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Any damaging attack other than Future Sight and Doom Desire used by the wielder has its Base Power multiplied by 5325/4096 (about 130%) if it moves after its target. If the target switches out, the Analytic boost still applies.
In essence, Analytic is a Life Orb boost without recoil. Analytic is only available from the Dream World; however, all competitively viable users of it are released and available to use. It is a technically good ability; however, many of its users are too frail or too fast to use this ability effectively. One of Starmie's biggest advantages in standard play is its base 115 Speed, and this combined with rather average 60 / 85 / 85 defenses means that it isn't going to be capitalizing on this ability anytime soon, not to mention that it has a much better ability in the form of Natural Cure. Magnezone, however, is a much better candidate, as not only is it rather slow, but it also has high defenses and a huge base 130 Special Attack stat. Of course, using Analytic means forfeiting Magnet Pull, which gives Magnezone its great niche in the metagame. The loss of Magnet Pull would hurt Magnezone, so think carefully before slapping Analytic on, even though its power is pretty incredible if Magnezone also carries Choice Specs. Lastly, the only other notable Pokemon to get Analytic are the Porygon family, and unfortunately they too have much better abilities to make use of. As a defensive Pokemon, Porygon2 would greatly prefer Trace, and Porygon-Z has Download and Adaptability to choose from already, not to mention that it isn't nearly bulky enough to be ripping through teams with Analytic.
Found in Dream World