A simulation of the effect of Strafe FPA with GoD: what’s the effect of going from 7 to 6 FPA? Is 9 FPA any good? How good is Valla?

The GoD 4pc effect makes you fire your last fired primary, typically Hungering Arrow, when a Stafe projectile hits an enemy. This effect has 9 frames internal cooldown (and the game runs at 60 fps). So let's say you and the target are both static, and your Strafe has 7 FPA (frames per attack). That means if your Strafe fires at, say, frame 0, then frame 7, then frame 14, you'll hit at X (how long it takes the projectile to travel), 7+X, and 14+X, and the first and third shot will yield a HA whereas the second will hit during the ICD, so you'll get one HA per 14 frames. Based on this model, it is often assumed that 9 FPA should be great, as you should get the maximum of one HA per 9 frames, whereas 8 FPA should be terrible. It should also be noted that with Valla's Bequest, Strafe projectiles pierce which means with infinite mob density, you'd have projectiles hitting mobs in every frame so that you'd get the perfect 9 frames per HA, and it is often assumed that using Valla means you have little use for IAS.

You can find the Strafe breakpoints at the d3planner. A few are:

  • 11 FPA: 1.2501 APS
  • 10 FPA: 1.3637 APS
  • 9 FPA: 1.5001 APS
  • 8 FPA: 1.6667 APS
  • 7 FPA: 1.8751 APS
  • 6 FPA: 2.1429 APS
  • 5 FPA: 2.5001 APS

I went and observed some projectiles in action, backed up for some of it by a free 10 fps recording program. Some observations: HA projectiles take about a second to travel off screen when fired up to the corner, and 0.7 off to the side, and their movement speed is about 350% (similar to DH with 100 + 25 from paragon + 15 hidden SS non-displacement bonus + 60 Tactical Advantage + 160 fully charged Momentum = 360). Strafe projectiles take about 0.4 seconds up to the corner, and 0.2 to 0.25 off to the side. Strafe projectiles don't just fly off in any direction, but pick a target as long as one exists within approximately the distance that a Strafe projectile covers in 0.1 sec (= 6 frames), which is similar to (perhaps a bit larger than) the radius in which enemies tend to be concentrated while you're fighting them.

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First let's assume that each Strafe takes 1 frame to reach the enemy (which gives the same result as assuming 5 or any other number of frames), and that we Strafe for a random number of frames from 60 to 180 before we stop to refresh Momentum (we want a wide spread to even out imbalances at particular frame totals). From 5 to 11 FPA, by simulation we find that the number of frames per HA is 9.7, 11.5, 13.3, 15.1, 8.7, 9.6, 10.6. We'd expect 10, 12, 14, 16, 9, 10, 11, but when you stop strafing, you don't seem to have to finish the animation so that the last projectile may only cost 1 frame depending on timing.

Now let's add the time it takes to fire that one HA to refresh Momentum before you continue strafing. By making some assumptions about how you'd end up at a particular Strafe FPA, we get how much APS you'd have, and then convert that to Hungering Arrow FPA. I assumed from 5 to 11 Strafe FPA, our Hungering Arrow FPA would be 17, 20, 22, 25, 27, 31, 33. Then I divided that by 3 to roughly account for the fact that we clearly don't have to finish the entire HA animation before we start Strafing again. The result was 10.1, 12.1, 14.1, 16.1, 9.4, 10.5, 11.5

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Now suppose each Strafe takes 1 or 2 frames to hit with equal probability (or equivalently 5 or 6 frames or w/e). We get 10.1, 12.1, 14.1, 14.5, 12.2, 10.5, 11.5. Even assuming this very small variability, 9 FPA is already worse than 10, and the advantage it has over 8 is greatly reduced. With 1-5 frames, it's 11.4, 11.8, 12.7, 13.5, 13.5, 13.3, 12.9 – here we also see the improvement when going from 7 to 6 significantly reduced.

Let's make a better, Valla-compatible model. The monster density up to 6 frames away is a certain value, and beyond that a certain lower value – let's say 1/10th as high in the 7-24-frame range, and after 24 frames (let's say) the projectile disappears. The Strafe projectile randomly picks a target within 6 frames to fire towards, thus the chance that it targets an enemy at R frames is proportional to R. It never misses its target (those projectiles are FAST) but it can hit other enemies before and/or after, the chance during each frame being proportional to the monster density at its current location. We determine the "close monster density" by estimating on average how many times we expect a Valla Strafe projectile to hit a target within 6 frames other than the intended one.

Say it's 0.5 extra hits on average; we'll call this "0.5 density"; without Valla, the frames per HA are 11.5, 12.0, 12.5, 13.4, 13.7, 13.7, 13.5. With 1 density, we actually get the exact same results (when rounded). 2 density, we get 11.2, 12.0, 12.8, 13.7, 13.3, 12.9, 12.8. 3 density (50% chance each frame), it's 10.8, 12.0, 13.2, 14.0, 12.7, 12.0, 12.2. With really high monster density, then, we see a decent improvement of 9 over 8 (although 10 is even better), and the improvement going from 7 to 6 grows back to somewhat respectable size.

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Taking a look at Valla, it's interesting to note that faster attack rate is not clearly less useful than without Valla. 5-7 Strafe FPA, 0.5 density: 10.5, 11.1, 11.6. 1 density: 10.0, 10.4, 10.9. 2 density: 9.2, 9.5, 9.9. 3 density: 8.8, 9.0, 9.3. So at 1 density, using Valla yields ~15.5% more HA's at all FPA's vs no Valla – not worth it compared to using Fortress Ballista to get a higher Squirt uptime. At 7 FPA and 0.5 to 3 density, using Valla yields +8% to +46% – at higher FPA, a bit less than that.

At 1 density, going from 7 to 6 FPA gives you +4.7% HA's without Valla and +4.3% with. With 1h+quiver, this is possible with 1 IAS trait, otherwise it takes 2 non-weapon IAS traits (with 1.6 weapon APS it requires 34% IAS). For comparison, if you're at 58% crit 560% crit dmg, +50% crit dmg gets you +6.8% dmg.


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