"Luck is a measure of your general good fortune, and affects the recharge rate of Critical Hits."
Luck has always been the king of Fallout games, and it largely retains its throne in Fallout 4. The base ability of Luck itself is quite nice - the more Luck you have, the faster your critical meter will fill. More Luck, more Critical Hits, just like always, except now Critical Hits are even more broken than they were in Fallout 3. But more on that later. If you like Critical Hits, you'll like Luck, both the attribute and its perks. If not, then it's not quite as impressive, although there are some perks in the tree that might interest other builds. Mostly it's about Critical Hits, though - something everybody should love.
This perk basically adds a handful of caps into pretty much every container you search (around one Cap to around a dozen Caps at rank four), with more Caps added per rank. Individually, it's a paltry sum, but if you loot everything, it can add up pretty quickly. Still, you get far more money from settlement shops over time (even though the start up on those can be pretty expensive) and selling gear you strip from fallen enemies. At rank four you'll also have the added benefit of getting a Caps explosion from enemies when you kill them. This is rather uncommon, but at least the Caps spawn as a pile that can all be collected at once, instead of forcing you to hunt for each cap, although the total Caps you'll get from this aren't terribly impressive. If you're a consummate looter and pick this early, it can prove rather lucrative in the long-term, but as far as survivability goes, there are far more important perks out there.
Basically "Fortune Finder", but for ammo, it'll add random ammo drops to containers and foes. It's more random than "Fortunate Finder", though, as with Scrounger you can't expect basically every container to have ammo in it, like you can with "Fortune Finder" and Caps. Ammo is a good thing, but honestly, if you switch out your weapons and don't use automatic weapons you'll end up with thousands of rounds of ammunition. Also, you're probably just better off getting Fortune Finder and buying the ammo you want, rather than relying on "Scrounger".
Bloody Mess is a long-standing Fallout perk, so it should have some sentimental value for any true Fallout fan. Granted, the gore in Fallout 4 just isn't as fun as it was in previous games, but Bloody Mess does give a brute damage bonus to all critters with all weapons, which makes it somewhat appealing. Sure, it's only 5% per rank (up to +15% at rank three), but a pure damage bonus is something everybody can enjoy. Rank four's contagious bloody explosion is somewhat dubious, however, so just stick to the first three ranks for the damage bonus, if you care to. At best, it should be saved for later levels when the better perks have all been picked up.
Another veteran Fallout perk, the Mysterious Stranger perk doesn't hold quite the same esteem as Bloody Mess, largely because, well, it just kind of sucks. In Fallout 4, the reason this perk falters is simply because of how rarely it triggers, and how it triggers (which makes it occur even less frequently). Mysterious Stranger will randomly show up at the end of a V.A.T.S sequence where an enemy survives, meaning you've got more of a chance to see it if you just take one shot at a time - if you kill the critter in V.A.T.S., he won't show. This pretty much works against a high Action Point/Concentrated Fire build though, and ideally you want to kill foes in a V.A.T.S. sequence, if for no better reason than to eliminate a threat but also to trigger Grim Reaper's Sprint. Even though the Mysterious Stranger does great damage, you're just better off picking a more reliable perk.
The lower your Intelligence, the higher chance this has to trigger, which will give you various XP bonuses based on the rank of the perk. At rank one you'll get 3x the XP from "any action" which generates XP, including killing, picking locks/hacking, crafting and turning in quests, and at rank two you'll get a x5 XP bonus. Rank three adds a chance that you'll trigger a x3 XP boost from all kills for a duration after making a kill, but since this prevents new XP boosts from happening during that time, you're probably better off sticking with rank two's x5 bonus.
So, you want to keep your Intelligence low (which gives you XP) in order to increase the proc rate of this perk, which gives you XP. Seems dubious on the surface, but the fact is, for most Intelligence values the benefit of this perk is worth it, because although this perk will have a lower proc rate the higher your Intelligence is, it's multiplying a greater amount of XP because your XP is higher. The best value for this is at four Intelligence, where you're getting a 10% bonus to earned XP and this perk has an 8% chance to increase your XP by x3 (or better yet, x5). Even up to an Intelligence score of eight, however, rank two of this perk is still giving you a +20% XP bonus on all earned XP, when you average things out.
Normally time-saving or convenience perks would be rated fairly low, but this perk affects almighty XP. Yes, yes, you can always kill more, pick more locks, craft more junk, but this perk in effect pays for itself if you pick it early. Heck, it triggering for one good quest reward could pay for a rank in itself. Pick it up early, get it to rank two, and enjoy the benefits for the rest of the game. It's not like there's an XP cap or anything, so the perk never stops being useful.
If you like Critical Hits, this perk is essential. It boosts the potency of your Criticals Hits by 50% per rank, up to a total bonus of +150% (or 2.5x normal damage). Perhaps not great on its own, but if you're investing in Luck and pick up Critical Banker and Four Leaf Clover, this perk synergizes with a Critical Hit build very, very well.
Critical Hits are already broken enough. They're insta-hits which deal extra damage (usually double the base weapon damage or more, depending on whether you have Better Criticals and various mods which boost critical hit damage) that charge (at a rate depending on your Luck score) every time you score a hit in V.A.T.S. What could make them better? How about storing numerous Critical Hits until you really need them? Enter Critical Banker, which allows you to store an extra Critical Hit per rank in Critical Banker, up to three extra Critical Hits at rank three (four with the Far Harbor DLC).
Rank three also has the added benefit of having a chance to store an extra Critical Hit every time you bank one. Charge these up by killing weak foes in V.A.T.S. that aren't worthy of a Critical Hit, then let loose on stronger foes with critical vengeance when you need to. It's basically an option to store an "I win this fight", and the dynamic never changes as you level. More and more foes become trash foes you use to charge Critical Hits, while the top-tier enemies keep getting stronger. A must-have for a critical build, anybody who uses V.A.T.S. should buy this. If you've got high enough Luck to have the option, you have enough Luck to exploit this.
Grim Reaper's Sprint
Another perk that synergizes well with the V.A.T.S. build - it's a package bundle, you see, and there's tons of these skills in the Luck tree. Any time you kill something in V.A.T.S. you have a chance to refill your Action Points, 15% at ranks one, 25% at rank two and 35% at rank three, which also has the added benefit of giving you a free Critical Hit. This of course works wonders with a high Luck score, Better Criticals and Critical Banker, which together make a big piles of perky awesome. And since Critical Hits are V.A.T.S.-only attacks that make it more likely that you'll kill something in V.A.T.S. - you can see where this goes. As long as you use V.A.T.S. regularly, this perk is good for you, which means it should be good for just about everybody who loves winning.
Four Leaf Clover
Not enough uber synergizing V.A.T.S./Critical Hit perks for you? Need one more, or will it be overkill? Probably overkill, but here it is: Four Leaf Clover gives you a chance to score a Critical Hit every time you take a shot in V.A.T.S. If you've boosted your Critical Hits with Critical Banker and Better Criticals, this is a no-brainer, even more-so if you invested in a high Action Point build and Concentrated Fire. At rank one you'll get a 7.5% chance of scoring a Critical Hit per shot (in addition to the normal growth rate of the Action Point bar, which with nine Luck has to be pretty darn fast already), at rank two this improves to 9.5%, rank three is 11.5% and rank four gives you a 13.5% chance. Diminishing returns, sure, and honestly, with eight or nine Luck you might not need this perk. Plus, there's the ironic bad luck (figurative, not in-game) that you might score this when your critical meter is almost full anyway. All in all, it's another layer of awesome to add to the V.A.T.S./Critical Hit build, but it might be a bit extraneous, all things considered. If you can, however, one rank in it has the best return per perk.
A perk that ironically synergizes with Nerd Rage!, of all things - the more injured you are, the greater chance you have to insta-kill a foe that's attacking you. As long as they're using ranged attacks, anyway, and a lot of dangerous foes in the game don't use ranged attacks. All in all, having low health and hoping that a dangerous shot will proc this perk and kill the enemy just seems like a bad battle plan.