVs into a stat, 252 will be used to increase the stat and 3 EVs will be wasted, since the game doesn't round up (4 goes into 255 63 times with 3 remainder). This means, it is better to put 252 EVs into 1 stat as it means you get 3 extra points to use elsewhere, take the 3 extra from the other stat and you get 6 points left over which is another stat point in another stat, this is why you see common EV spreads as 252/252/4.

At lower levels EVs have less of an effect, so at level 50 it takes 8 EVs to get 1 stat point, level 25 requires 16 EVs to get a stat point. SO you won't see the full 63 extra points until you hit level 100. However, this does not mean that you should EV train at level 100, since stats get recalculated at every level up and after every battle, it doesn't matter when you EV train as you will end up with the same stats whether you EV trained at level 1 or level 100.

As for the actual process, if you have no Power Items, or PKRS, or Macho Brace, then it will take a long time. Patrats give 1 Attack EV, so to get the 252 you need to kill 252. If you have the Macho Brace (which is easy to get), it doubles all EVs received in battle, so that Patrat will give 1EV*2 = 2 EVs, that means you will only need to kill 126 Patrats to get the 252 EVs.

PKRS acts the same as the Macho Brace (doubles all EVs gained in battle) however, it doesn't take up an item slot, so you could have PKRS and a Macho Brace and get 4 times the EVs, that means a single Patrat will give 4 EVs and so you will only need to kill 63. However, the best items to use are the power items, there are 6 of them, one for each stat, and they increase their respective stat by +4 EVs. So if you have the Power Bracer (which is for attack) and you kill a Patrat, you will get 5 Attack EVs from the battle. That means you would need to kill 50 with the Power Item and 2 without the power item to get 252 Attack EVs. If you use a Power Anklet, which increases Speed, and kill a Patrat, you will get 1 Attack EV (from the Patrat) and 4 Speed EVs (from the Power Anklet). I personally try and keep the Power item held that I am EV training for, just so it's easier for me to keep track of, but some do use this to increase 2 EVs at once.

Now, the best bit, PKRS and a Power Item. Keeping it simple, Killing Patrats and having the Power Bracer equipped. Now, PKRS doubles ALL EVs gained in battle, that includes the ones from the Power Item, so, Patrat + Power Item = 5 EVs in total, then double it and you get 10 EVs per battle. With that, you just need to kill 25 Patrats with the power item and 1 without for a total of 26 battles to max out that stat.

Hopefully that clears some things up.

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