Straight out of Area 51 or some thriller alien movie, you'd better pray that this little green man comes in peace; with base 85 Special Attack and Analytic boosting its attacks, Elgyem isn't something you want to get on the bad side of. Normally such a low Speed stat on an offensive Pokemon would be awful, but Elgyem somehow manages to make it work through the use of Analytic, above average 55 / 55 / 55 defenses, and Recover. Its Psychic typing even manages to make itself useful, giving Elgyem a nice resistance to Fighting-type attacks that allows it to switch in on most Fighting-types without much worry. Analytic really is what makes Elgyem so impressive though; its Speed is so low that it will almost always be slower than its opponent, so Elgyem consistently has the equivalent of a free Life Orb boost without the added recoil. Because of the sheer power that Analytic provides, Elgyem is easily the best bulky attacking Psychic-type in LC and one of the best bulky attackers in the tier.
Although Elgyem might have superior technology, impressive firepower, and adorable looks (it even has a little tail!), it's not without flaws. Once Elgyem has taken down a Pokemon, it's usually in range to be revenge killed. This issue is further compounded by Elgyem's weakness to three of the best offensive Pokemon in LC: Scraggy, Murkrow, and Misdreavus. Even though Elgyem can actually survive their attacks at full health, it will almost always have taken a hit or two before KOing a Pokemon and thus will very rarely be at full health against these three. Elgyem also takes quite a bit of skill to use effectively. The opponent will often switch out against Elgyem, and it can take good prediction to nail whatever is coming in... unless you can get Elgyem's mind probing devices working, that is.
Get in, hit hard, and get out. If that's not how you're using Elgyem, you're doing it wrong. Elgyem is bulky enough to come in on weaker Pokemon, such as Bronzor, Foongus, and Natu, as well as Fighting-types such as Timburr, and safely spam its high powered, Analytic-boosted attacks. Speaking of Analytic, it is Elgyem's most defining attribute and what sets it apart from other Psychic-types, especially in tandem with its base 85 Special Attack. There aren't many Pokemon in LC that can avoid a 2HKO from Elgyem, provided Elgyem uses the right combination of attacks. This of course means that when you're using Elgyem, prediction is key. However, if you can land the correct attacks, Elgyem becomes a beast. Psychic is an odd move to spam in a tier where Murkrow, Scraggy, Bronzor, and Ferroseed are ubiquitous, but it is Elgyem's most powerful attack against most Pokemon. Thunderbolt or Hidden Power will hit the aforementioned Pokemon hard though, so they usually aren't a problem with decent prediction. With Recover, Elgyem can stay in the game for the long haul against teams where it is able to switch in multiple times.
For a Pokemon that is meant to utilize Analytic to its full effect, running a Modest nature with Speed EVs might seem strange at first; with the given spread, Elgyem will hit a Speed of 11. This allows Elgyem to outspeed many slower walls, so it can hit them with an Analytic-boosted attack while they switch in and then finish them off before they can move. This Speed investment also gives Elgyem an easier time against specific Fighting-types, mainly Croagunk (and to an extent Timburr). With its Special Attack maxed out, Elgyem hits 19 Special Attack, and with what is essentially a free Life Orb boost to most of its attacks, Elgyem is one of the hardest hitting Pokemon in LC. Even with just 76 HP EVs, Elgyem will have the bulk to not only come in on weaker Pokemon but also take some STAB super effective moves at full health in a pinch.Team Options & Additional Comments >>>
Most Psychic-types have a myriad of disruptive and supporting moves, and Elgyem is no exception. These options include (but are not limited to): Calm Mind, Nasty Plot, Reflect, Light Screen, Thunder Wave, Trick Room, and a Choice Specs set. They all seem alright on paper, but most of the time other Pokemon pull off that particular option better or the set just isn't as viable as it seems. For instance, Elgyem doesn't have the Speed to effectively pull off a stat boosting set, with the possible exception of Calm Mind. If you're running a dual screens set, you should use the much faster Abra, or even Natu. Both Thunder Wave and Trick Room nullify Analytic (which is Elgyem's best attribute), and Elgyem is just not bulky enough for Choice Specs considering it has to take a hit or two before attacking. Elgyem has a solid niche, but it's not any of these.
Checks and Counters
One popular theory in Pokemon mythology is that Elgyem actually came to our planet in order to escape other Pokemon that were pursuing it in an attempt to harness its powers for evil. Not really, I just made that up. But if it was true, those evil Pokemon would be the common Dark- and Ghost-types in the tier, notably Murkrow, Scraggy, and Misdreavus. Each of these Pokemon has slight difficulty getting in due to Elgyem's ridiculous firepower, but, if they come in safely, they will either force Elgyem out or KO it if it's even slightly weakened. Other Dark-types, such as Stunky, Houndour, Vullaby, and even Pawniard can do the same. Stunky, Houndour, and Pawniard in particular possess Pursuit (and commonly run it), and Stunky is also not weak to any of Elgyem's attacks. Can't you just imagine a malicious Stunky or Houndour chasing down and knocking out a helpless Elgyem with Pursuit? That scenario just seems awful and scary, and I would probably cry if I saw that happen.
Elgyem's problems don't stop there however. Other Pokemon with super effective attacks and decent bulk can also be threatening to face. Larvesta has a powerful U-turn that will take a massive chunk out of Elgyem, and even if Elgyem switches out, the opponent will still have the upper hand. Even a Pokemon such as Dwebble could be potentially disastrous to face should it somehow come in safely. Bulky Pokemon that Elgyem can't 2HKO will also be a nuisance. Lileep is the most prolific example, as, even outside of sand, it can avoid a 2HKO in almost all circumstances and stall out Elgyem with Toxic and Recover. Similarly, Munchlax can tank attacks from Elgyem and hit back with Pursuit or a STAB move.
Elgyem's biggest problem is that its presence on the battlefield is limited due to its low Speed. While it isn't OHKOed by much, after it beats a Pokemon it'll probably be in range to be revenge killed by another powerful attacker. The trick to playing around Elgyem is to exploit this fact and accept that you might lose a Pokemon to it. Once it KOes something, any powerful Pokemon—such as Drilbur, Snover, Magnemite, or any of the offensive Pokemon listed above—will usually be able to revenge kill it, or at least force it out and make sure it can't easily come back in.