AOS Mathhammer - Judicators v. Vanguard Raptors

I'm creating a Stormcast army and I'm trying to decide between Judicators and Vanguard Raptors with longstrikes.

EDIT - My original calculations did not take into account the shockbolt bow nor the +1 to hit for the judicator prime, both of which will lower the Judicator's scores.  I've updated below.

EDIT 2 - I've fixed two errors in the text below pointed out to me by C4st3r. There happens to be a lot of text removed (but luckily, very little of the math). How embarrassing for me.

Judicators v. Vanguard Raptors

So the initial calculations against no armour is as follows:
Judicators (5) - 2/3 to hit, 2/3 to wound, 1 damage, 4 shots + 5/6 to hit, 2/3 to wound, 1 damage, 3.5 shots = 16/9 + 17.5/9 wounds = 33.5/9 = 67/18
Vanguard Raptors (3) -  4/6 to hit, 2/3 to wound, 2 damage, 3 shots = 8/3 wounds PLUS 1/6 to hit * 2 mortal wounds, 3 shots = 1 MW

Against armour: Judicators have -1 rend, and the VR have -2 rend.

Against 3+ armour, Judicators will do 33.5/18 (=1.86) wounds and VR will do 16/9 + 1 (=2.78)
Against 4+ armour, Judicators will do 134/54 (=2.48) wounds and VR will do 40/18 + 1 (=3.2)
Against 5+ armour, Judicators will do 335/108 (=3.10) wounds and VR will do 8/3 + 1 (=3.67)
Against 6+ armour, Judicators will do 67/18 (=3.72) wounds and VR will do 8/3 + 1 (=3.67)

Unsurprisingly (given their higher rend), VR will consistently do more damage against armoured targets. Against:
3+ armour, they do 1.49 times more damage,
4+ armour, they do 1.29 times more damage,
5+ armour, they do 1.18 times more damage, and
6+/- armour, they do 0.99 times more damage.

They are also 1.25 times more expensive (180 v 160 pts) which means that, in terms of damage output, Vanguard Raptors are a more efficient use of points when facing 3+ and 4+ armour and Judicators are a more efficient use of points when facing 5+ and 6+ armour.

Additional Considerations

Three KEY considerations that aren't included in the above analysis:

1. RESILIENCE - Judicators have 10 wounds instead of VR's 6. So if your squad takes 5 wounds, the Judicators are still going to be pumping out over 75% of their full strength damage and the VR squad will be pumping out only 33% of their full strength damage. If the squad takes 6 wounds, the Judicators are still dishing out approx 65% of their full strength damage and your VRs are wiped out.
2. BATTLELINE - Judicators happen to be battleline in any Stormcast army, whereas you need a Lord Acquilar to make your Vanguard Raptors battleline. Vanguard Raptors are never battleline. This can be a big deal depending on the rest of your army (i.e. you need to fill out battleline slots).

EDIT - The below is not true. The easily accessible +1 to hit bubble in the SE book is the Lord Celestant on foot, but his bubble only applies in the combat phase (and these guys obviously shoot in the shooting phase.  Keeping the text below in case you have access to a +1 to hit from some other source. 

1. SYNERGY - By combining with a +1 to hit bubble, the VRs will do an average of one extra MW per turn (which is pretty awesome). However, they'll do a little less damage through regular wounds (since the Rule of One states that a natural roll of one before modifiers fails). So although the VRs will do an average of 2 MW per shooting phase, they'll do 25% less damage otherwise (because 4/6 to hit becomes 3/6).  Note that under these new percentages (set out below), the VR's do 1.29 times more damage to 5+ armour and 1.08 times more damage to 6+ armour. It's still increasing their damage output as follows:

Against 3+ armour, VR will do 12/9 + 2 (=3.33) (increase of about 20%)

Against 4+ armour, VR will do 30/18 + 2 (=3.67) (increase of about 15%)
Against 5+/6+ or no armour, VR will do 6/3 + 2 (=4) (increase of about 9%)

Lord Celestant (on foot) synergy

So the synergy is pretty great, but is it worth it? I'm going to do a little thought exercise.  Against 3+ armour, the Lord Celestant is worth about 36 pts per phase of shooting at full strength. Against 4+ armour, this becomes 30 pts and against 5+/6+ this becomes 16 pts. A Lord Celestant costs 100 pts. So, approximately, the Lord Celestant justifies his cost (on this alone) if you can boost a full strength squad of VRs through 3 shooting phases against 3+ or 4+ armour (or three full strength squads of VRs through one phase).

We shouldn't ignore the LC's synergy with the Judicators. He won't effect the prime (who already hits on 2+), but the others will do 25% more damage (because a 4/6 to hit becomes a 5/6 to hit) resulting in a total of 37.5/9 instead of 33.5/9, which represents a 12% boost. As Judicators cost 160 pts, that's a benefit of 19 points, which means you'd need to boost a squad through 5 phases to justify the cost.

Conclusion - so are Judicators or Vanguard Raptors better?

Ultimately, it depends. It depends on whether your opponent has a horde of lightly armoured guys or few heavily armoured warriors. It depends on how you plan to use them - are they meant to take out the enemy's force multipliers? Are those force multipliers going to only be visible for one turn (in which you want to have the highest output possible for that turn)? Does your enemy have more shooting than you in which case their resilience will matter?

Personally, I already have a unit of Judicators so I'm likely to grab a squad of VRs so I can see which work better with my style. Ultimately, it will probably depend on whether I also end up running a Lord Celestant on foot and the rest of my army's target saturation. There's no point in running VRs if they're the easiest models to kill per point and they always die first.  Anyway, we'll see how it works!