Synergy: Bad. Ashe doesn't have proper burst to follow up on a Blitzcrank grab, so you won't be able to get kills - and she can get zoned out by poke supports because of her lack of mobility. Once you both have 6, you might be able to grab kills - but you have to play early game very defensively and hope she can stay even in farm.
Matchup: Very good. Ashe is extremely vulnerable because of her lack of escapes. Even with the slow from her auto-attack, it's very easy for you to get within range to pull her, so you can zone her off a lot of CS.
Synergy: Good. What Caitlyn lacks in burst she makes up for with her range and her CC. Whenever you hit a pull, Caitlyn can place a trap immediately underneath you. After that trap snare wears off, you can use E to knock-up your opponent. This 4 second lock-up is an extremely strong combination that can net you some nice kills.
Matchup: Difficult. Because Caitlyn has such long range, it's unlikely that you are going to get an opportunity to pull her. You will have to play aggressively and focus her support, and hopefully your ADC has solid burst so that your side will win the 2v2 all-in.
Synergy: Awesome. Corki has very big burst, and can immediately follow up on your hook thanks to his Valkyrie. Whenever Corki is matched with a kill lane support such as Blitz, Thresh, or Leona, you should do well.
Matchup: Average. Although Corki has an escape with Valkyrie, it can be interrupted with your knockup. He also has pretty short range. If you pull him, watch out for him being super aggressive and taking the opportunity to fight the 2v2, since he could very well win it even though he's initially out of position.
Synergy: Good. Draven has a good amount of burst that goes well with Blitzcrank's 2v2 all-in nature.
Matchup: Excellent. It's easy to predict Draven's movements as he attempts to catch his axes, which gives you an advantage to try to pull him out of position and take the lead in lane. If you can't, that's fine, because Draven's late game is designed to be awkward, so your team will scale better out of laning phase.
Synergy: Average. It's worth picking Ez with Blitzcrank just to make sure that the opposing team doesn't take it. If Ezreal hits his skillshots, he can have a pretty good amount of burst, but he's traditionally considered more of a poke champion.
Matchup: Awful. Ezreal has long range poke that outranges your hook, which means he has the potential to get free harass without having to be afraid of counter engages. Even worse, if he does go out of position, he can just arcane shift out of your pull and you're still worthless.
Synergy: Excellent. Graves not only has big burst (like Draven) but can apply it very quickly thanks to his dash. He is also innately very tanky, which sets him up nicely for 2v2 all-in fights.
Matchup: Average. You can take advantage of his short range to zone him, but he's also very strong in a lane fight so you should be careful to pull him unless he's already taken some damage and your side is full health. if you do pull him, try to do it while his buckshot is on cooldown.
Synergy: Bad. Kog'Maw has a weak early game, and Blitzcrank won't be any help. Kog will get poked out and you can't force an engage because Kog doesn't have the damage to follow it up.
Matchup: Excellent. Kog's weak early game makes him vulnerable to your hooks, especially when his W is on cooldown and his range goes back down. When this happens, try to force him away from CS and if he gets greedy and still tries to take it, hook him.
Synergy: Amazing. MF has a HUGE amount of damage, and by landing a pull she goes in range to be able to apply all of it. She is one of the burstiest champs in the game so you will get kills - just make sure to ward up your lane heavily because she is more vulnerable to ganks than many other ADC's.
Matchup: Good. You probably want jungle help to ensure that you win lane, because pulling her can lead to a risky 2v2 - but if you have back-up, she has no escapes to avoid your pulls.
Synergy: Very Good. Quinn is highly underrated right now, but she is able to do quite a bit of damage with her e and passive, and a pull means that should be able to get off a Q on the enemy without it being blocked by minions. Although her focus tends to be pushing the lane, you can definitely grab kills thanks to her damage and the slow that she applies, which will be stacked when she completes her cutlass.
Matchup: Difficult. There's no point in trying to pull Quinn while her E is up, because she will just use it to bounce off you and apply some counter-harass. Be careful for a split-push Quinn late game - if she attempts this, grab a Shurelya's and force 4v5 fights as often as you can, because she takes down towers very quickly.
Synergy: Good. Sivir can get poked out early game, but she has quite a bit of damage so she should be able to follow up your hooks. Once she hits level 7, she will become a pushing machine and split push very quickly - just make sure to ward up the enemy jungle so she can do her thing.
Matchup: Average. A good Sivir can stop your hooks with her spellshield, but you can sometimes bait out the spellshield just by rushing towards her to threaten a hook. Because of her short auto-attack range, your threat alone is enough to make her fall behind in CS.
Synergy: Excellent. Trist has big burst and her jump applies a slow, plus she has a healing debuff to ensure that champs like sona or soraka will definitely die to your hook.
Matchup: Difficult. Trist can jump away from your hooks, similar to Ez - although her jump is slightly harder to time correctly. Regardless, you have to try to win lane because she will be safe from your hooks late game because of her insane range.
Synergy: Good. Twitch has a very similar early game mechanic to Draven, so he can follow up your hook with a huge amount of damage. He also has an excellent late game, so it's important that you peel for him once teamfights come around.
Matchup: Good. Make sure to always carry a pink - if you get a hook but don't have a pink, he'll be able to stealth before you can pick up the kill. If you keep vision, he has no escape - so you'll have no problem taking him down.
Synergy: Good. Your hook makes it very easy for Urgot to hit his E-Q combo, so he will be able to get a lot of damage on the enemy ADC.
Matchup: Average. It depends on how he builds - if he gets very tanky, you can't really force the 2v2 and you have to rely on your ADC to poke him down. Otherwise, you can get kills and take advantage of his short range.
Synergy: Excellent. Especially at level 6, either one of you can initiate a fight and probably get a kill.
Matchup: Good. Although his hail of arrows will apply a slow that makes him difficult to chase, if you rush at him once he is 6 it's easy to force him to burn his ult just to keep you from killing him, and he won't be able to initiate off it unless he has a big lead.
Synergy: Excellent. Your pull gives her the opportunity to condemn the enemy into the wall, which is pretty much a guaranteed kill, especially if she has completed her cutlass.
Matchup: Difficult. Vayne can avoid your pulls with tumble and if you don't shut her down early, she becomes unstoppable. Request jungle help to make sure that you are able to set her behind early.