Paragon: Difference between revisions

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{{lede image|BTD6 tutorial ParagonIcon.png|Icon used to represent Paragons}}
{{lede image|BTD6 tutorial ParagonIcon.png|Icon used to represent Paragons}}
'''Paragons''' are a special kind of [[upgrade]] in ''[[Bloons TD 6]]'', introduced in {{BTD6 version|27.0}}. They are exceptionally powerful (and exceptionally expensive) upgrades that combine major elements of all three of the [[tower]]'s tier 5 upgrades. Paragons have massive [[damage]] bonuses against [[Boss Bloon]]s, making them quintessential against high-tier bosses in [[Boss Bloon Event]]s, [[Boss Challenge]]s, and [[Boss Rush]]es.
'''Paragons''' are a special kind of [[upgrade]] in ''[[Bloons TD 6]]'', introduced in {{BTD6 version|27.0}}. They are exceptionally powerful (and exceptionally expensive) upgrades that combine major elements of all three of a [[tower]]'s tier 5 upgrades. Paragons have massive [[damage]] bonuses against [[Boss Bloon]]s, which were introduced in the same update, making them essential against high-tier bosses in [[Boss Bloon Event]]s, [[Boss Challenge]]s, and [[Boss Rush]]es.


Upgrading a tier 5 tower into a Paragon requires having all three tier 5 versions of the same tower on the map at the same time. For example, creating the [[Dart Monkey (BTD6)|Dart Monkey]]'s Paragon requires having a Dart Monkey with the [[Ultra-Juggernaut (BTD6)|Ultra-Juggernaut]] upgrade, a Dart Monkey with the [[Plasma Monkey Fan Club (BTD6)|Plasma Monkey Fan Club]] upgrade, and a Dart Monkey with the [[Crossbow Master (BTD6)|Crossbow Master]] upgrade all on the map at the same time. In [[Sandbox (BTD6)|Sandbox]] mode, the option to upgrade to a Paragon does not appear unless the player has already used that Paragon at least once in another game mode. Once one of the tier 5 towers is upgraded into a Paragon, it absorbs all other towers of the same tower type and [[Paragon Power Totem]]s on the map, merging them into a single tower. Paragons come with a Degree stat that affects how powerful it is, which is determined by multiple factors:
Upgrading a tier 5 tower into a Paragon requires having all three tier 5 versions of the same tower on the map at the same time. For example, creating the [[Dart Monkey (BTD6)|Dart Monkey]]'s Paragon requires having a Dart Monkey with the [[Ultra-Juggernaut (BTD6)|Ultra-Juggernaut]] upgrade, a Dart Monkey with the [[Plasma Monkey Fan Club (BTD6)|Plasma Monkey Fan Club]] upgrade, and a Dart Monkey with the [[Crossbow Master (BTD6)|Crossbow Master]] upgrade all on the map at the same time. In [[Sandbox (BTD6)|Sandbox]] mode, the option to upgrade to a Paragon does not appear unless the player has already made that Paragon at least once in another game mode. Once one of the tier 5 towers is upgraded into a Paragon, it absorbs all other towers of the same tower type and [[Paragon Power Totem]]s on the map, merging them into a single tower. Paragons come with a Degree stat that affects how powerful it is, which is determined by multiple factors:
*The amount of extra cash invested on the Paragon menu plus the total amount of cash invested into the towers absorbed
*The amount of extra cash invested on the Paragon menu plus the total amount of cash invested into the towers absorbed
*The total number of upgrade tiers on non-tier-5 towers absorbed
*The total number of upgrade tiers on non-tier-5 towers absorbed
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*The total amount of damage dealt and cash produced by all towers absorbed
*The total amount of damage dealt and cash produced by all towers absorbed
*The total number of [[Paragon Power Totem]]s absorbed
*The total number of [[Paragon Power Totem]]s absorbed
The maximum possible Paragon Degree is 100. With the exception of Paragon Power Totems, each factor has a limit to the amount it can contribute to the Paragon's Degree. Without Paragon Power Totems, it's only possible to create a maxed-out Paragon in Co-op because it requires having additional tier 5 towers from other players.
The maximum possible Paragon Degree is 100. With the exception of Paragon Power Totems, each factor has a limit to the amount it can contribute to the Paragon's Degree. Without Paragon Power Totems, it's only possible to create a maxed-out Paragon in Co-op because it requires having additional tier 5 towers from other players, otherwise the max degree from the rest of the requirements is 91.


==Terminology and notation==
==Terminology and notation==
*Paragons are referred to as their own upgrade tier,<ref>{{cite|quote=Paragon Tier has a significant XP cost and can only be unlocked after unlocking the Tier 5 upgrade of all 3 paths|url=https://www.reddit.com/r/btd6/comments/ornebj/bloons_td_6_update_notes_version_270/}}</ref><ref>{{cite|quote=All Lych Soul variations can now be stunned/slowed by paragon tier upgrades|url=https://www.reddit.com/r/btd6/comments/142y1xm/bloons_td_6_update_notes_version_370/}}</ref> and internally are considered a sixth upgrade tier.
*Paragons are referred to as their own upgrade tier,<ref>{{cite|quote=Paragon Tier has a significant XP cost and can only be unlocked after unlocking the Tier 5 upgrade of all 3 paths|url=https://www.reddit.com/r/btd6/comments/ornebj/bloons_td_6_update_notes_version_270/}}</ref><ref>{{cite|quote=All Lych Soul variations can now be stunned/slowed by paragon tier upgrades|url=https://www.reddit.com/r/btd6/comments/142y1xm/bloons_td_6_update_notes_version_370/}}</ref> and internally are considered a sixth upgrade tier.
*Despite being their own upgrade tier, they are notated as '''5-5-5 towers''' in Co-op mode.
*Despite being their own upgrade tier, they are notated as '''5-5-5 towers''' in Co-op mode and in win-screens.
*In {{BTD6 version|28.0}}, [[Sentry Champion (BTD6)|Sentry Champion]] and its Champion Sentry sub-towers were renamed from "Sentry Paragon" and "Paragon Sentry" respectively to avoid confusion, as they are not Paragons. The Sentries of the [[Master Builder]] are now called Sentry Paragons.
*In {{BTD6 version|28.0}}, [[Sentry Champion (BTD6)|Sentry Champion]] and its Champion Sentry sub-towers were renamed from "Sentry Paragon" and "Paragon Sentry" respectively to avoid confusion, as they are not Paragons. The Sentries of the [[Master Builder]] are now called Sentry Paragons.


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*In [[Sandbox (BTD6)|Sandbox]] mode, the option to upgrade to a Paragon does not appear unless the player has already used that Paragon at least once in another game mode. This restriction does not exist in the [[Challenge Editor]], however.
*In [[Sandbox (BTD6)|Sandbox]] mode, the option to upgrade to a Paragon does not appear unless the player has already used that Paragon at least once in another game mode. This restriction does not exist in the [[Challenge Editor]], however.
*Only one of each Paragon can exist at a time, even in [[Co-op (BTD6)|Co-op]].
*Only one of each Paragon can exist at a time, even in [[Co-op (BTD6)|Co-op]].
*In Boss Bloon Events, there is a limit to the number of Paragons that can be in play at the same time (usually 4, though it depends on the event).
*In Boss Bloon Events, there is a limit to the number of Paragons that each player can have at the same time (usually 4 per player, though it depends on the event).


Once the conditions are met, the option to upgrade to a Paragon appears on all of the tier 5 towers' upgrade panels. Selecting it presents the player with the option to invest more cash into the Paragon before upgrading. Once upgraded, the Paragon absorbs all other towers of the same tower type and [[Paragon Power Totem]]s on the map (including those owned by other players in Co-op), merging them into a single tower.
Once the conditions are met, the option to upgrade to a Paragon appears on all of the tier 5 towers' upgrade panels. Selecting it presents the player with the option to invest more cash into the Paragon before upgrading. Once upgraded, the Paragon absorbs all other towers of the same tower type and [[Paragon Power Totem]]s on the map (including those owned by other players in Co-op), merging them into a single tower.


Unlike Temple sacrifices, the [[sell]] value of a Paragon does not change based on the towers absorbed; it is solely determined by the amount of cash spent on the tier 5 tower that was upgraded to create the Paragon. Thus, Paragons sell for more if they're upgraded from towers with more expensive upgrades.
The [[sell]] value of a Paragon does not change based on the towers absorbed; it is solely determined by the amount of cash spent on the tier 5 tower that was upgraded to create the Paragon. Thus, Paragons sell for more if they're upgraded from towers with more expensive upgrades.


===Properties===
===Properties===
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*Paragons cannot be relocated by [[Support Chinook (BTD6)|Support Chinook]]s or [[Special Poperations (BTD6)|Special Poperations]].
*Paragons cannot be relocated by [[Support Chinook (BTD6)|Support Chinook]]s or [[Special Poperations (BTD6)|Special Poperations]].
*Paragons cannot be sacrificed to [[Sun Temple (BTD6)|Sun Temple]]s, [[True Sun God (BTD6)|True Sun God]]s, or [[Adora (BTD6)|Adora]].
*Paragons cannot be sacrificed to [[Sun Temple (BTD6)|Sun Temple]]s, [[True Sun God (BTD6)|True Sun God]]s, or [[Adora (BTD6)|Adora]].
*In ''[[Rogue Legends]]'', Paragons are unaffected by [[Artifact]]s and [[Boost]]s.
*In ''[[Rogue Legends]]'', Paragons are affected by [[Artifact]]s (including [[Boost]]s).
*Some Heroes, like [[Striker Jones (BTD6)|Striker Jones]], have abilities, e.g. Artillery Command, that affect Paragons, such as the [[Ballistic Obliteration Missile Bunker]], while others do not, such as [[Admiral Brickell (BTD6)|Admiral Brickell]]'s Naval Tactics.


===Paragon power===
===Paragon power===
'''Paragon power''' is a measurement of the total "value" of the towers absorbed by the Paragon. It is determined by multiple factors of the towers it absorbed, split into four different "categories", each with a limit on how much power it can contribute. Paragon power determines the Paragon's Degree, though it is not shown directly to the player.
'''Paragon power''' is a measurement of the total "value" of the towers absorbed by the Paragon. It is determined by multiple factors of the towers it absorbed, split into four different "categories", each with a limit on how much power it can contribute. Paragon power determines the Paragon's Degree, though it is not shown directly to the player.
*Cash invested — 60,000 power max
*Cash invested — 60,000 power max
**1 power per <math>\frac{\text{Paragon Cost}}{20,000}</math> spent on towers absorbed — the three cheapest tier 5 towers on the map are ignored
**1 power per <math>\frac{\text{Paragon Cost}}{20,000}</math> spent on towers absorbed — any tier 5 towers on the map are ignored
**1 power per <math>\frac{\text{Paragon Cost}\times1.05}{20,000}</math> spent on the Paragon cost slider (this means using the slider is slightly less cost-efficient)
**1 power per <math>\frac{\text{Paragon Cost}\times1.05}{20,000}</math> spent on the Paragon cost slider (this means using the slider is slightly less cost-efficient)
***Note: This is based on the Paragon's cost on the current [[difficulty]], so [[Easy]] requires less cash per power and higher difficulties require more cash per power
***Note: This is based on the Paragon's cost on the current [[difficulty]], so [[Easy]] requires less cash per power and higher difficulties require more cash per power
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The '''Degree''' of a Paragon determines its stats, affecting its [[attack speed]], [[pierce]], [[damage]], and [[Activated Ability]] cooldowns (if applicable). The Degree is determined by the amount of Paragon power it has, with higher Degrees requiring exponentially more power to reach than lower Degrees. The Degree cannot be changed after the Paragon is created. Cosmetically, Paragons have different models for every multiple of 20 Degrees. The formula to determine how much power is required for each degree is:
The '''Degree''' of a Paragon determines its stats, affecting its [[attack speed]], [[pierce]], [[damage]], and [[Activated Ability]] cooldowns (if applicable). The Degree is determined by the amount of Paragon power it has, with higher Degrees requiring exponentially more power to reach than lower Degrees. The Degree cannot be changed after the Paragon is created. Cosmetically, Paragons have different models for every multiple of 20 Degrees. The formula to determine how much power is required for each degree is:


<math>P = \begin{cases} 0, & D = 1 \\ \frac{50D^3 + 5065D^2 + 168324D + 843000}{600}, & 2 \leq D \leq 99 \\ 200000, & D = 100\end{cases}</math>,
<math>P = \begin{cases} 0, & D = 1 \\ \frac{50D^3 + 5025D^2 + 168324D + 843000}{600}, & 2 \leq D \leq 99 \\ 200000, & D = 100\end{cases}</math>,


where P is the power required and D is the target Degree.
where P is the power required and D is the target Degree.
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|484
|484
|5,615
|5,615
|
|This is the minimum Degree that can be reached with just an additional tier 5 tower (by using {{BTD6 mk|Master Double Cross}} or Level 13+ [[Silas (BTD6)|Silas]]).
|-
|-
!12
!12
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|650
|650
|9,654
|9,654
|
|This is the minimum Degree that can be reached with just upgrade tiers. In practice, the cost of the base towers and the cheapest possible upgrades will result on a Degree 20+ Paragon in nearly all scenarios.
|-
|-
!19
!19
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|2,601
|2,601
|88,011
|88,011
|
|This is the highest Degree that can be reached with just pops (16,200,000).
|-
|-
!70
!70
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|3,660
|3,660
|147,738
|147,738
|
|This is the highest Degree that can be reached without additional towers or Paragon Power Totems (only max pops and cash slider).
|-
|-
!89
!89
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|3,844
|3,844
|159,085
|159,085
|In other versions, this is the highest Degree that can be reached without Paragon Power Totems or additional tier 5 towers.
|This is the highest Degree that can be reached in single player without Paragon Power Totems or additional tier 5 towers.
|-
|-
!92
!92
|3,906
|3,906
|162,991
|162,991
|For the Apex Plasma Master in Mobile and Steam versions, this is the highest possible degree without Paragon Power Totems or additional tier 5 towers when Master Double Cross is enabled.
|For the Apex Plasma Master and Herald of Everfrost, this is the highest possible degree without Paragon Power Totems or additional tier 5 towers when Master Double Cross is enabled or when Silas is used.
|-
|-
!93
!93
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|4,096
|4,096
|175,089
|175,089
|
|This is the highest Degree that can be reached for 2 player Co-op without Paragon Power Totems (3 additional tier 5s).
|-
|-
!96
!96
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|4,290
|4,290
|187,764
|187,764
|
|This is the highest Degree that can be reached for Apex Plasma Master and Herald of Everfrost for 2 player Co-op without Paragon Power Totems (5 additional tier 5s).
|-
|-
!99
!99
|4,356
|4,356
|192,120
|192,120
|
|This is the highest Degree that can be reached for 3 player Co-op without Paragon Power Totems (6 additional tier 5s).
|-
|-
!100
!100
|7,880
|7,880
|200,000
|200,000
|Requires Paragon Power Totems to reach in single player or 9 tier 5s in Coop
|If all other sources of Paragon Power are maxed out, reaching this Degree requires 20 Paragon Power Totems or 7 additional tier 5s in Co-op
|}
|}


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In other words, it lowers cooldowns more at higher Degrees, but it has diminishing returns. The difference in cooldown between Degrees 99 and 100 is much smaller than the difference between Degrees 1 and 2.
In other words, it lowers cooldowns more at higher Degrees, but it has diminishing returns. The difference in cooldown between Degrees 99 and 100 is much smaller than the difference between Degrees 1 and 2.


Note that Activated Abilities are affected by [[Global Ability Cooldowns]] Monkey Knowledge and attack speed is affected by [[Veteran Monkey Training]] and [[Paragon of Power]] Monkey Knowledge.
Note that Activated Abilities start with full cooldown after creating the Paragon and are affected by [[Global Ability Cooldowns]] Monkey Knowledge and attack speed is affected by [[Veteran Monkey Training]] and [[Paragon of Power]] Monkey Knowledge.


{|class="wikitable mw-collapsible mw-collapsed"
{|class="wikitable mw-collapsible mw-collapsed"
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<math>\text{Pierce}=\begin{cases}\lfloor\text{BasePierce}\times(1+0.01(\text{Degree}-1))\rfloor+0.1(\text{Degree}-1)&\text{for Degree}<100 \\ 2\times \text{Base Pierce}+10&\text{for Degree}=100\end{cases}</math>
<math>\text{Pierce}=\begin{cases}\lfloor\text{BasePierce}\times(1+0.01(\text{Degree}-1))\rfloor+0.1(\text{Degree}-1)&\text{for Degree}<100 \\ 2\times \text{Base Pierce}+10&\text{for Degree}=100\end{cases}</math>


====Damage to Bloons Bloons====
====Damage to Boss Bloons====
All Paragons deal 25% more damage to Boss Bloons for every 20 Degrees they have. This is in addition to most Paragons' projectiles and [[damage over time]] effects having an inherent damage bonus against Boss Bloons (which is different for each projectile and effect, and scales with its Degree), and this multiplies the ''total'' damage dealt to Boss Bloons by the Paragon. In other words, the extra damage the multiplier grants is based on the sum of the attack's base damage, bonus damage to MOAB-Class, bonus damage to bosses, and any other bonuses the boss may be vulnerable to (such as [[Phayze]] being affected by the bonus damage to Camo Bloons from the [[Ascended Shadow]]). It also applies to projectiles and effects that do not inherently deal bonus damage to bosses, such as the [[Glaive Dominus]]'s MOAB shredding effect. On top of this, Elite Bosses take double damage from Paragons.
All Paragons deal 25% more damage to Boss Bloons for every 20 Degrees they have. This is in addition to most Paragons' projectiles and [[damage over time]] effects having an inherent damage bonus against Boss Bloons (which is different for each projectile and effect, and scales with its Degree), and this multiplies the ''total'' damage dealt to Boss Bloons by the Paragon. In other words, the extra damage the multiplier grants is based on the sum of the attack's base damage, bonus damage to MOAB-Class, bonus damage to bosses, and any other bonuses the boss may be vulnerable to (such as [[Phayze]] being affected by the bonus damage to Camo Bloons from the [[Ascended Shadow]]). It also applies to projectiles and effects that do not inherently deal bonus damage to bosses, such as the [[Glaive Dominus]]'s MOAB shredding effect. On top of this, Elite Bosses take double damage from Paragons.


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===Takeaways===
===Takeaways===
*Without Paragon Power Totems, the only way to max out a Paragon's power is to have at least seven additional tier 5 towers of the same tower type (nine in the console version), which is only possible in Co-op mode. For most towers, this requires four players, though the Dart Monkey only requires three players if one player has an extra Crossbow Master from {{BTD6 mk|Master Double Cross}}. In the console version, three extra Crossbow Masters are required, so all three players must have the Monkey Knowledge.
*Without Paragon Power Totems, the only way to max out a Paragon's power is to have at least seven additional tier 5 towers of the same tower type (nine in the console version), which is only possible in Co-op mode. For most towers, this requires four players, though the Dart Monkey only requires three players if one player has an extra Crossbow Master from {{BTD6 mk|Master Double Cross}} or all players are using [[Silas (BTD6)|Silas]] to upgrade a fourth Ice Monkey tier 5 each.
*It takes three Paragon Power Totems to substitute the power contribution of one tier 5 tower.
**In the console version, three extra Crossbow Masters are required, so all three players must have the Monkey Knowledge.
**Without any additional Tier 5 towers, the maximum Degree is 91.
*It takes 3 Paragon Power Totems to substitute the power contribution of one tier 5 tower, and 9 totems to get a degree 100.
*Higher Degrees require exponentially more power than lower Degrees and don't give as much of an attack speed bonus as lower Degrees, so going for higher Degrees has diminishing returns. In events, it's generally more efficient to go for multiple mid-Degree Paragons than to try to max out Paragons as much as possible.
*Higher Degrees require exponentially more power than lower Degrees and don't give as much of an attack speed bonus as lower Degrees, so going for higher Degrees has diminishing returns. In events, it's generally more efficient to go for multiple mid-Degree Paragons than to try to max out Paragons as much as possible.
*Paragons receive significant damage boosts against bosses for every 20 Degrees they have, so it's most cost-efficient to reach a multiple of 20 Degrees without going over. The difference in damage output between Degree 19 and Degree 20 is much bigger than between Degree 20 and Degree 21, for example.
*Paragons receive significant damage boosts against bosses for every 20 Degrees they have, so it's most cost-efficient to reach a multiple of 20 Degrees without going over. The difference in damage output between Degree 19 and Degree 20 is much bigger than between Degree 20 and Degree 21, for example.
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==List of Paragons==
==List of Paragons==
{{#cargo_query:table=btd6_paragons
{{generic cargo query
|fields=_pageName, image, name, CONCAT("[[", _pageName, "|", name, "]]<br>([[", tower, " (BTD6)|", tower, "]])") = Text
|table=btd6_upgrades
|for
|where=tier=6
 
|extra col 1=CONCAT("$", FORMAT(cost, 0))=Cost
|order by=introduced, name
|extra col 2=xp=XP to unlock
|format  =gallery
|extra col 3=CONCAT("[[Update history:Bloons TD 6/Version ", introduced, "{{!}}Version ", introduced, "]]")=Introduced
 
|order by=(introduced+0), name
|link field   =_pageName
|image field=icon
|alt field    =name
|caption field=Text
 
|show bytes    =0
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}}


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==Related achievements==
==Related achievements==
{{BTD6 achievement list by name|Apotheosis;Perfect Paragon;Heavy Investment}}
{{BTD6 achievement list|exclude others=y|include=Apotheosis;Perfect Paragon;Heavy Investment}}


==Gallery==
==Gallery==
{{image needed|Teaser images, screenshots, icons, etc}}
{{image needed|Teaser images, screenshots, icons, etc}}
<gallery>
File:ApexPlasmaMasterDegree1.png|Recently upgraded Apex Plasma Master at Degree 1
</gallery>


==See also==
==See also==