Paragons

"Upgrade one of your Tier 5 Monkeys into a Paragon! Paragons absorb all Monkeys of their type, including the Tier 5 Monkeys from the other two paths. The degree of the Paragon is influenced by how much power is absorbed at the moment of the upgrade."

- Info Pop-Up for First Paragon Purchase "This action will create a Paragon [tower name] . All other [tower name] s will be destroyed in the process, feeding the Paragon's Power!"



Paragons or 5-5-5 Towers (Tier 6 Upgrades prior to update 28.0) are the final tier of upgrades that were introduced to Bloons TD 6 in update 27.0 on 25th July 2021. Combining major features from all three upgrade paths of a specific tower, Paragons are intended to be the ultimate culmination of a tower's capability, dealing enormous damage to all bloon types (including camo), with bonus damage to boss bloons and more.

Paragons are created by placing one of each of the three Tier 5 Upgrades of a desired tower and upgrading any of the tier-5 towers. Doing so will merge all three tier-5 towers, along with any lower tier towers of that type into the Paragon. The strength or "degree" of the Paragon ranges from 1-100 and is determined by the "number and effectiveness" of the merged/sacrificed towers. This is calculated using the total cost, pop count, bonus income generation, upgrades, and number of monkeys sacrificed as explained here. Paragons are also unaffected by most tower interactions, like buffs and discounts. In addition, only one paragon of a specific tower may exist at a time (including in co-op), but the sacrificial Tier 5 towers may be rebought after creating the Paragon.

Towers can only be upgraded to Paragons in normal game modes and Challenge Editor. Like the Vengeful True Sun God, Paragons cannot be obtained in Sandbox Mode, but unlike the Vengeful True Sun God, they can be obtained in C.H.I.M.P.S.

List of Paragons
As of Version 29.0, there are 4 Towers with Paragon upgrades in the game. The other tower Paragons are slated for future updates. According to the version 30.0 patch notes, the fifth Paragon has been slated to be for the Engineer Monkey.

Description
Paragons merge visual elements from each of the three contributing tier-5 towers while still retaining a look largely independent from any of the sacrificial towers. In addition, the name of the Paragon usually derives from some combination of the constituent tier-5 towers, though not necessarily. Paragons appear larger in size compared to the base tower (but the footprint is unchanged) and gain more striking adornments every 20 degrees.

Creating a Paragon
First, ensure that the Paragon has been unlocked using XP on the tower's upgrade page. Then, A base Paragon can be created by having one of each tier 5 tower for a specific monkey on screen, at which point, the upgrade icon for the Paragon will become available on any of the tier 5 towers. Purchasing the upgrade will change the selected tower into the Paragon, while sacrificing every other tower of that type on screen (including those belonging to co-op players). Only one Paragon of a specific tower may exist at a time, even in co-op.

Degree and Requirements
''The following sections contain in-depth formulas unnecessary for most use cases. To skip to the max sacrifice requirements, click here.''

Sacrifice Requirements
In addition to cosmetic changes every 20 degrees, higher degrees increase the damage output of the Paragon. The degree is determined by a hidden value known as "power", which itself is dependent on total pop count and cash generated, tier 5 upgrades, non-tier 5 upgrades, cost, and number of sacrificed towers as follows:


 * Each tier 5 tower will contribute 10,000 power (for a maximum of 90,000 power). Excludes the first three tier-5 towers.
 * Each non tier 5 tower upgrade will contribute 100 power (for a maximum of 10,000 power). Excludes the first three tier-5 towers.
 * Every $25 spent on sacrificed towers will contribute 1 power (for a maximum of 10,000 power). Excludes the first three tier-5 towers.
 * Every 180 pops achieved by sacrificed towers will contribute 1 power (for a maximum of 90,000 power). For towers that directly produce income, total generated income will convert into pops at a rate of 4 pops per 1 income. Includes the first three tier-5 towers.

The power needed for each degree is determined by the formula:

Power = \begin{cases} 0, & \text{for D }=1 \\ \frac{50*D^3+5025*D^2+168324*D+843,000}{600}, & \text{for D between }2-99 \\ 200,000, & \text{for D }=100 \end{cases}$$

Where "D" is degree. As a result, there is no unique combination of upgrades, prices, etc. that will place the Paragon at a certain degree, only the total power matters. Notice that a maximum of 110,000 power is obtainable in single-player (120,000 if using the Master Double Cross MK), and 200,000 power is achievable in co-op.

Attack Statistics
The attack speed, pierce, damage, bonus damage, and boss damage scale with degree as follows.

Regular Damage: The regular damage of each attack for all Paragons scales with Degree according to the equation:

Where "D" is degree and d0 is the Damage of that attack at Degree 1. This can be found on each individual Paragon's page.

Ceramic Damage: The Bonus Damage to Ceramics scales with degree according to the equation below. Add it to the Regular Damage to calculate Total Ceramic damage. Many attacks have 0 bonus Ceramic Damage.

Where "D" is degree and cd0 is the Bonus Ceramic Damage of that attack at Degree 1. This can be found on each individual Paragon's page

MOAB Damage: The Bonus Damage to MOABs scales in exactly the same way as Bonus Damage to Ceramics. Add the Bonus MOAB damage to the regular damage to calculate total MOAB damage. Many attacks have zero bonus MOAB damage.

Fortified Damage: The Bonus Damage to Fortified Bloons scales in exactly the same way as Bonus Damage to Ceramics. Add the Bonus Fortified damage to the regular damage (and Ceramic or MOAB damage, if the Bloon possesses those properties) to calculate total Fortified damage. Most attacks do not have bonus fortified damage.

Boss Bloon Damage: Total Boss Bloon Damage per each degree for each attack (except DoT effects) can be calculated as follows:

Where "D" is degree, bd0 is the boss bloon bonus damage at Degree 1, and dD and mdD are the Regular Damage and MOAB Damage for each degree as outlined above.

Boss Bloon Damage Over Time: Total Boss Bloon Damage per each degree for Damage Over Time (DoT) attacks can be calculated as follows:

Where "D" is degree, bd0 is the boss bloon bonus damage at Degree 1, and dD and mdD are the Regular Damage and MOAB Damage for each degree as outlined above.

Elite Boss Bloon Damage: Total damage done to Elite Boss Bloons per degree for each attack is ideally equal to twice the Total Boss Damage. However, this currently only applies to Degree 1-19.

Pierce: The pierce of each attack scales with degree according to the following formula:

Where "D" is degree and p0 is the pierce of that attack at Degree 1. This can be found on each individual Paragon's page

Attack Speed: The delay between attacks shortens with degree according to the formula:

Where "D" is degree and r0 is the rate of that attack at Degree 1. This can be found on each individual Paragon's page

''Note: The wiki is currently planning to add a direct JavaScript widget on this page to calculate Paragon degrees directly. For now, to determine the degree requirements, use a mathematics engine such as WolframAlpha to calculate it (an example of this is a question about determining Degree 2 requirements).''

function degreeToPower(D) { if (D==1) return 0; if (D==100) return 100; return ((50*D**3)+(5025*D**2)+(168324*D)+(843000))/600 }

function powerToDegree(P) { //solving cubic required }

Higher Degree Paragons
Listed are some general guidelines on how to make select 20 degree increment Paragons.

Degree 1

 * 0 Power Needed.
 * Purchase the first three tier-5 upgrades.

Degree 20

 * 11,032 Power Needed.
 * Purchase the first three tier-5 upgrades.
 * Have at least 17 tier 4 towers with maxed cross pathing (i.e. 2-4-0 as opposed to 0-4-0)
 * Have $125,000 invested in the non-tier 5 sacrifices.

Degree 40

 * 31,360 Power Needed.
 * Purchase the first three tier-5 upgrades.
 * Have at least 17 tier 4 towers with maxed cross pathing (i.e. 2-4-0 as opposed to 0-4-0)
 * Have $250,000 invested in the non-tier 5 sacrifices.
 * Have 2,040,000 pops (or $510,000 cash generated) achieved across sacrificial towers.

Degree 60

 * 66,387 Power Needed.
 * Purchase the first three tier-5 upgrades.
 * Have at least 17 tier 4 towers with maxed cross pathing (i.e. 2-4-0 as opposed to 0-4-0)
 * Have $250,000 invested in the non-tier 5 sacrifices.
 * Have 8,350,000 pops (or $2,087,500 cash generated) achieved across sacrificial towers.

Degree 76 (Single Player Max)
For most Paragons, excluding Apex Plasma Master, Degree 76 is the highest degree possible in single-player mode. This is because Degree 77 requires 110,706 power, which is only achievable by placing additional tier 5 towers.


 * Purchase the first three tier-5 upgrades.
 * Have 100 tier-4 or below upgrades distributed among the other sacrificial monkeys, excluding the first three tier 5 towers.
 * Invest at least $250,000 on the sacrificed towers, excluding the first three tier 5 towers.
 * Accumulate 16,200,000 pops (or $4,050,000 cash generated) across all sacrificed towers.

Degree 100 (Max)

 * 200,000 Power Needed
 * 3 Additional Co-Op players.
 * Buy the first three tier-5 upgrades, and 9 additional tier 5 towers.
 * Have 100 tier-4 or below upgrades distributed among the other sacrificial monkeys, excluding the first three tier 5 towers.
 * Have $250,000 spent on the sacrificed towers, excluding the first three tier 5 towers.
 * Accumulate 16,200,000 pops (or $4,050,000 cash generated) across all sacrificed towers.

Troubleshooting
If, after following the guidelines above, the Paragon is not created or reaching the desired degree, ensure the following:


 * The gamemode is not sandbox.
 * The Paragon upgrade has been unlocked in the upgrade menu.
 * There are no other Paragons of that type on screen. Only one of that type is allowed at a time, even in co-op.
 * Discounting effects, such as those provided by Monkey Business, Monkey Commerce, or a Support Temple, are not used to detract from the cost investment.
 * Purchase a maxed crosspath of each Tier 4 tower. e.g. using a 2-4-0 or 0-4-2 tower as opposed to the 0-4-0 version.
 * For example, the most expensive Tier 4 combination possible for Dart Monkey is a 2-4-0, rather than a 0-4-0 or 0-4-2.
 * The minimum pop count and cash generated has been achieved across all sacrificial monkeys. This may be difficult to calculate, as it requires adding up pop count and cash generated with multiplication across many towers. However a good rule of thumb is to wait until at least round 136 to let the sacrificial monkeys accumulate enough pops (unless playing Boss Events or Double HP MOABs).

Behavior and Interactions
For a full list of all standard tower Interactions, click here.

Paragons behave in large part, like any other tower. However, they are not able to receive most buffs or participate in most tower interactions. A few of these behavior quirks are listed.


 * Only one Paragon of a specific tower is allowed on screen at a time (even in co-op)
 * If placed on an Arctic Wind ice platform, the Paragon will not disappear when the Arctic Wind is sold.
 * Paragons will disappear if placed on a Carrier Flagship when the Flagship is sold.
 * Paragons cannot be buffed in any ways possible.
 * Paragons can deal increased damage to bloons via debuffing status effects such as the "Glue Storm", "Cripple MOAB" or "Super Brittle".
 * Paragons are not affected by the powers: Energizing Totem, Monkey Boost, or Time Stop.
 * As a result, Time Stop allows the Paragons to attack at their normal speed while bloons are immensely slowed, effectively acting like a significant buff.
 * Paragons can not have their upgrade price reduced (except by the difficulty).
 * Paragons cannot be moved by the Support Chinook's Redeploy Ability.
 * Paragons cannot be sacrificed to a Temple, or Sun God.
 * Although paragons can not be buffed, Favored Trades can still increase their sellback value.

Strategy
To best strategize Paragon use, see each tower's individual paragon page. Otherwise, here are some general guidelines.

Summary
Paragons combine all three attacks of their constituent tier 5 towers to deal immense damage to all bloon types. However, the high cost of these upgrades and lack of ability to receive buffs makes them difficult to justify in the presence of cheaper combinations of towers (such as Ultraboost and Flying Fortress). As a result the main use cases for Paragons, as of now, are during late game and Boss Events.

In any case use of a Paragon requires a robust farming set up, setup of the sacrificial towers, and time to accumulate pops in order to maximize damage output.

Tips

 * Paragons can greatly help with getting achievements obtained through Freeplay grinding (Super BAD, Sapper, Impoppable, etc.), especially to minimize lag (Apex Plasma Master excluded).
 * In order to achieve the most pops for a single tower type, try focusing on a single Paragon first. Use the most of one tower type. Try the strategies used for the Tier 5 Upgrades of the same tower type, to maximize pops.
 * As most the RBE is concentrated towards the latter rounds, it is still possible to get a high total pop count with boomerang monkeys starting from round 98 or later.
 * Note that round 132 is the first round where the game's cumulative RBE exceeds 16.2 million pop threshold. Waiting until round 136 before upgrading to Paragon should provide enough buffer to achieve the 16,200,000 pops for max degree, assuming the sacrificial towers are responsible for ~80% of all pops until that point. These rounds will be earlier on Double HP MOABs and Boss Events due to the RBE from Boss Bloons and spawns, so it is always best to confirm by summing manually.
 * Use all Tier 5 upgrades of the same type in order to rack up the most pops and costs, which can be then utilized for a much stronger Paragon. After obtaining all Tier 5 upgrades possible, buy the most expensive possible Tier 4 crosspath.
 * As a rule of thumb when investing for a single high-level Paragon, try aiming for ~$300,000+ total value of a specific tower type and ~17,000,000+ damage count when taking into account the sum of all towers of the same type.
 * The precise monetary and damage count amounts are actually $250,000+ and 16.2M pops, respectively, but aiming for $300K+ and 17M+ pops should almost guarantee that any unexpected miscalculations are negligible.
 * Like Temples, Paragons are unaffected by sold ice platforms, so this makes certain water locations ideal for placement.
 * While most paragons are capable of soloing to round 100, they are not viable for popping Golden Bloons since it will only result in the Golden Bloon rapidly jumping to the end of the track due to the invulnerability.
 * Using Bloon Debuffing abilities effects such as the "Cripple MOAB", "Super Brittle", and "Glue Storm" is highly advised. As these are indirect buffs, they are able to increase the damage output of the Paragon.

Comparison to the Vengeful True Sun God
Paragons share a number of similarities to the Vengeful True Sun God (VTSG) in terms of function and gameplay mechanics.


 * Both the VTSG and Paragons sacrifice other towers to increase their own power.
 * Both require all three tier-5 towers of their tower type to be created.
 * However, the constituent tier-5's of the Paragon can be rebought. The Legend of the Night, and Anti-Bloon can not be purchased by the player again once the VTSG is on screen.
 * Both are considered 5-5-5 towers. This is confirmed by the Victory Callout image for the paragons, and the internal game files which label the VTSG as a 5-5-5 True Sun God. (Though Paragons were previously incorrectly known as 6-0-0 towers).
 * Only one VTSG and one of each Paragon type are allowed on screen at a time (even in co-op). These are the only towers with such a limit.
 * Both Paragons and the VTSG are at the apex of their tower type, in terms of cost and damage output.
 * Both are Crosspath Hybrids which merge certain elements from their constituent tier-5s.
 * Neither is available in Sandbox, but Paragons are available in C.H.I.M.P.S. This is likely due to Ninja Kiwi wanting to reserve the "rarity" of these upgrades for the more active gamemodes.
 * Paragons and the VTSG are the only land towers that will stay on an Arctic Wind ice platform after the arctic wind is sold. This may be a reference to their immense power transcending the game mechanics of water placement.
 * Though, Paragons will disappear if on a Carrier Flagship being sold. Super Monkeys, and therefore the VTSG, can not be placed on carrier flagships.

For these reasons, Paragons may be seen as the "Vengeful True Sun God" analog for each tower.

History
Paragons were first teased here on Twitter, at July 1st/2nd, 2021, and were later revealed at July 8th/9th, 2021, here. Another teaser was shown on Facebook on July 15th/16th, 2021.

The first Paragon to be revealed was the Paragon Dart Monkey, the "Apex Plasma Master", as part of the second teaser for Paragons. The same teaser also features a mysterious language whose letters arrange to form the word "paragon". The second Paragon revealed is a merge for the Boomerang Monkey, the "Glaive Dominus", as seen in the third teaser for Paragons; this teaser features the same mysterious language writing seen in the Dart Monkey Paragon teaser.

Ninja Kiwi confirmed with their 16th July 2021 blog that the There Can Be Only One MK would remain the same. Unlike VTSG, the Super Monkey Paragon is expected to not need Monkey Knowledge, will not require Sacrifices for the Temple and True Sun God upgrades, and can allow The Anti-Bloon and Legend of the Night to be spawned after its own upgrade. Potentially, the VTSG can be summoned after the Super Monkey Paragon is upgraded.

In that blog, when asked whether the Sentry Paragon would receive a name change after the release of Paragons, Ninja Kiwi said "Probably not!" However, the upgrade was later was renamed to Sentry Champion in Version 28.0.

Weekly since the release of Version 27.0, starting from the first Friday since the release date of said update, Ninja Kiwi answered several questions regarding Paragons, including their development and some lore about them. Ninja Kiwi's 30th July 2021 blog reveals a response that stated that they are working on releasing all Paragons but will need time to balance every Paragon before they can officially make any announcement for releases of them. Paragons were further revealed on their August 6th 2021 blog, with refinements on what is being developed in regards to the Paragons and how each Paragon will be released and dealt with in the future.

On 6th October 2021, Ninja Kiwi teased the Ascended Shadow, as shown on their Twitter page. It was later released in the 28.0 update.

On 4th December 2021, Ninja Kiwi teased the Navarch of the Seas on their Twitter. It was later released in the 29.0 update.

Engineer Monkey Paragon has been announced in Ninja Kiwi's Version 30.0 patch notes as the next Paragon.

NK Blog reveals
Almost week since Version 27.0, information related to Paragons is answered in the NK Blogs. It may contain an indiscriminate amount of information about them, but the below information is all the information gathered out of the blogs since the release of Paragons.


 * According to Ninja Kiwi's 30th July 2021 blog, all other variants of Paragons will eventually be released but not always on every update, due to the need to balance each and every possible Paragon of the existing towers at the time. In fact, it may take forever for certain Paragons to be eventually released. Information for all other paragons aside from the first two have not been confirmed as of the release of that blog.
 * Canonically, Paragons do not need abilities as part of their attacks, hence the lack of abilities for Paragons.
 * However, Navarch of the Seas contradicts this, as it has an ability that can instakill BADs.
 * Sentry Paragon (now known as Sentry Champion) canonically may have contributed in creating Paragons.
 * According to Ninja Kiwi's August 6th 2021 blog, further information about Paragons has been revealed.
 * Each Paragon is created from merging all of their tower kind into a single being.
 * Paragons will be chosen based on what NK believes "would be best".
 * Blocking Paragons in Challenge Editor is not planned yet but Ninja Kiwi said that blocking any Tier 5 upgrade of a certain tower kind will restrict Paragons of that tower kind.
 * According to Ninja Kiwi's September 17th 2021 blog, Paragons were once planned to be available in Sandbox Mode if used in non-Sandbox gameplay first, but Ninja Kiwi decided not to implement that.
 * According to Ninja Kiwi's October 29th 2021 blog, all Paragons have the same degree formula. Also, if more Paragons arrive, balance changes will be done to accommodate their increased total power. Also, Paragons will not have Insta variants.

Trivia

 * The popup for "Paragon Upgrade Enabled!" is triggered upon buying all Tier 5 upgrades of the same tower type for the first time.
 * The option to upgrade a Tier 5 into a Paragon is locked until all Tier 5's of the same tower type are placed on screen. Until then, the upgrade button for the Tier 5 will read "Max Upgrades" as usual.
 * Paragons join the Sun Temple, True Sun God, Monkeyopolis, Adora, and previously Soulbind as a tower that can sacrifice or absorb other towers. Unlike the others mentioned, Paragons can only sacrifice towers of their type.
 * Paragons are some of the most expensive upgrades in the game. The Apex Plasma Master and the Glaive Dominus are the 4th and 3rd most expensive upgrades respectively, with the 2nd being the Navarch of the Seas tied with the True Sun God, leaving the Ascended Shadow to take 1st place (as of update 29.0).
 * It is technically possible to obtain a paragon in C.H.I.M.P.S mode, though it is incredibly difficult to save up the required cost without income. An Apex Plasma Master was achieved by YouTuber "Baumfall."
 * The Paragon upgrades join Prince of Darkness as being completely new upgrades that were introduced after their base tower was added.
 * Paragons may have taken inspiration from crosspath hybrids like the Wizard Lord in Bloons TD 5.
 * Confusingly, Paragons used to not be officially considered 5-5-5 towers, but rather 6-0-0 towers, regardless of which path the paragon upgrade is bought on. This was due the structure of the upgrade path, and notation on the victory card screen. This was changed as of update 28.0.
 * A "paragon" is "someone or something that is the very best" (source: Vocabulary.com), fitting their nature as the very best of the tower they represent.
 * Since update 28.0 fixed Degree 1-19 not dealing double damage to Elite Bosses, the equation for extra boss damage changed. This equation is then simply multiplied by 2 without a bracket, leaving the last term "-bdD" as is. This made all Degree 20+ dealing an extra boss damage bonus worth of damage.
 * It is not yet known if this is intended or not, as the equation just misses a bracket to multiply extra boss damage by 2 cleanly for all Degrees. However, it may also be a mistake-turned-feature to encourage players to aim for at least Degree 20 paragons, especially for elite bosses because this is not yet change in 29.0.