Bow damage formula?

[bcbrown]

The problem's all solved. We already know that melee weapons have a modal value equal to 2*dmg + bonus. I've already parsed the modal values for BFG with 1 and 3dmg arrows. They fit a pattern of damage + arrow damage + 1 + 2h damage bonus, with double damage not including the damage bonus. The modal value when unrooted with Tolan's arrows is 82. SBOZ is (2*11+10)/18 = 1.77, and 82/50 is 1.64 for BFG. Against Bloodmaw a while back I got:

bloodmaw_bfg_no_disc   0:08:49    529    72.36    89.74%    
bloodmaw_zek           0:07:22    442    74.49    93.70%

So the modal values for SBOZ and BFG pretty well predict performance against Bloodmaw, as expected. And obviously if you care about damage against a specific mob you'll want to run parses against that mob.

My ranger's out adventuring in Stonebrunt right now and I don't have fletching high enough to craft +8s yet so it'll be a while before I can run those parses, but I'm pretty confident when I run do they'll be 63 and 92.

Oh, and one more thing:

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

23 * 2 + 34 = 80 damage for the non-double damage values. But he was getting mostly 82's. His double damages should be 23 * 4 + 34 = 126, but he doesn't have that many 126 damage hits.

82 is the value for the doubled hits. 58 is the value for the non-doubled hits. You're multiplying by 2 one too many times, and there's a weird +1 in the calculation.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

82 is the value for the doubled hits. 58 is the value for the non-doubled hits. You're multiplying by 2 one too many times, and there's a weird +1 in the calculation.

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

We already know that melee weapons have a modal value equal to 2*dmg + bonus.

This is the core problem with your logic. You are ignoring the weapon damage * 2 + damage bonus formula for BFG specifically by simply adding weapon damage and damage bonus together to get 23 + 34 = 56.

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Look, I think my explanation is dumb as hell and likely wrong, but at least I can make my way to the right number. Your argument is that 75.7 is "close to 78"?

56 does not equal 58. If you are going to attack someone for being off by two on an admitted guess, don't also be off by two yourself!

Your flawed logic and flawed insults aside, you may be right. If you take a look at the EQEMU code, they do actually have a line of code where they divide archery damage specifically by two before applying the double damage 2x multiplier, and before applying the damage bonus.

https://github.com/EQEmu/EQEmu/blob/...tack.cpp#L6370

For example, normally a 23/50 2h weapon at level 57 would have a modal hit of 23 * 2 + 34 = 80.

The Archery equivalent with the division by 2 would be (23 * 2) / 2 + 34 = 56.

Archery Double Damage with the division by 2 would be ((23 * 2) / 2) * 2 + 34 = 80.

I didn't initially bring up this damage / 2 line of code because it applies to all classes doing archery. It acts like the equivalent of a global damage modifier, so there wasn't a point in making things more complicated.

However, this would mean all classes other than Rangers would have their archery damage cut in half before the damage bonus is applied, with no double damage to get it back. We would need to get more data from non-Ranger classes to confirm that they are getting their archery damage halved before applying the damage bonus.

Finally, we still can't account for why your damage values are off by two. We would need more data to see if archery always gets a +1 to damage somewhere. It isn't likely that BFG is the only bow to get +1 weapon damage if bows do get this bonus. We should see the same trend for other bows.

This is why you should supply your raw data, so we can see if you did something incorrectly. I don't mean that as an insult, but everybody makes mistakes.

[Botten]

Speaking of double damage

At player level 60
Weighted Axe = adds flat 110 bonus damage
Earthshaker = adds flat 56 bonus damage

The Weighted Axe is providing almost double bonus damage compared to Earthshaker.

Max haste is 100%
Floor delay on P99 is about 18 or
Delay is rounded up. IE a ‘New (Hasted) Delay’ of 17.02 would result in a delay of 18

...considering Primal Velium Reinforced Bow 33/35 with 100% haste
New Delay 35/1.99 = Roundup 18 delay

Hasted Damage/Delay = 33/18

1. Warriors and Rangers both get 240 skill points in Archery
2. Excluding the discipline Trueshot (Ranger)
3. Excluding the discipline Precision (Warrior)
4. And considering Troll/Barbarian/Ogre Warriors and SKs can only use Weighted Axe while rangers can't

Is double damage from a ranger result in more or less damage compared to Warriors?

[bcbrown]

Looking back at when I measured modal values for Huntsman and Rain Caller, I found the modal value to be bow damage + arrow damage + 1 + damage bonus. At the time I was focused on bow damage + arrow damage + damage bonus and dismissed the off-by-one, saying it "does predict the modal value pretty well."

I think that about wraps it up. Archery by anyone will have a modal damage of bow damage + arrow damage + 1 + damage bonus, with the average damage being higher or lower than the modal damage depending on what mob you're fighting. If you're specifically a ranger above 50 shooting at a stationary unrooted mob, modal damage is 2 * (bow damage + arrow damage + 1) + damage bonus. If you're using the BFG in primary, the damage bonus will be the 2h damage bonus.

So to compare bows purely for bow-rotting rooted targets, you want to look at (bow damage + arrow damage + 1 + damage bonus) / delay. If you're gonna be shooting at targets someone else is fighting and you're a 50+ ranger, look at (2 * (bow damage + arrow damage + 1) + damage bonus) / delay.

And always take into account Snaggle's point about arrow efficiency and Botten's point about fast bows being in danger of overcapping on haste.

Case closed.

[Snaggles]

Originally Posted by Botten [You must be logged in to view images. Log in or Register.]

Speaking of double damage
Is double damage from a ranger result in more or less damage compared to Warriors?

I haven’t seen enough warrior bow parses to know but the weighted axe + bow game for them is very interesting. Especially if one is beserking.

In most situations it seems they are fairly even (maybe the edge to a zerking warrior). Rooted targets or moving targets really ruin the ranger fun. The BFG in some ways makes up for this, both in peak dps and not relying on ranged attacks on root or snare. It’s just nice two opposite classes can both share in an eclectic hobby, lol.

Also…

Thanks bcbrown and Tytos!

As a big BFG nerd it’s always confused me a bit. It doesn’t seem to have massive crits like the multiplying factors would make you believe. Most my crits on disc with 8 damage arrows are in the mid 300 range…yet it churns out dps in an underrated fashion. It using a 2h modifier similar to how the archery skill relies on MH delay actually makes a ton of sense. It must be that fat middle of the Bell Curve pays off in the end.

As for rotting efficiency, I hate to say it but I might have to pull the Skydarkener out of the bank. 28/44 is a horrid ratio but the damage is only 5 base points from a Primal. With an Earthshaker you get those 56 damage bonus hits and with a lot of Dex it’s likely 4ppm at minimum. At 184 per DD that’s just stretching your arrow budget. I’m still not enough of a sadist to quad kite with one though but it might let me delusionally pretend I have a Windstriker.

[Cecily]

Sky has the biggest nuke on any bow if you ignore the quad gimmick. It's legitimately a neat bow just for that.

[bcbrown]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

Your initial explaination added 1 damage randomly, didn't multiply the weapon damage by 2, and used the wrong damage table. I am not sure why you think your idea should be taken seriously, while other ideas shouldn't be taken seriously.

Let me try to help you understand. It's very simple. Any idea has two fundamental criteria it must meet for me to take it seriously. It needs to explain the existing data. And it needs to make a prediction for a future experiment to evaluate. My ideas matched the measurements. I thought (bow + arrow + 1) + bonus was crazy at first but it matched the data. You said it "added 1 damage randomly". It turns out that was correct. You say it "didn't multiply the weapon damage by 2". It turns out that was correct. You say it used the "wrong damage table". It turns out that was correct.

Originally Posted by Goregasmic [You must be logged in to view images. Log in or Register.]

Seeing my sarnak war bow is slightly worse than a windsaber which is second highest that's pretty nice. Huntsman is cool too but there's only a 5dly difference in the end, no huge arrow savings to be made there. The stats on the sarnak are pretty nice too.

Indeed surprising that exquisite sits on top of huntsman when the former has an extra 12dmg for only 6delay.

DPS and damage/delay ratios suffer from the same counter-intuitive problem as MPG as a metric for cars. What you actually care about is the inverse of the metric. Imagine you have a 100 mile daily commute. What's the bigger upgrade? Going from a 20mpg to a 30mpg car, or going from a 50mpg to a 100mpg car? It's the former even though the latter looks bigger. Going from 20mpg to 30mpg means you go from 100 mi / 20 mpg = 5 gallons to 100 mi / 30 mpg = 3.3 gallons, or 1.7 gallons in savings. Going from 50mpg to 100mpg means going from 100 mi / 50 mpg = 2 gallons to 100mi / 100 mpg or 1 for 1 gallon in savings. It's the same thing with DPS versus time-to-kill.

Let's assume the Sarnak War Bow is the current bow, the level for damage bonus is 57, and the mainhand bonus is Earthshaker. Lets look at damge, number of arrows to kill and time to kill for a mob with 3k hp:

Earthshaker: 45 bonus

    Wind Saber:          62, 48 arrows, 1056 delay
    Sarnak War Bow:      61, 49 arrows, 1225 delay
    Bow of the Huntsman: 69, 43 arrows, 1290 delay
    Exquisite Velium:    81, 37 arrows, 1332 delay

So upgrading to Wind Saber means no change in number of arrows, but 17 seconds less time per kill. Upgrading to Huntsman means 6.5 seconds longer per kill, but 6 less arrows. Upgrading to the Velium means 10 seconds longer per kill and 12 arrows less per kill.

Here's the same chart with Swamcaller: 27 bonus

    Wind Saber:          44, 68 arrows, 1496 delay
    Sarnak War Bow:      43, 69 arrows, 1725 delay
    Bow of the Huntsman: 51, 58 arrows, 1740 delay
    Exquisite Velium:    63, 47 arrows, 1692 delay

The way I interpret these numbers: Since this is assuming you're rooting the mob, time to kill isn't super important since you're not taking damage you'll need to heal. Summoning Tolan arrows gives you 20 per 15 seconds or 1.3 seconds each. So saving 6 arrows at the cost of 6.5 seconds per kill in time spent shooting means 6.5 seconds more spent shooting while saving 7.8 seconds summoning arrows. So with this (unhasted) perspective Bow of the Huntsman beats out Sarnak War Bow.

Now, this is napkin math with multiple serious caveats. This isn't taking into account hit rate, haste, or the fact that the average damage per hit will differ from the modal damage based on level difference, offense stats vs defense stats, etc. I think my takeaway is that no matter which of these 4 bows you have you're gonna ball out, and which you choose is as much down to personal style and personal access as anything else. If I had a Sarnak bow I'd try it out and see if I liked it more than the Huntsman. But these numbers reassure me that I'm not really at any disadvantage with my Huntsman.

Originally Posted by Snaggles [You must be logged in to view images. Log in or Register.]

Thanks bcbrown and Tytos!

As a big BFG nerd it’s always confused me a bit. It doesn’t seem to have massive crits like the multiplying factors would make you believe. Most my crits on disc with 8 damage arrows are in the mid 300 range…yet it churns out dps in an underrated fashion. It using a 2h modifier similar to how the archery skill relies on MH delay actually makes a ton of sense. It must be that fat middle of the Bell Curve pays off in the end.

Appreciate it! It's still a little confusing to me. With +8 arrows it looks like it behaves like a 29/50 2h weapon but you can dual-wield an offhand with it. I think it's just got so many weird interactions with enough combat mechanics that you just gotta enjoy the dps and not ask too many questions about how. So I guess we agree.