Level 50 Statistics (see level 5, 50, 100)
Drowzee is an interesting Pokemon; it is capable of performing several different roles thanks to its even base stat spread, but many more specialized Pokemon can fill each role better because of Drowzee's decidedly average stats. However, Drowzee does have a unique niche as a physically oriented Psychic-type. It can easily counter many Pokemon, especially Fighting-types (other than Scraggy, which gives Drowzee a hard time). Although it struggles to stand out, Drowzee can easily fit on a team if it is given the right role.
Drowzee has both the stats and the movepool to be an effective revenge killer, thanks to its interesting STAB and great coverage moves. The first moveslot is given to the STAB move of choice; Zen Headbutt has a chance to flinch, while Psycho Cut has slightly lower Base Power but a high chance to get a critical hit and perfect accuracy. Both moves easily take out weakened Pokemon, especially Ghost- and Fighting-types. The main targets for Ice Punch are Dragon-types, but it also hits Flying- and Grass-types as well. ThunderPunch hits Frillish and other Water-types hard, bar Chinchou, which has Volt Absorb. Drain Punch is used not only as a form of pseudo-recovery, but also as Drowzee's only way of hitting Steel-types super effectively, especially Ferroseed, which otherwise walls this set. A Jolly nature is required here, as it allows Drowzee to hit 21 Speed with a Choice Scarf.
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Hypnosis can be used as filler on the Choice Scarf set, though this is not advised. In terms of other sets, Drowzee has the ability to fill many other roles besides that of a revenge killer, although it doesn't always perform up to snuff when given those roles. It can run a SubPunch or Substitute + 3 attacks set, but this is somewhat gimmicky on Drowzee. The same goes for any dual screens or status set. It can set up Trick Room thanks to its access to Hypnosis, but Bronzor greatly outclasses it in this regard. Drowzee has access to Nasty Plot, as well as a decent special movepool to use it with, but Croagunk has higher Special Attack and better coverage. Drowzee can also run an interesting set with Psych Up, Wish, Zen Headbutt, and Drain Punch, allowing it to set up alongside Pokemon such as Timburr; if pulled off correctly, Drowzee can become a major threat.
Checks and Counters
In general, Dark-types can easily counter Drowzee, especially if they have Pursuit. The most important of these are generally Stunky and Houndour. Diglett also checkmates Drowzee with Sucker Punch. Scraggy can come in on a Psychic-type move and set up with Dragon Dance. The same scenario applies for almost anything that resists whatever move Drowzee is locked into. Pokemon with at least 22 Speed can also take out Drowzee if they carry the right move. Slowpoke can simply toy around with Drowzee if it's locked into anything but ThunderPunch. Wynaut can just spam Counter, while Drowzee can't do anything about it.