Power Split

[ReshiramBlackZekromWhite]

Name: Power Split
Power: --
Accuracy: 100
Type: Psychic
Category: Status
PP: 10 (max. 18)
Targets: Any one Pokemon adjacent to user
Effect: Averages out Attack and Special Attack with target, then splits it equally. This attack ignores stat modifiers when calculating average.

Pokemon that learn Power Split:
Pokemon | Type | Method
Shuckle | Bug / Rock | Level (55)
Baltoy | Ground / Psychic |Level (48)
Claydol | Ground / Psychic |Level (54)
Latios | Dragon / Psychic | Level (75)
Yanmask | Ghost | Level (33)
Cofagrigus | Ghost | Level (33)
Elgyem | Psychic | Level (50)
Beheeyem | Psychic | Level (58)
Mime Jr. | Psychic | Breeding (parents: Elgyem, Beheeyem)

Competitive Value:
This move would be most effective with walls against sweepers, as the sweeper would most likely have a significantly lower attacking stat. It's also good if you have a Pokemon such as Wobbuffet that can Encore a weak move after trapping a foe with Shadow Tag, then switching into a set-up sweeper or something like that. For an example of the first situation, we can use a Claydol as a special wall, having to face a physical sweeper. Claydol could use Power Split, and the sweeper would be significantly less powerful.
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Examples below have a Lv. 100 Bold (+Def, -Atk) Claydol with 252 HP, 252 Sp. Def, and 6 Def. Atk IV is 0
The attack stat calculated is after Power Split
Claydol vs. Lv. 100 252 Atk Adamant Tyranitar: 267 Atk from 403
Claydol vs. Lv. 100 252 Atk Jolly Tyranitar: 249 Atk from 367
Claydol vs. Lv. 100 252 Atk Adamant Haxorus: 281 Atk from 432
You get the point.
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Another Pokemon that greatly benefits from Power Split is... Shuckle. Shuckle has the highest Base Stat of Def. and Sp. Def out of all Pokemon, with each of them being base 230. This means, with a +Nature and 252 EVs they can be at 614. Neutral-natures leave it at 559. I personally use Shuckle on the main Pokemon Online server, with the following set:
Shuckle @Leftovers
Sturdy
Careful Nature (+Sp. Def -Sp. Atk)
252 Def, 52 Sp. Def, 204 HP.
Sp. Atk IV: 0
Moves:
Power Split
Acupressure
Rest
Rollout
Details:
This spread gives you 559 in both defenses and puts the remainder in HP, giving you 232. Leftovers provide constant recovery, and Rest deals with status. The two sleep turns don't matter, because after a Power Split, an opponent will have a hard time hitting it well. Acupressure sharply raises a random stat (if it can be raised), so after 21 turns of constant use, you're guaranteed +6 in all stats including Accuracy and Evasion. Rollout is unresisted, gains STAB, and builds power with each constant hit. It also OHKOs Shedinja, which is nice as there's no status on this set. The only thing that Shuckle needs to watch out for is a critical hit, more so when it's with a status-inducing move such as Flamethrower. Yes, this is completely stall-related, but it is fun watching your opponent being swept by a SHUCKLE.

Counters:
Anything that uses only fixed-damage attacks, such as Eviolite Chansey with Seismic Toss or Eviolite Dusclops with Night Shade. These will 3HKO not factoring in Rest. They could possibly 2HKO with status such as Burn or Poison. Phasing moves such as Whirlwind, Dragon Tail, Haze, and Clear Smog get rid of Shuckle's boosts, and with Whirlwind / Dragon Tail, Shuckle no longer has the boosts from Power Split. Shuckle is also complete Taunt bait, as with the above set, its only attack is Rollout.

Other Options:
Sand Tomb / Wrap: This keeps a foe in battle after using Power Split. Sand Tomb is ineffective against Levitate users, while Wrap is ineffective against Ghosts.
Toxic: Toxic works well against opposing walls, especially the ones listed as counters. However, Eviolite Chansey may carry Heal Bell.
Grip Claw: It sounds gimmicky, but Grip Claw with **trapper move**, Power Split, Attract, and **insert filler here** may work well. Attract gives opposite genders a 50% chance of immobilization, Power Split decreases their Atk and Sp. Atk, Toxic causes continuous damage, and Wrap / Sand Tomb prevents the opponent from escaping. The only bad thing about this set is that it lacks any recovery and dies to Taunt and Status.

All in all, Power Split can be either very helpful or unhelpful depending on the role of the Pokemon using it. Though its distribution is very limited, most of the Pokemon that learn it can benefit from it. It is a phenomenal aid to walls, and is the perfect opportunity to switch in to a Pokemon such as Wobbuffet to Encore-trap a weak move and switch to something that can setup on it. It may also help increase the usage of Shuckle!

[LafondaOnFire]

I've used power Split Shuckle on SS teams before. It's very gimmicky and hard to pull off but if you can do so successfully, it's an amazing feeling to sweep with a Shuckle. Personally, this is what I ran:

Shuckle @ Leftovers/Grip Claw
Sturdy
Impish Nature (+Def, -SpA)
252Def, 252HP, 4SpDef
SpA IV: 0
Power Split
Rest
Rollout/Wrap
Defense Curl/Mud Slap

Essentially I have used two strategies here. First off, I pumped all the EVs into defense rather than special defense because this set really benefits off the x1.5 special defense boost given from sandstorms. As much HP as possible because let's face it, Shuckle has pretty pitiful HP for such a defensive Pokemon.
I won't cover Power Split and Rest since that's pretty much a given for what we're discussing here. Power Split is the topic and Rest to heal up HP.
Defense Curl will increase your defense even more to add to longevity while it will power up future Rollouts, given that it is used immediately before one. Despite Power Splitting with something powerful such as Tyranitar or Metagross for example, Shuckle's attack stat has more to be desired. The extra power is appreciated. Also, since you will be locked into Rollout, the extra defense helps if the opponent switches in something rock resistant.
The second set involves Mud Slap and Wrap with a Grip Claw. The idea is to trap the opponent while you whittle them down to -6 accurary. It's pretty funny for the lulz and can be pulled off if you can Power Swap with something with high attack.

The main problem with Shuckle is that you cannot win a stall war. Anything with instant recovery will trump over sleeping for two turns. Sleeping to remove status can become a nuisance as well. Also, be careful to not get out predicted and Power Swap an incoming Forretress, for example, while they proceed to set up entry hazards. You have to be very careful as to remove all counters and any stalling 'mons.

[ReshiramBlackZekromWhite]

I quite like that. I didn't think of using Sandstorm support... I'll edit that in later.

[danmo96]

This is a set i tend to use with him:

Shuckle @ Leftovers
Adamant Nature
252 HP/ 128 Def/ 128 SpD
Power Split
Toxic
Rest
Rock Slide/Rollout

i know it's completely walled by Steel-types, but it's still fun to mess around with.
Power Split to limit their damage (duh), Toxic to make them die faster (unless, of course, Steel or Poison types), Rest for healing and status removal when needed. i personally prefer Rock Slide over Rollout so that i'm not locked into it, and thus can toxic/rest when needed.

[Psycho Cut]

My best use of Power Split was on a max def, min speed Forretress with Gyro Ball. In a trick room. Needless to say, it was the most satisfying sweep ever, but it's hard to pull off.

[locoghoul]

accupressure and rollout together are not legal iirc

[Maverick Hunter]

Originally Posted by Fat locoghoul

accupressure and rollout together are not legal iirc

rollout is a Level Up move from Shuckle.

[ReshiramBlackZekromWhite]

Originally Posted by Fat Psycho Cut

My best use of Power Split was on a max def, min speed Forretress with Gyro Ball. In a trick room. Needless to say, it was the most satisfying sweep ever, but it's hard to pull off.

Forretress can't learn Power Split. I already listed everything that could.

[By Myself]

I think Cofagrigus could actually be pretty viable getting some strong attacks in with it's Defense's being that high, especially since it learns Nasty Plot/Calm mind.