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Attack Speed is the rate of attacks per second. Attack Cooldown is the cooldown time between each attack. All attacking towers when triggered will create attacks at a specific rate, or inversely, attack after a specific amount of time. If bloons are detected by the tower, they will make an attack, and will persist until there are no longer any detected bloons. Most of the time, enemy bloons have to be within the tower's range to trigger attack, but there are exceptions. Some towers such as the Sniper Monkey can make attacks from any distance, ignoring Range limitations. Other towers such as the Monkey Ace sporadically create attacks every so often for as long as they appear on the map.
An attack is usually done every time bloons are detected by the tower, and will persist to create a constant rate of attacks if the attack is still triggered. Once an attack is made, there is a brief cooldown before the same attack can be created again. If the attack's trigger is off, the attack can still refresh while under cooldown, but the tower only makes an attack once the trigger is turned back on. Attack speed and attack cooldown both calculate the way the attack is created with respect to time.
"Attack speed" is strictly measured in terms of attacks per second. However, there is an inverse of this called the "attack cooldown". Attack cooldown calculates in terms of seconds per attack, which can be used to find the amount of time it takes to make a single attack. An attack can be created at a maximum rate equivalent to the inverse of the attack cooldown.
Attack speed bonuses are calculated in three unique ways: additive attack speed bonuses (e.g. +25% attack speed), multiplicative attack speed bonuses (e.g. 1.25x attack speed), and attack cooldowns (e.g. 0.80x attack cooldown). An additive attack speed bonus is calculated by either multiplying the attack speed multiplier or multiplying the sum of the attack speed percentage bonus plus 100% (e.g. 100% + 25%). On the other hand, an attack cooldown is always calculated by multiplying the attack cooldown multiplier. In order to interchange between attack speed and attack cooldown, convert to multiplier form and then calculate the inverse to obtain the opposite counterpart.
For example, suppose we took the BTD6 Jungle Drums. The attack cooldown provided from this buff is 0.85x. Its attack speed bonus is equivalent to roughly 1.176x attack speed, or +17.6% attack speed. Now take a BTD6 Tack Shooter with Faster Shooting, which has a 0.75x attack cooldown (equivalent to 1.33x attack speed or +33% attack speed) compared to its base 1.4s attack speed. Say that this Tack Shooter is supported by the same Jungle Drums. To find the upgraded Tack Shooter's new attack speed, multiply the upgraded Tack Shooter's attack speed with the attack speed bonus of the buff, or inversely multiply the upgraded Tack Shooter's attack cooldown with the attack cooldown of the buff. Ensure that both variants of these attack speed/cooldown calculations are of the same type.
Before Bloons TD 4
In BTD1, the only upgrade that increased attack speed was for the Tack Tower's (Tack Shooter) Faster Shooting upgrade. In later generations, however, more and more towers have received upgrades that are able to increase attack speed for itself or other nearby towers. The formerly only way to universally increase attack speed was from Jungle Drums, it starting from BTD3.
Bloons TD 4
In addition to more towers being able to gain attack speed via upgrades, towers are also able to gain attack speed via buff from Jungle Drums.
Bloons TD 5
Starting from Bloons TD 5, towers also can gain increase attack speed from towers' various Abilities, including both from self buffs (such as Turbo Charge, boosting the tower's own attack speed for a limited time,) or from Tower Buffs (such as MIB Call to Arms, which increases the attack speed of nearby towers for a limited of time).
Bloons TD 6
Attack speed works the same as it did in previous games, with the addition of some new types of buffs: Some tower upgrades first introduced in BTD6, such as Shinobi Tactics and Poplust, only increase the attack speed of certain tower types within its radius, in this case Ninja Monkeys and Druids respectively. Also introduced, are more conditional attack speed modifiers, such as Elite Defender (scales with bloon progress), Heart of Vengeance (scales with lives lost), and Druid of Wrath (scales with bloons popped by said tower).
Bloons Adventure Time TD
In addition to via upgrades, the attack speed of towers can also be modified by equippable Weapons and Trinkets. Towers have a maximum amount of extra speed that can be given to them before speed boosts cease to do anything; for instance, Supermonkey's Sun God upgrade cannot be made to fire more than 20% faster.