The Effects of Speed on Combat.

Hits Per Turn

Three variables affect your speed in combat and together they combine to give your number ofhits per turn(HPT). The variables are global speed, attack speed, and weapon speed.

The game mechanics use energy to track all this. 100% global speed gives you 1000 energy points per turn (EPT), and a regular attack costs 1000 energy points per hit (EPH).

So for a normal character at 100% global speed, with regular 100% attack speed, and with a regular weapon at 100% weapon speed, you simply get exactly 1 hit per turn (1000 EPT/ 1000 EPH = 1.00 HPT).

Naturally, we can eliminate 1000 from this formula, as the 1000 number is arbitrary. The hits per turn formula is therefore simply

Hits Per Turn = Global_Speed x (1 + Attack_Speed) / Weapon_Speed.

But if Weapon Speed is slower than 100% (a negative number in the Character Sheet, it is counted as zero). This can happen with talents like Aim and Precise Strikes. So strictly the formula is:

Hits Per Turn = Global_Speed x MAX [ (1 + Attack_Speed)/Weapon_Speed), (1 + Attack_Speed) ].

However, I find it helpful to think using 1000 energy, so I'll stick with this in the calculations below. Also, and more importantly, the addon uses this as the 1000 base for energy/speed, rather than as percentages, so it is important to know where the figures come from.

Weapon speed and Attack speed both affect Energy per Hit EPH. We will look at these first.

The effect of weapon speed

Weapon speed is listed on the weapon as 100% for regular melee weapons, 90% for quick weapons, 80% for regular shooters, 70% for swiftstrike shooters, and gauntlets vary from 50% to 80%.

This percentage is multiplied by the energy per hit (EPH). Thus a sling at 80% weapon speed costs 800 EPH.

Example 1: Regular bow/sling at 80% weapon speed. 1000 EPT / 800 EPH = 1.25 HPT.
Example 2: Quick weapon at 90% weapon speed. 1000 EPT / 900 EPH = 1.11 HPT

The effect of attack speed

Attack speed also reduces/increases the amount of energy per hit EPH. Attack speed is reduced/increased by many talents, such as Rapid Shot, Precise Strikes, and equipment differences (e.g. gloves vs gauntlets, amulets of enraging, etc). So rapid shot at 5/5 for at talent level 1.3 gives 65% increase in attack speed. To calculate the energy required, divide 1000 by 1 + the percent increase. So 65% increase gives 1000 / 1.65 = 606 energy points per turn (as indicated by lukep's addon).

Some talents decrease attack speed, such as precise strikes and aim. In this case, the EPH increases.

Example 3: Rapid shot gives 65% attack speed increase and an (hypothetical) bow at 100% weapon speed (as they have lower than this, see next section). 1000 EPT / 606 EPH = 1.65 HPT.

The effect of attack speed and weapon speed combined
Attack speed and weapon speed stack, so, using my example, rapid shot at 5/5 gives me 606 EPH and weapon speed of 80% gives 0.8 x 606 = 485 EPH. Thus the hits per turn are 1000 EPT / 485 EPH = 2.06 HPT.

However, when weapon speed is over 100%, as in Precise Strikes on a regular weapon, or for Aim, EPH is not multipled again (otherwise it would be calculated twice in the equation). This is example 1 below.

So precise strikes of 10% decrease in attack speed with no other mods is 1000 EPT / (1 - 0.1) = 1111 EPH. Thus the hits per turn are 1000 EPT / 1111 EPH = 0.9 HPT.

Example 4: Precise Strikes at 10% decrease to attack speed, with regular weapon. 1000 EPT / (1 - 0.1) = 1111 EPH. 1000 EPT / 1111 EPH = 0.9 HPT.
Example 5: Rapid Shot at 65% increase to attack speed, with swiftstrike bow at 70% weapon speed. 1000 EPT / 0.7 x 606 EPH = 2.36 HPT
Example 6: Rapid Shot at 65% increase to attack speed, with Precise Strikes 10% decrease to attack speed, giving attack speed of 48.5% in char sheet, with regular bow at 80% weapon speed. EPH = 1000 / 1.485 = 674. 1000 EPT / 674 EPH = 1.86 HPT. This makes sense, as it is slightly lower HPT than without precise strikes (2.06 HPT, see above)

Incidentally, if you want to calculate how to get the 48.5%, it is Increase - (Decrease x (1 + Increase)). (e.g. 0.65 - (0.1 x (1.65) = 0.485). That is, you decrease based on the increased amount.

The effect of global speed

Global speed increases the amount of energy per turn EPT. So 40% increase gives you 1400 EPT. So you get more time (= energy) to do stuff.

Equipment and talents can increase global speed, some temporarily and some permanently.

Eden's Guile for instance, gives you 29% increase to global speed. We simply then change EPT to 1290 and calculate accordingly. This is where we see significant changes to HPT.

Example 7: Eden's Guile at 129% global speed, regular weapon. 1290 EPT / 1000 EPH = 1.29 HPT.
Example 8: Eden's Guile at 129% global speed, regular shooter at 80% weapon speed. 1290 EPT / 800 EPH = 1.61 HPT
Example 9: Eden's Guile at 129% global speed, swiftstrike shooter at 70% weapon speed, Rapid shot at 65% increase attack speed. 1290 EPT / 424 EPH = 3.04 HPT.
Example 10: Blinding Speed at 141% incrase, swiftstrike shooter at 70% weapon speed, Rapid Shot at 65% increase attack speed. 1410 EPT / 424 EPH = 3.31 HPT

Theoretical Maximum for HPT

This is hard to estimate precisely.

I think it would be a Yeek Archer: Yeek (global speed 15% increase) + global speed prodigy (15% increase), Rapid Shot with extra talent point + Ring of War Master + enraging amulet at 10% increase would give close to 100% attack speed increase I think. Randart sling with double swiftstrike for 60% attack speed (is this possible?) and 5% global speed increase, with offhand blazebringer at 5% global speed increase. Blinding Speed (but not with extra talent point, as to get global speed prodigy you need 20 in equi, which requires 2 unlocks, and we've spent 2 already), so 41% increase, to base of 140% global speed of yeek 15% + prodigy 15% + sling 5% + offhand 5%, giving total (temporary) global speed of 97.4% increase.

That is, hypothetically, you might get temporarly 97.4% increase in global speed, 100% increase in attack speed, and 60% increase in weapon speed!

This would give then, using generic formula above 1.974 * (1 + 1) / 0.6 = 6.58 hits per turn!

The other class that might outdo this even is a Yeek Brawler, but I'll leave it to someone else to calculate.

The 3.31 HPT (example 10 above) with max Blinding Speed, Swiftstrike, and max Rapid Shot, can be achieved by an archer by about lvl 17, if you save class points for this effect, and find a swiftstrike, which are quite rare. When your ammo has on hit effects, this means you increase your chance of landing one of these per turn.

When do I get my extra hits per turn?

You have to accumulate the energy to the point when you have enough to do more than one action per turn. For example, you have weapon speed of 80% and no other modifier. In turn one you'll accumlate 200 energy, then 400, then 600, then 800. At this stage, you use 800 for your first shot, using up your spare energy and then you get your second shot. You can see this by putting on a regen infusion, and shooting randomly, and seeing when you get two shots per turn.

So then, can you assume that you have to wait, in such an example when HPT = 1.25, for 4 turns before an extra shot? No, because the complication is that you can accumlate energy from all sorts of places. You might have movement speed increase, and so you move, giving you some spare energy each move. Move 3 times, to pump up your stock, and then shoot twice. Hard to coordinate, but it happens. So in practice, the extra shot appears anywhere in the 5 turn period.

But this also illustrates why getting HPT 2 is so valuable. In this case, you always get 2 and sometimes 3 shots in a turn. And if you get to example 10, which can be done by about lvl 17, you can get HPT = 3.31 HPT. In 4 turns you'll shoot about 13 times with Blinding Speed! And that makes a BIG difference.

Acknowledgements

The clock addon by lukep, and the many forums posts on speed and on Rapid Shot vs Aim, and some code delving, and running lots of archers, finally gave me the tools to figure this out properly I hope.

Conclusion

I hope this guide helps you understand more how speed affects combat in the game, as of version 1.0 of Tome.

Please post any corrections or comments or clarifications, and I'll do my best to answer them. I've probably made some errors, but I did check everything as carefully as possible.