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− | {{Stub|reason= | + | {{Stub|reason=[[Sleep accelerator]]{{IdeologyIcon}} and [[circadian assistant]] {{RoyaltyIcon}} effects should be reflect in math.}} |
'''Rest''' is the game mechanic that controls [[Characters]]' [[needs]] for sleep. A character with a higher rest value has slept recently, and is less tired than another character with a low rest level. | '''Rest''' is the game mechanic that controls [[Characters]]' [[needs]] for sleep. A character with a higher rest value has slept recently, and is less tired than another character with a low rest level. | ||
− | == Levels of Rest == | + | ==Levels of Rest== |
− | Characters' rest level is grouped into four thresholds: Rested, Tired, Very Tired, and Exhausted. Each threshold exhibits different effects on a character | + | Characters' rest level is grouped into four thresholds: Rested, Tired, Very Tired, and Exhausted. Each threshold exhibits different effects on a character, especially their [[Thoughts]]. When a character's rest level is zero they may collapse from exhaustion; they will immediately begin sleeping on the ground wherever they are. |
The rest levels are as follows: | The rest levels are as follows: | ||
{| class="wikitable" | {| class="wikitable" | ||
+ | |- | ||
! Label | ! Label | ||
! Rest | ! Rest | ||
! Mood Debuff | ! Mood Debuff | ||
− | |||
− | |||
|- | |- | ||
− | + | | [[Thoughts#Exhaustion|Rested]] | |
| >= 28% | | >= 28% | ||
| ''None'' | | ''None'' | ||
− | |||
− | |||
|- | |- | ||
− | + | | [[Thoughts#Exhaustion|Drowsy]] | |
| >=14% and <28% | | >=14% and <28% | ||
| {{--|6}} | | {{--|6}} | ||
− | |||
− | |||
|- | |- | ||
− | + | | [[Thoughts#Exhaustion|Tired]] | |
| >=1% and <14% | | >=1% and <14% | ||
| {{--|12}} | | {{--|12}} | ||
− | |||
− | |||
|- | |- | ||
− | + | | [[Thoughts#Exhaustion|Exhausted]] | |
| <=1% | | <=1% | ||
| {{--|18}} | | {{--|18}} | ||
− | |||
− | |||
|} | |} | ||
− | Rest caps at 0% and 100% | + | Rest caps at 0% and 100%. |
− | == Rest Changes == | + | ==Rest Changes== |
− | ==== Negative ==== | + | ====Negative==== |
When awake, rest goes down every 150 ticks (1/400 of a game day) depending on the character's current rest. | When awake, rest goes down every 150 ticks (1/400 of a game day) depending on the character's current rest. | ||
{| class="wikitable" | {| class="wikitable" | ||
+ | |- | ||
! | ! | ||
! Threshold range | ! Threshold range | ||
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| {{#expr: 150 * 1.5833333*(10^-5) * 1 * 100 round 3}}% <!--RestFallPerTick has eqn of 1.5833333E-05f * this.RestFallFactor; x150 for 150ticks, x100 to convert into percentage--> | | {{#expr: 150 * 1.5833333*(10^-5) * 1 * 100 round 3}}% <!--RestFallPerTick has eqn of 1.5833333E-05f * this.RestFallFactor; x150 for 150ticks, x100 to convert into percentage--> | ||
| {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 100 round 0}}% <!--RestFallPerTick has eqn of 1.5833333E-05f * this.RestFallFactor; x60000 for number of ticks in a day, x100 to convert into percentage--> | | {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 100 round 0}}% <!--RestFallPerTick has eqn of 1.5833333E-05f * this.RestFallFactor; x60000 for number of ticks in a day, x100 to convert into percentage--> | ||
− | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) round 0}} }} <!--72% of the bar/percentage per tick = ticks--> | + | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) round 0}}}} <!--72% of the bar/percentage per tick = ticks--> |
| {{#expr: (72/(1.5833333*(10^-5) * 1 * 100))/2500 round 3}} hours <!--ticks/2500 ticks per hour = hours--> | | {{#expr: (72/(1.5833333*(10^-5) * 1 * 100))/2500 round 3}} hours <!--ticks/2500 ticks per hour = hours--> | ||
| {{Ticks|0}} | | {{Ticks|0}} | ||
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| {{#expr: 150 * 1.5833333*(10^-5) * 1 * 0.7 * 100 round 3}}% | | {{#expr: 150 * 1.5833333*(10^-5) * 1 * 0.7 * 100 round 3}}% | ||
| {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 0.7 * 100 round 0}}% | | {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 0.7 * 100 round 0}}% | ||
− | | {{Ticks|{{#expr: 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) round 0}} }} | + | | {{Ticks|{{#expr: 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) round 0}}}} |
| {{#expr: (14/(1.5833333*(10^-5) * 1 * 0.7 * 100))/2500 round 3}} hours | | {{#expr: (14/(1.5833333*(10^-5) * 1 * 0.7 * 100))/2500 round 3}} hours | ||
− | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) round 0}} }} | + | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) round 0}}}} |
| {{#expr: (72/(1.5833333*(10^-5) * 1 * 100))/2500 round 3}} hours | | {{#expr: (72/(1.5833333*(10^-5) * 1 * 100))/2500 round 3}} hours | ||
|- | |- | ||
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| {{#expr: 150 * 1.5833333*(10^-5) * 1 * 0.3 * 100 round 3}}% | | {{#expr: 150 * 1.5833333*(10^-5) * 1 * 0.3 * 100 round 3}}% | ||
| {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 0.3 * 100 round 0}}% | | {{#expr: 60000 * 1.5833333*(10^-5) * 1 * 0.3 * 100 round 0}}% | ||
− | | {{Ticks|{{#expr: 13/(1.5833333*(10^-5) * 1 * 0.3 * 100) round 0}} }} | + | | {{Ticks|{{#expr: 13/(1.5833333*(10^-5) * 1 * 0.3 * 100) round 0}}}} |
| {{#expr: (13/(1.5833333*(10^-5) * 1 * 0.3 * 100))/2500 round 3}} hours | | {{#expr: (13/(1.5833333*(10^-5) * 1 * 0.3 * 100))/2500 round 3}} hours | ||
− | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) round 0}} }} | + | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) round 0}}}} |
| {{#expr: (72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100))/2500 round 3}} hours | | {{#expr: (72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100))/2500 round 3}} hours | ||
|- | |- | ||
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| - | | - | ||
| - | | - | ||
− | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) + 13/(1.5833333*(10^-5) * 1 * 0.3 * 100) round 0}} }} | + | | {{Ticks|{{#expr: 72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) + 13/(1.5833333*(10^-5) * 1 * 0.3 * 100) round 0}}}} |
− | | {{#expr: (72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) + 13/(1.5833333*(10^-5) * 1 * 0.3 * 100))/2500 round 3}} hours | + | | |{{#expr: (72/(1.5833333*(10^-5) * 1 * 100) + 14/(1.5833333*(10^-5) * 1 * 0.7 * 100) + 13/(1.5833333*(10^-5) * 1 * 0.3 * 100))/2500 round 3}} hours |
|} | |} | ||
{{Reflist}} | {{Reflist}} | ||
+ | ====Positive==== | ||
+ | When a character rests in a bed, their Rest value increases over time. At 100% Rest Effectiveness and 100% Rest Rate Multiplier, a character requires 10.5 hours (26,250 ticks) to full rest from 0% to 100%. | ||
− | + | Every 150 ticks (2.5 seconds at 1x speed), rest increases by 100% * (Ticks in interval (150) / Ticks Per Game Day (60000)) * (Hours per day (24) / Sleep Hours for Full (10.5)) * Rest Effectiveness * Rest Rate Multiplier | |
− | + | = 100% * (150 * 24) / (60000 * 10.5) * Rest Effectiveness * Rest Rate Multiplier | |
− | + | = (100%/175) * Rest Effectiveness * Rest Rate Multiplier | |
− | + | = ~0.57143% * Rest Effectiveness * Rest Rate Multiplier | |
− | |||
− | |||
− | |||
175 of these 150-tick intervals is the 26,250 ticks (10.5 in-game hours) required to fully rest from 0%. | 175 of these 150-tick intervals is the 26,250 ticks (10.5 in-game hours) required to fully rest from 0%. | ||
− | == | + | ====Multipliers==== |
− | + | [[Rest Rate Multiplier]] is a character (pawn) stat that defaults at 1.0 and is based off blood pumping, metabolism, and breathing capacities (and thus is affected by relevant injuries, bionics, etc.) | |
− | |||
− | |||
− | |||
− | + | *Blood Pumping has a .3 weight | |
+ | *Metabolism has a .3 weight | ||
+ | *Breathing has a .3 weight | ||
− | |||
[[Rest Effectiveness]] depends on the object the character is sleeping on: | [[Rest Effectiveness]] depends on the object the character is sleeping on: | ||
− | {| class="wikitable" | + | {|class="wikitable" |
+ | |- | ||
! Object | ! Object | ||
− | ! Rest Effectiveness | + | ! Rest Effectiveness at Normal quality |
! Rest increase per 150 ticks | ! Rest increase per 150 ticks | ||
! Rest increase per full 24-hour game day | ! Rest increase per full 24-hour game day | ||
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|} | |} | ||
− | + | and the [[quality]] of that object: | |
− | {| class="wikitable" | + | {|class="wikitable" |
+ | |- | ||
! Quality | ! Quality | ||
− | ! | + | ! Rest Effectiveness Multiplier |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
− | + | | Awful | |
− | | 0.86 || 0.92 || 1.0 || 1.08 || 1.14 || 1.25 || 1.6 | + | | 0.86 |
+ | |- | ||
+ | | Poor | ||
+ | | 0.92 | ||
+ | |- | ||
+ | | Normal | ||
+ | | 1.0 | ||
+ | |- | ||
+ | | Good | ||
+ | | 1.08 | ||
+ | |- | ||
+ | | Excellent | ||
+ | | 1.14 | ||
+ | |- | ||
+ | | Masterwork | ||
+ | | 1.25 | ||
+ | |- | ||
+ | | Legendary | ||
+ | | 1.6 | ||
|} | |} | ||
− | + | Therefore, when a character with 100% Rest Rate Multiplier reaches the Tired threshold (28%), it takes them this long to return to full (100%) rest: | |
− | + | {|class="wikitable" | |
− | + | |- | |
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− | |||
− | |||
− | |||
− | |||
− | {| class="wikitable" | ||
! Object | ! Object | ||
! Ticks to Full Rest | ! Ticks to Full Rest | ||
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|} | |} | ||
− | === | + | ====Analysis==== |
− | + | There exists a balance point for every type/quality of bed (and character, if that character has offsets to Rest Rate Multiplier or Rest Fall Rate), in which the hours spent sleeping and the hours spent awake during a 24-hour period precisely balance. This is ultimately a piecewise equation, as the rest fall rate is piecewise based on the current rest level (see above). We can ignore the Exhausted category, as a character must spend >24 hours awake (if starting at 100% rest) before reaching that threshold. | |
− | |||
− | + | As long as the character is awake for less than 18.189 hours per day, however, this is a single-part equation, as the character will never reach Tired. The percentage of the day that the character may stay awake, expressed as a decimal value, with a given RestMult (equal to Rest Effectiveness * Rest Rate Multiplier) is reached by solving the following equation for %DayAwake: | |
− | |||
− | + | 0.95 * %DayAwake = (1 - %DayAwake) * (24/10.5) * RestMult | |
− | |||
− | |||
This gives the following equation: | This gives the following equation: | ||
− | + | %DayAwake = (320 * RestMult) / (320 * RestMult + 133) | |
− | At 1.0 RestMult (normal unmodified character in a normal quality regular bed), this gives a value of 70.64% of the day awake, or ~16.95 hours. Higher RestMults will grant more hours per day awake per this equation, up to 18.189 hours (75.789% of the day) awake. | + | At 1.0 RestMult (normal unmodified character in a normal quality regular bed), this gives a value of 70.64% of the day awake, or ~16.95 hours. Higher RestMults will grant more hours per day awake per this equation, up to 18.189 hours (75.789% of the day) awake. |
− | Beyond that point, we need a piecewise equation. The RestMult needed to be awake for 18.189 hours per day (0.75789 %DayAwake) is 1.301, which can be achieved with only a masterwork Royal Bed. After this point, we can use a fixed value for the ~75% of the day awake before hitting Tired, which results in a 72% drop in rest, and then compute the remainder of the time awake off of the | + | Beyond that point, we need a piecewise equation. The RestMult needed to be awake for 18.189 hours per day (0.75789 %DayAwake) is 1.301, which can be achieved with only a masterwork Royal Bed. After this point, we can use a fixed value for the ~75% of the day awake before hitting Tired, which results in a 72% drop in rest, and then compute the remainder of the time awake off of the rest fall rate when Tired (66.5% per day rather than 95% per day). This can be found by solving: |
− | + | 0.72 + (%DayAwake - (0.72/0.95))*0.665 = (1 - %DayAwake) * (24/10.5) * RestMult | |
This gives: | This gives: | ||
− | + | %DayAwake = (16000*RestMult - 1512) / (16000*RestMult + 4655) | |
At 1.3125 RestMult (an unmodified character in a masterwork Royal Bed), which is just past the threshold where this equation is needed, this gives a value of 75.962% 0f the day awake, or 18.231 hours. | At 1.3125 RestMult (an unmodified character in a masterwork Royal Bed), which is just past the threshold where this equation is needed, this gives a value of 75.962% 0f the day awake, or 18.231 hours. | ||
− | At 1.68 Rest Effectiveness (the legendary quality Royal Bed in the table above) and a character with the Quick Sleeper trait (50% Rest Rate Multiplier), a Bionic Heart (+25% Blood Pumping = 7.5% Rest Rate Multiplier), and a Bionic or Royalty stomach (all of which are +25% part efficiency -> +12.5% Metabolism -> 3.75% Rest Rate Multiplier), for a net of 1.5*1.075*1.0375 = 1.673 Rest Rate Multiplier, the RestMult = 1.68 * 1.673 = 2.811. At that level, the character can be awake for 87.573% of the day, or 21.017 hours. | + | At 1.68 Rest Effectiveness (the legendary quality Royal Bed in the table above) and a character with the Quick Sleeper trait (50% Rest Rate Multiplier), a Bionic Heart (+25% Blood Pumping = 7.5% Rest Rate Multiplier), and a Bionic or Royalty stomach (all of which are +25% part efficiency -> +12.5% Metabolism -> 3.75% Rest Rate Multiplier), for a net of 1.5*1.075*1.0375 = 1.673 Rest Rate Multiplier, the RestMult = 1.68 * 1.673 = 2.811. At that level, the character can be awake for 87.573% of the day, or 21.017 hours. |
− | In theory, there also exists a point at which the Very Tired piece of the equation becomes a factor, but this would require a pawn to be awake for at least 96.84% of the day (23.242 hours). This would require a RestMult of at least 11.915 (ie. 1191.5%), which is impossible to hit in the base game (and even with most mod setups), and thus can be ignored. | + | In theory, there also exists a point at which the Very Tired piece of the equation becomes a factor, but this would require a pawn to be awake for at least 96.84% of the day (23.242 hours). This would require a RestMult of at least 11.915 (ie. 1191.5%), which is impossible to hit in the base game (and even with most mod setups), and thus can be ignored. |
− | + | If the character is using a [[Circadian assistant]], their rest fall rate is reduced by 20%, meaning it takes 25% longer to reach each threshold. The equations in this case must be re-derived (derivation is left as an exercise for the reader), but the simple answer is: | |
− | If the character is using a [[Circadian assistant]] | ||
* A character otherwise unmodified except for the Circadian Assistant, using a normal quality bed, can be awake for ~75.047% of the day (~18.011 hours), about 6.3% more of the day than without the implant. | * A character otherwise unmodified except for the Circadian Assistant, using a normal quality bed, can be awake for ~75.047% of the day (~18.011 hours), about 6.3% more of the day than without the implant. | ||
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* None of these characters would ever reach "Tired", which takes ~94.737% of a day, or ~22.737 hours, with a Circadian Assistant installed. | * None of these characters would ever reach "Tired", which takes ~94.737% of a day, or ~22.737 hours, with a Circadian Assistant installed. | ||
− | + | == See Also== | |
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− | == See | ||
Pawn sleeping furniture: | Pawn sleeping furniture: | ||
* [[Sleeping spot]] - a free method to designate a place to sleep, but uncomfortable with terrible rest effectivness. | * [[Sleeping spot]] - a free method to designate a place to sleep, but uncomfortable with terrible rest effectivness. | ||
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* [[Animal sleeping box]] - An animal-only bed with stats equivalent to the bedroll | * [[Animal sleeping box]] - An animal-only bed with stats equivalent to the bedroll | ||
* [[Animal bed]] - An animal-only bed equivalent to the bed. | * [[Animal bed]] - An animal-only bed equivalent to the bed. | ||
− | + | {{nav|status levels|wide}} | |
− | {{ | ||
[[Category:Status Level]] | [[Category:Status Level]] |