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I've heard that the math has been done, but I couldn't find it with some searching of my own and wanted to take a crack at it myself anyway. I found some interesting results after setting up a spreadsheet. I'll summarize here. Unless specified otherwise, wound averages are based off 10 shots from basic Glade Guard just for readability's sake. I'll try and put a TLDR summary at the bottom, but there's plenty of nuances to be aware of, so try to get through it all!

This is under the assumption that the ruling of 'only one unit per army can take each enchanted arrows choice' is correct, which I've seen debate about. If this is wrong, then disregard anything about 'secondary choices'.

Overall Winners: Hagbane and Trueflight

As everyone seems to agree on already, Hagbane and Trueflight are the most consistently well-performing choices. Depending on what you're facing, Hagbane may be the better overall 'go to' choice. Here's what you need to know about where they differ:

Hagbane is, as you might expect, strictly better at close range with no penalties to hit. 10 shots at close range against a T3 target with 6+ or worse armor generates 4.17 wounds. Trueflight generates 3.33.

At long range, Hagbane and Trueflight are equal against T3 targets. The -1 penalty evens up the score at 3.33 apiece against a T3 target with 6+ or worse armor.

When taking a penalty of -2 or more against T3 targets, Trueflight wins out. Hagbanes drop down to 2.5 wounds on average, while Trueflight remains at 3.33.

As soon as you shoot at anything with T4 or higher, Hagbane is always as good or better than Trueflight (until 7+ to hit kicks in).

Against T4 with no armor, Hagbane gets 3.33 wounds. Trueflight drops to 2.22. Against T5+, Hagbane gets 2.5, while Trueflight is down to 1.11.

At long range against T4, Hagbane drops to 2.78, which is still higher than Trueflight's 2.22. At long range against T5+, Hagbane is down to 2.22, still double Trueflight's 1.11.

When the penalty kicks up to -2, Hagbane STILL wins out. Against T4, that's 2.22 wounds, while Trueflight is matching it at 2.22. Against T5+, Hagbane pulls ahead again with 1.94 against Trueflight's 1.11.

Trueflight only starts to win against T4+ targets when the modifiers go up to -4 or worse. This is the point where you need 7+ to hit, so poison does nothing. This would be something like long range against skirmishers in hard cover, for the record.

Armor affects both equally. Neither pulls ahead of the other at higher armor values.

TLDR for Hagbane vs Trueflight: Trueflight is better against T3 targets at long range and in cover or worse. Hagbane is better against T4+ targets with any modifiers short of -4 and against all targets at -1 modifier to hit or better.

Rich man's Hagbane: Moonfire and Starfire

These are a bit odd, as they're basically begging for list tailoring. They really should've just been one option. Ah well. On the bright side when it comes to feeling guilty over tailoring, they're just not that particularly good compared to the alternatives anyway. The ONLY time they're going to average more wounds than Hagbane or Trueflight is against T3 targets in close range (armor irrelevant). At that point they average 4.44 wounds before armor, while hagbane is a measly 4.17. Totally worth the extra point per model, right? Everywhere else, Hagbane beats them or is better. T4 they're equal, T5 and up Hagbane is better, and Hagbane is cheaper anyway.

Ignoring the comparison to Hagbane, they're still a substantial boost in killing power if they're actually used against the correct army type. Against T3 targets, normal shots give 3.33 wounds while *fire gives 4.44 (33% boost). At T4, it's 2.22 vs 3.33 (50% boost). And at T5+, that's 2.22 vs 1.11 (100% boost!).

TLDR: Hagbane is better 99% of the time and it's cheaper, but it's still a nice boost against higher toughness targets if you already have Hagbane elsewhere and don't mind essentially list tailoring.

Skavenslavicide: Swiftshiver

Swiftshiver excels in one and only one area: Close range versus unarmored or lightly armored T3/T4 targets. Against unarmored T3 targets it actually provides the most wounds at a nice round average of 5, beating even Hagbane and *fire. Against a 5+ armor save it squeaks out 4.17, beating *fire's 3.7 and staying ahead of Arcane Bodkins at 3.33. At a 4+ armor save it matches Bodkins at 3.33, and then drops off.

Giving any modifiers (long range, cover, etc) makes its effectiveness drop rapidly. At long range it'll at least match Hagbane, Trueflight, and *fire against T3 at 3.33 wounds. At -2 or worse, it drops to the bottom at 1.67 against T3 targets, tied with normal shots and making them a waste of points.

SUDDENLY EDITS! Swiftshiver does shine in one place in particular. When you start applying positive to-hit modifiers and get to at least +1, Swiftshiver actually becomes pretty damned amazing compared to the other choices. The problem with this is that you're now relying on magic (such as Hand of Glory), which is never a good idea. That same magic still helps the other options as well, it's just that Swiftshiver benefits the most from it. So if you really want to put out a bajillion shots, pick up High Magic and hope that your opponent lets Hand of Glory go through, and that you roll high enough to get to +1 or better after applying any negative modifiers in the first place.

TLDR: Swiftshiver is only good against 5+ or worse armored T3/T4 at close range or buffed by magic. It fails terribly at -2 modifiers or worse.

Mildly annoying: Arcane Bodkins

As you'd expect, Arcane Bodkins only kick in at higher armor values. They actually tie Swiftshiver against T3 targets at close range against a 4+ armor save, and finally pull ahead against a 3+ or better. Against a 2+ armor save (common on heavy cavalry) at close range, Arcane Bodkins offer 2.22 wounds. That's double the effectiveness of normal shots at 1.11, and beats out the #2 place of Swiftshiver at 1.67. Hagbane, for reference, offers 1.39 here. So hey, that's nice.

At long range, Bodkins are still in the lead against armor. They offer 1.67 wounds against T3 2+ armor at long range while everything but normal shots are at 1.11.

Against T4, Bodkins stay in the lead against high armor. At T5 and up, they begin to fall behind Hagbane. Anything that's T5+ with 2+ armor is going to be pretty intense anyway, though.

The problem for Bodkins begins when you start hitting -2 penalties or worse to hit. Long range + moved, long range + soft cover, etc. At this point Trueflight Arrows actually match the Bodkins despite a 2+ armor save to get through! They're still ahead of everything else, though. #3 at this point is Hagbane at 0.83. When you take into account that the Bodkins are 2 more points per model than Hagbane and Trueflight, they seem less appealing.

TLDR: Arcane Bodkins are good against 4+ or better armored T3/T4 targets at close or long range. They become significantly overpriced once any other to-hit modifiers are added on (cover, move, etc).

The final verdicts

Here's the big TLDR:

Hagbane and Trueflight Arrows are the most consistently good choices as well as being the cheapest. They should be the no-brainer go-tos, with Hagbane the winner if in doubt. They're not always going to be the 'best' choice for every possible situation, but they will be consistently good in the largest variety of situations. Trueflight is better if you expect to be shooting through a lot of cover or be moving constantly (and thus taking penalties), while Hagbane is better if you want to be able to take down higher toughness things or plan on having few to hit penalties (long range at worst).

The 'fires aren't bad if you KNOW you're going to be facing that army, but for being more expensive they're not as good as Hagbane. Not a bad second choice if you want some high toughness killing power and already have a unit with Hagbane.

Swiftshiver is decent if you're expecting large numbers of low toughness baddies, such as skaven hordes. Don't take them otherwise.

Arcane Bodkins are solid against 1+ to 4+ armor, but only if you're careful about your to-hit modifiers. While better than Hagbane against T3/T4 armored units, remember that they're also nearly twice as expensive. Possibly take against Dwarfs and WoC, but if you're going for an all-comers list, pass on them.

Something similar to this has cropped up on Asrai.org reaching very similar conclusions. One thing though:

As soon as you shoot at anything with T4 or higher, Hagbane is always as good or better than Trueflight.

Not quite- at 7+ to hit when poison doesn't trigger Trueflight is obviously better.
But yeah! Pretty much spot on.

 Aben Zin wrote:
Something similar to this has cropped up on Asrai.org reaching very similar conclusions. One thing though:

As soon as you shoot at anything with T4 or higher, Hagbane is always as good or better than Trueflight.

Not quite- at 7+ to hit when poison doesn't trigger Trueflight is obviously better.
But yeah! Pretty much spot on.

Yep!

Trueflight only starts to win against T4+ targets when the modifiers go up to -4 or worse. This is the point where you need 7+ to hit, so poison does nothing. This would be something like long range against skirmishers in hard cover, for the record.

I mentioned that in their own section, but probably wouldn't hurt to clarify that in the TLDR.

Aaaactually, Ben Curry posted the averages on Twitter a while back. I'll try and link to it when I'm not on my phone. There is no clear cut winner because each of the arrows does a different thing. I remember arcane Bodkins being the most reliable after true flight and hag bane against infantry, but once we hit cavalry, the rolls reverse.

 thedarkavenger wrote:
Aaaactually, Ben Curry posted the averages on Twitter a while back. I'll try and link to it when I'm not on my phone. There is no clear cut winner because each of the arrows does a different thing. I remember arcane Bodkins being the most reliable after true flight and hag bane against infantry, but once we hit cavalry, the rolls reverse.

I'd be curious to see. And yes, each arrow does different things... but some are also more situational. Bodkins are great against 4+ or better armor, but if your opponent doesn't bring any, then... well... eh. And if those armored units get to -2 modifiers or better (soft cover + long range, hard cover, move + long range, etc), then Trueflights are actually equal in effectiveness. The 'fires are only good against one type of army at a time, and Hagbane is cheaper anyway. Swiftshiver only really excels against high numbers of lightly armored or naked T3/T4 models at close range.

The thing about Hagbane is that when it's not excelling (high toughness, no armor), it's still just plain good. Every other option can drop down to being completely ineffective. Bodkins give you nothing against unarmored or 6+ foes. 'Fires don't do anything against the wrong army type. Swiftshiver gives you no more wounds than normal shots once you start hitting more modifiers than just long range. Hagbane only becomes 'useless' once you hit -4 modifiers or worse, which is not unheard of but pretty rare compared to the other situations described. At its worst it's usually not that far behind whichever arrow is technically the best choice for that particular situation, which makes it consistent. Trueflights, in a similar vein are only ever a waste of points when you're firing at close range in the open. As nice as that situation is, it's relatively rare. On top of that, both Hagbane and Trueflight are the cheapest upgrades in the bunch, making their value per point all the better.

I wouldn't say that it's 'wrong' to choose another arrow type, but I think if you're trying to build a TAC list, Hagbane and Trueflight are the two priorities by a clear margin for their consistently good bonuses in the largest variety of situations.

Great exercise! Good reading here, and its much appreciated. I'm very interested to see how the math plays out relative to in-game experience.

Another factor: Since Wood Elves get to bring their own forest, and Venom Thickets are a very attractive option: Some WE players may expect do a lot of shooting with "free" poison, which reduces the value of Hagbane... Edit: I am a bad.

I was going to make mention of the differing points values, but I think once the value of the model itself is calculated, the difference between the most expensive arrow and the least expensive are not very significant.

Anyhow, thanks again- great read.

Awesome work. Well done!

@Red_Zeke: alas, for Venom Thickets only make your close combat attacks Poisoned. So Hagbane is still #1.

Whoops! So much for my contribution!

Glad you guys find it useful!

 Red_Zeke wrote:
I was going to make mention of the differing points values, but I think once the value of the model itself is calculated, the difference between the most expensive arrow and the least expensive are not very significant.

This is an interesting point. There's something to say for 'It's already expensive, why should I care about a few extra points?' Supposing you're looking at 14 points vs 16 points (don't shoot me GW lawyers!), that's not as significant as, say, 5 points vs 7 points; that's ~14% vs ~40%! Still, it can add up a bit over time. A unit of 20 glade guard would cost 40 more points if you went with Bodkins instead of Hagbane, for example. That's room for a few more Glade Guard that took Hagbane instead, which might even up the average wounds to get even closer to Bodkins while being all the more deadly against everything else anyway.