Attack speed

For C4 Charlie's upgrade, see Attack Speed (upgrade).

Buff icon for attack speed in BTD6

Attack speed is a mechanic in the Bloons TD series and Bloons Supermonkey series of games, which determines the amount of time that a Tower needs to perform an specific attack. It is typically measured in frames in the older games and seconds in the newer entries. It is one of the three main mechanics that determine the offensive capability of a tower alongside Damage and Pierce.

Name

There is not a unique way to name this mechanic, not even in the same game or in official patch notes. In the list below there are examples of different notations across the Bloons TD franchise:

• Attack Speed is used in the description of the Rapid Reload upgrade in Bloons TD 5.
• Reload time is used in the description of the Monkey Knowledge Veteran Monkey Training in Bloons TD 6.
• Attack rate in the description of Jungle Drums upgrade in the Flash version of Bloons Monkey City.
• Attack cooldown or reload rate is used sometimes in official patch notes. Attack cooldown is sometimes simply referred as cooldown, but the former is preferred because it can also be used to refer to the recharge time of an Activated Ability.
• Rate of fire is used in Adora Level 20 description in Bloons TD 6.

Mechanics

Bloons Supermonkey 2

Attack speed in Bloons Supermonkey 2 is implemented with a mechanic that in the mobile version, is internally named cooldown. This cooldown is the amount of time in seconds which a certain weapon or powerup will take before performing an attack. In the Flash version it is measured in frames, while in the mobile versions it is measured in seconds, and each weapon has a separate cooldown value. However, if the player notices the amount of damage that a tower is dealing before and after an attack speed or buff is applied, sometimes the tower seem to be doing better than expected, and this is because on how the actual attack speed / cooldown mechanic is implemented.

While there is no way of buffing attack speed in the Flash version, in the mobile version Turbo Boost will reduce the attack cooldown of Supermonkeys by a certain multiplier. In the mobile version, it is mechanically similar with how Attack Speed is handled in Bloons TD 6, where if an attack exceeds 1 attack per frame, it will simulate multiple attacks per frame. The entire Energy arm weapon line (excluding Epics) has a fixed cooldown of 0, resulting in it attacking every frame, and cannot be buffed by attack speed.

Bloons TD 5 / Bloons TD Battles / Bloons Monkey City

This section is incomplete. You can help out by expanding it. The editor who added this notice elaborates: flash game stuff, such as attack speed caps

In the mobile versions, most attacks have a separate CooldownTime and FireDelayTime stat. The cooldown time determines the amount of time it takes to initiate the next attack, while the fire delay time determines the delay between when an attack is initiated and when the attack fires. The sum of these two values determines the overall attack speed of a tower. For example, the Dart Monkey has a CooldownTime of 0.7 seconds and a FireDelayTime of 0.2 seconds, giving it an overall delay between attacks of 0.9 seconds, or roughly 1.11 attacks per second. Most tower buffs that "increase attack speed" reduce both the cooldown time and fire delay time, but some, such as the Attack Speed modifier of the Monkey Lab, only reduce the cooldown time. This makes them less effective on attacks with long fire delay times, such as the Mortar Monkey's main attack.

Bloons TD 6

Attack speed in BTD6 is implemented with a mechanic internally named cooldown. This cooldown is the amount of time in seconds which a tower will take before executing an attack or performing certain actions such as producing spikes or spawning sub-towers. This is measured in seconds, and the upgrades modify the value of this stat to a certain number. However, if the player notices the amount of damage that a tower is dealing before and after an attack speed or buff is applied, sometimes the tower seem to be doing better than expected, and this is because on how the actual attack speed / cooldown mechanic is implemented.

For example a 0-0-0 Dart Monkey has an attack cooldown of 0.95s, this is the amount of time that will pass between shots. Upon being upgraded to 0-1-0 Quick Shots, which claims to increase the attack speed by 15%, this cooldown is reduced to 0.8075s, which is a 15% reduction of the cooldown of the 0-0-0 tower, and the 0-2-0 Very Quick Shots upgrade further reduces it to 0.6365s which is a 33% reduction of the base monkey giving the number stated in the upgrade's description.

However if the Dart Monkey is tested in a mode such as Sandbox, the upgrades will seem to be doing better than expected, with the 0-1-0 upgrade increasing the damage a little bit higher than the 15% expected increase in damage, and the 0-2-0 doing nearly 50% more damage.

To explain this difference, the first thing that should be noticed is that what most people understand as Attack Speed is a similar but not exactly same thing as the Attack Cooldown concept used in the game. Attack Speed could be defined as the number of attacks a tower performs in a certain amount of time, and Attack Cooldown as the inverse, the amount of time that the tower needs to perform an attack. This definition makes Attack Speed directly proportional to the damage (higher attack speed equals more damage) and the attack cooldown inversely proportional to the damage (lower cooldown equals more damage).

With those definitions and going back into the Dart Monkey example, the cooldown of 0.95s means the tower will throw ~63 darts per minute, with the 0-1-0 upgrade this increases to ~74 darts per minute and the 0-2-0 goes to ~94 darts per minute. The proportions of those numbers mean a ~17% and ~49% increase of the amount of darts, corresponding with the amount of damage that the tower produces.

In general if an upgrade of buff description states that the attack speed of a tower is being increased by a certain percentage, what it actually does is reducing the cooldown in that proportion by applying a multiplier, which in most situations is $1-\text{Bonus percentage }$. And different bonuses stack multiplicatively:

$$\text{Cooldown}=\text{Base Cooldown}\times {\text{Multiplier}}_1\times {\text{Multiplier}}_2\times \cdots$$A list of all attack cooldowns available in BTD6 are listed in the following table (multipliers in this table are rounded to 4 decimals and percentages to the nearest integer).

Cooldown multipliers in BTD6

Icon	Source	Cooldown multiplier	Attack speed / damage increase	Applies to	Notes
	Turbo Charge ability	0.1429	600%	Itself
	Glaive Dominus	0.9	11%	Primary towers in range
	Absolute Zero ability	0.6667	50%	All Ice Monkeys
	Elite Sniper	0.75	33%	All Sniper Monkeys
	Elite Defender Bloon progress passive ability	1.0 to 0.5	0% to 100%	Itself	Attack speed increase percentage is the same as the Bloons progress in the track. Not standard multiplier, see notes of Heart of Vengeance.
	Elite Defender lives lost passive ability	0.25	300%	Itself	Triggers when lives are lost.
	Nautic Siege Core	1.3	–23%	Heroes in range	Only while submerged.
	Carrier Flagship / Navarch of the Seas	0.85	18%	All towers placed in water
	Artillery Battery ability	0.25	300%	Itself
/ /	Sun Temple / True Sun God / VTSG	0.9 or 0.8	11% or 25%	All other towers in range	Depends on the amount of Support sacrifices given to the tower.
	Shinobi Tactics	0.92Stacks 0.92 at 1 stack 0.1887 at 20 stacks	9% at 1 stack 430% at 20 stacks	All Ninja Monkeys in range	Shinobi tactics buff is 0.92 elevated to the power of the number of stacks. For intermediate values, attack speed increase can be calculated with the formulas below.
	Berserker Brew	0.9	11%	Towers targeted by the potion
/	Stronger Stimulant / Permanent Brew	0.85	18%	Towers targeted by the potion
	Heart of Vengeance	0.9091 at no lives lost 0.6667 at 40 lives lost	10% + 1% per life lost 50% maximum (40 lives lost)	Itself	This multiplier is not standard, the bonus actually works over the attack speed. The multiplier can be calculated by $\text{Multiplier}=\frac{1}{\text{Increase}+1}$.
	Druid of Wrath	0.9524 at 10 damage 0.5 at 200 damage	5% per 10 damage inflicted 100% maximum at 200 damage	Itself	Not standard multiplier, see notes of Heart of Vengeance. Multiplier expires at the end of the round, or after not dealing damage for 2s.
	Poplust	0.8696 at 1 stack 0.5714 at 5 stacks	15% per stack 75% at 5 stacks	All other Druids in range	Not standard multiplier, see notes of Heart of Vengeance.
	Smart Spikes passive ability	0.25	300%	Itself
	Jungle Drums	0.85	18%	All other towers in range
	Call to Arms	0.6667	50%	All towers	Not standard multiplier, see notes of Heart of Vengeance. Overrides Homeland Defense if active.
	Homeland Defense	0.5	100%	All towers	Not standard multiplier, see notes of Heart of Vengeance. Overrides Call to Arms if active.
	Overclock	0.6	67%	Targeted tower
	Ultraboost	0.96Stacks 0.96 at 1 stack 0.6648 at 10 stacks	4% at 1 stack 50% at 20 stacks	Targeted tower	Ultraboost buff is 0.96 elevated to the power of the number of stacks. For intermediate values, attack speed increase can be calculated with the formulas below. Also applies the Overclock boost but does not stack with it.
	Master Builder passive ability	0.7692 after 1 round	30% per round	Itself	Keeps stacking until Master Builder attack speed is 0.15s. Not standard multiplier, see notes of Heart of Vengeance.
	Gwendolin passive ability	0.9 at Level 5+ 0.8 at Level 18+	11% at Level 5+ 25% at Level 18+	All Ring of Fire, Signal Flare or Dragon's Breath and their upgrades
	Striker Jones passive ability	0.9 at Level 5+ 0.8 at Level 18+	11% at Level 5+ 25% at Level 18+	All Bomb Shooters and Mortar Monkeys
	Obyn Greenfoot Nature's Wrath	0.75	33%	Druids in range
	Obyn Greenfoot Nature's Clarity	0.95	5%	Magic towers in range
	Ezili Sacrificial Totem	0.85	18%	All towers in range
	Ezili Sacrificial Totem	0.95	5%	All towers in range	Additional buff to Wizard Monkeys.
	Adora Blood Sacrifice	0.9 – 0.01 per $100 on the sacrificed tower	11% minimum 100% maximum	Herself, Sun Avatars and their upgrades	Multiplier capped to 0.75 ($1,500) in Levels 7 – 19 (33% maximum attack speed increase), and 0.5 ($4,000) at Level 20.
	Admiral Brickell Naval Tactics	0.5	100%	Herself and all towers placed in water in range, at Level 19+ is all towers in water
	Geraldo Jar of Pickles	1.3333	–25%	Targeted tower	Not standard multiplier, see notes of Heart of Vengeance.e.
	Corvus Aggression	0.5	100%	Spirit
	Phayze Slow Aura	1.1 (1st skull) 1.15 (2nd skull) 1.2 (3rd skull)	–9% (1st skull) –13% (2nd skull) -17% (3rd skull)	All towers
	Elite Phayze Slow Aura	1.1 to 2.2	–9% to –55%	All towers	Varies depending on the tier and skull, consult Phayze's page for more information.
	One Two Tree / Polyphemus map mechanic	0.85	18%	All towers placed in the corresponding area
	Ancient Portal map mechanic	0.7	43%	Heroes placed in the corresponding area
	Fast Glue	0.9	11%	Glue Gunners
	Fast Tack Attacks	0.92	9%	Tack Shooters
	Come On Everybody!	0.95	5%	Primary towers of Tier 2 or lower
	Gun Coolant	0.9	11%	Monkey Aces
	Flanking Maneuvers	0.9	11%	Monkey Snipers, Subs and Buccaneers
	Speedy Brewing	0.95	5%	Alchemists
	Veteran Monkey Training	0.97	3%	All towers
	Paragon of Power	0.8333	20%	Paragons
	Quick Hands	0.96	4%	Heroes
	Monkey Boost	0.5	100%	All towers
	Time Stop	1.6667	–40%	All towers	Not standard multiplier, see notes of Heart of Vengeance.
	Energizing Totem	0.75	33%	All towers in range

For example, the attack cooldown of a 0-0-0 Dart Monkey which is in the range of a 2-4-0 Monkey Village (Jungle Drums, Call to Arms) and 4-0-0 Stronger Stimulant while all temporal bonuses are active and the player has the Come On Everybody! and Veteran Monkey Training Monkey Knowledge is:

$$\text{Cooldown}=0.95\left[\text{s}\right]\times 0.85\times 0.6667\times 0.85\times 0.95\times 0.97\approx 0.4267\left[\text{s}\right]$$

The actual attack speed / damage increase can be calculated as follows:

$$\text{Increase}=\left(\frac{1}{\text{Multipliers}}-1\right)\times 100\mathrm{\%}$$

Or if the percentage indicated in the game is known:

$$\text{Increase}=\left(\frac{\text{Bonus}}{1-\text{Bonus}}\right)\times 100\mathrm{\%}$$

For example, in the attack cooldown example, the total attack speed increase is:

$$\text{Increase}=\left(\frac{1}{0.85\times 0.6667\times 0.85\times 0.95\times 0.97}-1\right)\times 100\mathrm{\%}\approx 125.3\mathrm{\%}$$

And going back into the the 0-1-0 upgrade for a Dart Monkey the actual attack speed increase is:

$$\text{Increase}=\left(\frac{0.15}{1-0.15}\right)\times 100\mathrm{\%}\approx 17.6\mathrm{\%}$$

And for the 0-2-0 upgrade:

$$\text{Increase}=\left(\frac{0.33}{1-0.33}\right)\times 100\mathrm{\%}\approx 49.3\mathrm{\%}$$

The attack cooldown has no correlation with the frame rate of the game, as it is possible to have attacks that are faster than a single frame, in this case the animations can be visually skipped, show inconsistencies, or produce multiple projectiles per animation, but the damage dealt is properly applied on average. This will also be the case with high game lag, with the only difference being that in-game time might run slower than real time producing visual slow motion.