On Pokemon Tankiness, Sweepiness and Stats Ratings

(Also known as: What X-Act Has Been Doing These Past Days And Why Was He Barely Posting In The Smogon Forums)

http://users.smogon.com/X-Act/sweeptank_stats_ratings.pdf

(requires Adobe Reader to view)

A 20-page document, written in a formal mathematical way, explaining in detail:

• How the formulae for Tankiness and Sweepiness were found
• What is the practical significance of Tankiness
• What is the practical significance of Sweepiness
• How the formula for Stats Ratings was found

WARNING: This document contains a lot of mathematics, so, unless you have the necessary mathematical background (a.k.a. you passed your algebra exams), you'll find it difficult to understand.

WARNING: It is written in a formal way, because that's how mathematical arguments should be presented. I don't consider this document any differently from, say, discussing fullerenes in a mathematical chemistry paper (although its format is slightly less formal, so that you're not completely shocked).

Feedback (positive and negative) is appreciated.

This is why you're Smogon's resident mathematician. I normally hate reading formal proofs, but this was fairly easy to not tl;dr, probably because the material was actually interesting and relevant to my interests.

Good job and all. ^_^

(I think you're the reason I haven't yet condemned math in all forms.)

That was a very good read. Bravo to Smogon's math genius.

I NOW HAVE X-ACTS NAME AND CAN COMMIT IDENTITY FRAUD!

In all seriousness, great Job X-Act.

I got kind of lost in the middle with all the signs and subscript, but the practical use section is really awesome.

One thing I would make a note of is that the stat number given is the unboosted number. Modest Specs Starmie has a listed 492 SA in Shoddy, but still won't OHKO 0/0 Dusknoir, because its stat is not the base 398 required to KO Dusknoir with Specs Surf.

Great work X-Act/Alexander

EDIT: Whoops lemme re-read that.

EDIT2: I think it means total, boosted and unboosted.

In the Starmie example, Starmie needs to have 895 total SpA (with STAB and Choice Specs) in order to OHKO 0/0 Dusknoir. That means 597 Stat if you take Choice Specs into account, and 398 if you don't. Just to clarify.

EDIT: I changed the link to my Smogon webspace, since I can access it again (yay!).

I don't quite understand it all, but at the start, where you mention normalized stats you use "/", is that division or "or"

Quite interesting, X-Act, thanks for putting it all together. Now I know where the constants come from, which was the only non-obvious thing in the original Stat Ratings topic. Specially, the derivation of the 315 constant (which, being additive in the formula made it pretty important) is now crystal-clear. It is obtained in a very elegant way.

So, yeah, I really don't have any questions, but I wanted to post to let you know it's been interesting.

billymills666 said:

I don't quite understand it all, but at the start, where you mention normalized stats you use "/", is that division or "or"

Click to expand...

In that case, it's "or".

I skimmed the document (I only know GCSE Math...) but I used CTRL-F to find the mentions of EVs, you do not include them in the stat rateings. I can see this makes them more simple, but in some cases it will distort the rating of a Pokemon if that Pokemon can get more out of its EVs than other Pokemon (Blissey can almost double its Phy. Def ability with EVs, and Shuckle really benefits from HP evs) would it be possible to write an applet that calculates what EV spread gives the highest stat rating and use that rather than the no EVs rating?
Also if the applet suggests giving Skarm max Sp. Def and investing heavily in Heracross's Sp.A it could show that you may need a (greater) bias toward specializing in a specific stat.