Jolteon vs Alakazam

[t3h Icy]

This isn't a full analysis of the match-up, but just a particular detail on what move Jolteon should be using. Thunderbolt or Pin Missile? The reason why it's hard to know which is best is due to the high variability. Thunderbolt is stronger, but has a smaller multiplier, Pin Missile varies in all the different amounts it hits, etc. It can be hard to intuitively get an accurate idea of how effective Pin Missile is due to its accuracy, its variety in the number of hits, and CHs, since Jolteon has a significantly high chance to CH.

First off, Jolteon's CH chance is 25.39%.

Thunderbolt non-CH: 106-90
Thunderbolt CH: 204-174

And to get a nice CH-factored average, we just multiply the damage by the chances of them actually occurring. That is, non-CHs by 0.7461 and CHs by 0.2539. This gives an average damage range of 130.88-111.33.

Pin Missile is much more complex due to all the variability. The important things to note are that it hits 2, 3, 4, or 5 time with chances of 3/8, 3/8, 1/8, and 1/8 respectively. It also has 85% accuracy, and 14 base damage.

Pin Missile x2: 61-51
Pin Missile x3: 89-76
Pin Missile x4: 118-100
Pin Missile x5: 146-124
CH Pin Missile x2: 115-98
CH Pin Missile x3: 171-145
CH Pin Missile x4: 226-192
CH Pin Missile x5: 282-240

At a glance, there are a lot of cases where it's doing high damage, and some where it's rather low, so we have to take a nice average. This is done by multiplying the damage ranges by their chances to occur, and then summing everything together.

Miss: (0.15) 0-0
Pin Missile x2: (0.23782) 61-51
Pin Missile x3: (0.23782) 89-76
Pin Missile x4: (0.07927) 118-100
Pin Missile x5: (0.07927) 146-124
CH Pin Missile x2: (0.0809) 115-98
CH Pin Missile x3: (0.0809) 171-145
CH Pin Missile x4: (0.02698) 226-192
CH Pin Missile x5: (0.02698) 282-240

Which gives an average damage range of 93.44-79.27. This is lower than Thunderbolt's average damage and by a lot! Although it's possible to get high damages, the chances of them happening rely on too many factors all happening positively, and the 15% chance to miss hurts a lot too. For a better perspective, the chance of getting CH Pin Missile x5 is 85% to hit, 25.39% to CH, and 12.5% to get 5 hits, which is a mere 2.7% chance of happening. And just for fun, the chance of doing the absolute maximum of 282 damage is 0.069%, or 1 in ~1446.

So while I could go through Reflect, I think it's quite visible that Pin Missile should not be used against Alakazam. The only case I would suggest using it against him is if you're very desperate to take him out, and hoping for getting some form of high damage, but it's incredibly risky. Not only is Thunderbolt stronger, but it's much more consistent, which let's you plan with it better and rely on it.

If you're still not convinced, let's consider the case where Alakazam has lowered Special twice with Psychic. This drops Jolteon's Special to 159.

Thunderbolt non-CH: 54-46
Thunderbolt CH: 204-174

Which brings the average damage range to 92.9-78.5, literally only one point each under Pin Missile normally! So even if Alakazam is knocking down Jolteon's Special to a puny size, it's still nearly equal on average to use Thunderbolt. In this case, I may suggest using Pin Missile however since Thunderbolt needs to rely on Critical Hits, which has some undesirable inconsistency. In fact, Pin Missile always does more so long as it hits. The reason why the average is still so high is because CH Thunderbolt does so much and happens nearly a quarter of the time.

So to conclude, if you use Jolteon vs Alakazam, stick to Thunderbolt unless you're in an absolutely desperate situation where you need the as much damage possible, regardless of how low the chance of it happening is.

[WaterWizard]

Pin Missile is really only for Exeggutor, but I think Sand-Attack or Substitute makes a better fourth move.

[t3h Icy]

It's a very high risk, high reward in other applications, but yeah, it's mainly for Exeggutor and the odd Victreebel.

[longfellow]

Thunderbolt can also paralyze whereas Pin Missile has no such secondary effect.

[Zilch]

Pin Missile's also there in case Alakazam lowers Jolteon's Special, though this is desperation as Jolteon's going down immediately afterwards without parahax.

[t3h Icy]

Haha, you missed the bottom bit! With Special lowered twice, Thunderbolt is almost equally effective than Pin Missile.

[Nyara?]

But Pin Missile is just for Venusaur/Victreebel/Exeggutor, otherwise they can wall you to the oblivion, and he doesn't had more options at all to consider other move, Sand-Attack if you like the "I'm gonna lucky annoy you" stuff, and Substitute if you want to aim for a full-paralyze on something paralyzed or for wasting PP, because Jolteon doesn't have too much options to attack, so, you're not easing too much the prediction with Substitute.