Coaster Stat Calculation Guide

Preface
Knowing about some of the exact details that are about to be revealed herein can easily feel like cheating the game, and in fact, may ruin the fun for someone if they use all the information herein meticulously. While the game does not let someone know what one should design for when creating a coaster outside of the what someone should not do, be aware that some of this information may promote a minmax situation to the point where someone would only build coasters that are optimised for the maximum excitement. That said, some information detailed in this guide may actually still be useful, such as what the game cares about for the purposes of excitement, intensity and/or nausea, and should help someone understand why their coaster got the stats it did. '''If someone does not want to spoil the game for themselves, they should avoid clicking the links to each coaster type's bezier curves in the table under the Intrinsic Excitement subsection of Excitement. The bezier curves will literally reveal the optimal stats for the maximum excitement of any given coaster type.'''

As well, this guide will explain how the game calculates the three primary stats of the coaster: Excitement, Intensity & Nausea. The information detailed herein has been obtained through disassembling Parkitect script, up to date as of 1.7r3, as well as information from other Parkitect users who compiled information from the game.

Note that while these calculations apply to any tracked ride, it is mainly concerned with coasters' primary stats.

Excitement
This primary stat is probably the most complicated stat to explain as the game uses non-formulaic functions instead of variables and formulae to calculate it. Excitement is also divided up into intrinsic and extrinsic parameters.

Intrinsic Excitement
Intrinsic excitement is the excitement rating obtained from the ride layout itself. The basis for which intrinsic excitement is calculated is a set of nine bezier curves, unique to each coaster type. For each curve, the game uses a particular secondary stat in order to obtain a value on the the curve. This value is treated as an excitement contribution by the game. To get a final excitement of a coaster, each of these excitement contributions are added together.

The nine different stats that influence the different excitement contributions are as follows:


 * Ride time (Minutes)
 * Number of direction changes (Turns [?]) (Per minute)
 * Number of drops
 * Number of inversions
 * Airtime
 * Maximum velocity
 * Maximum Vertical G-force
 * Maximum Longitudinal G-force (Acceleration)
 * Average Lateral G-force

The different bezier curves for each stat for each coaster, due to being 9 separate graphs for each coaster type, can be seen in the pictures in the table below, which also contains the maximum value in each graph totalled to give an approximate maximum intrinsic excitement rating of two significant digits. Note that when looking at the graphs yourself, the obtained excitement value on the graph must be multiplied by 100 to obtain the values shown in-game. E.g 0.05 in the graph will produce +5 excitement when in-game.

Finally, there is also the base excitement of a coaster type. However, for all coasters currently in the game, this variable is set to 0. Regardless, these have also been included in the table below.

Extrinsic Excitement
Extrinsic excitement are factors that do not depend on the coaster's design itself, but rather what is around it. Factors that come into play here are things such as going underground, decoration rating, number of vehicles per train, track attachments and synchronized stations. Track attachments are currently not understood and will be omitted for the moment, and the purposes of this guide.

Underground Excitement
For the purposes of calculating the excitement of a coaster, the game only cares about the number of underground transitions. In other words, how many times the coaster goes below ground. Note that an underground segment typically requires going below ground to then go above ground again. This constitutes two underground transitions. Hence, obtaining an odd number of underground transitions is typically not possible. How much excitement is gained for a set number of underground transitions is determined by a quadratic function and is clamped between 0 to 15 bonus excitement. Note that if the coaster has too many underground segments, further segments may even start contributing negatively to this excitement boost, ultimately removing the boost altogether if too many underground segments are utilized.

The exact excitement boost given a certain number of underground transitions is shown in the below table.

Vehicles per Train Excitement
Excitement gained from vehicles per train is simply a +1 excitement per vehicle on the coaster's train(s). This bonus is clamped between 0 to 5.

Synchronized Station Excitement
Synchronized stations impacts the ride's excitement by multiplying the coaster's intrinsic excitement stat plus underground excitement and excitement from number of vehicles per train by a factor determined by each station's number of synchronised stations. The number of synchronized stations the game accounts for clamps between 0 to 4. The excitement multiplier is calculated using a parabolic function and as such suffers diminishing returns as more stations are synchronized.

The exact excitement multiplier is shown in the below table.

Decoration Excitement
Excitement gained from decoration rating can vary for each ride, however whether this varies between different coaster types is unknown. By default, the max excitement gained from decoration is clamped between -10 to 10. For the purposes of ride decoration, the game cares not just about the ride's decoration itself, but also the queue-line's decoration. This by default has been weighted to a 3:1 ratio, or 75%/25% for the ride and the queue-line respectively. A maximum decoration contribution is achieved when the weighted average decoration score of the ride & queueline exceeds approximately 57.1%.

Excitement Penalties
There are two additional factors stemming from a coaster's stats that may impact the coaster's final excitement: High intensity, as well as short duration. If the coaster's intensity is above 90, the excitement rating of the coaster will be reduced using a complicated formula that is currently not entirely understood. Additionally, if a coaster has a duration of less than 35 seconds, it loses a certain percentage of its excitement rating, up to 75% of its excitement rating if its duration is 0 seconds.

Intensity
The Intensity rating of a tracked ride is determined by the following factors:


 * Base Intensity factor
 * Max Positive Vertical G-forces
 * Max Negative Vertical G-forces
 * Max Lateral G-forces
 * Max Negative Longitudinal G-forces (Deceleration)
 * Highest drop height
 * Number of inversions
 * Max velocity
 * Track attachments

These factors are then calculated based on individual coasters' intensity multipliers and are finally added together to give the coaster's intensity rating. If this intensity rating is negative, it is set to 0. Coasters also have an intensity multiplier, which is multiplied with the calculated intensity rating to obtain the final value. The intensity multiplier by default is 1, and the only coaster with known non-1 intensity multiplier is the Vertical Spinning Coaster, for which this is 1.5. It is not known whether any other coaster carry a different intensity multiplier. How each factor, except track attachments for the same reasons to that of Extrinsic Excitement, is calculated will be detailed in each subsection below.

Base Intensity
Each coaster has a base intensity factor defined in code, which defines a starting intensity for the coaster. For every type of coaster currently in the game except one, this value is 0. The only coaster that has a non-zero base intensity is the Bobsled coaster, which has +5 intensity. A table detailing the base intensity for each coaster can be found below.

Positive Vertical G-Forces
The intensity contribution from vertical G-forces is determined only by the maximum positive vertical G-forces ever experienced on the ride. The formula is cubic, clamped between 0 to 1000, and is as below.

$$I_{G_{maxV}} = M_{G_{maxV}}(0.0807645{G_{maxV}}^3 - 0.0864681{G_{maxV}}^2 + 6.01511G_{maxV} - 6.0094)$$ Where:


 * GmaxV is the maximum positive vertical G-forces experienced on the ride.
 * MGmaxV is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost every coaster, this multiplier is 1. The only exception currently in the game is the Vertical Spinning Coaster, which has an intensity multiplier of 2.

Negative Vertical G-Forces
The intensity contribution from vertical G-forces is determined only by the maximum negative vertical G-forces ever experienced on the ride. How the game determines the intensity contribution is a bit different to other contributions in that if the maximum negative vertical G-forces are above -5 Gs, it is set to 100, independently of any intensity multipliers. Otherwise, it is determined through a quadratic formula clamped between 0 to 100, with the formula seen below.

$$I_{G_{minV}} = M_{G_{minV}}(3.11111{G_{minV}}^2 - 5.11111G_{minV} - 3.33333)$$

Where:


 * GminV is the maximum (signed) negative vertical G-forces experienced on the ride.
 * MGminV is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost every coaster, this multiplier is 1. The only two exceptions currently in the game are the Vertical Spinning Coaster, which has an intensity multiplier of 2, and the Flying Coaster with an intensity multiplier of 0.6.

Lateral G-Forces
The intensity contribution from lateral G-forces is calculated using either of the two maximum lateral G-forces ever experienced on the ride, whichever is highest by its absolute value. The formula is quadratic, clamped between 0 to 1000 and is shown below.

$$I_{G_{lat}} = M_{G_{lat}}(3.20149{G_{lat}}^2 + 4.28867G_{lat} - 0.985793)$$

Where:


 * Glat is the peak unsigned lateral G-forces experienced on the ride.
 * MGlat is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost every coaster, this multiplier is 1. The only two exceptions currently in the game are the Vertical Spinning Coaster, which has an intensity multiplier of 0, and the Stand-up Coaster with an intensity multiplier of 1.25.

Deceleration (Negative Longitudinal G-Forces)
The intensity contribution from deceleration is determined only by the maximum negative longitudinal G-forces ever experienced on the ride. The formula is quadratic, clamped between 0 to 100, and is shown below. $$I_{G_{minL}} = M_{G_{minL}}(1.21212{G_{minL}}^2 - 10.303G_{minL} - 5.45455)$$

Where:


 * GminL is the maximum (signed) negative longitudinal G-forces experienced on the ride.
 * MGminL is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For every coaster currently in the game, this multiplier is 1.

Drop Height
The intensity contribution from drop height is determined only by the maximum drop height in meters on the ride. The formula is cubic, clamped between 0 to 100, and is shown below.

$$I_{D_{max}} = M_{D_{max}}(2.05128*10^{-5} {D_{max}}^3 - 2.97436*10^{-3} {D_{max}}^2 + 0.337436D_{max})$$ Where:


 * Dmax is the maximum drop height in meters on the ride.
 * MDmax is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For every coaster currently in the game, this multiplier is 1.

Inversions
The intensity contribution from inversions is determined only by the total number of inversions on the ride. The formula is cubic, clamped between 0 to 100, and is shown below: $$I_{i} = M_{i_{}}(0.014881 {i_{}}^3 - 0.357143 {i_{}}^2 + 5.65476i_{})$$ Where:


 * i is the number of inversions on the ride.
 * Mi is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost every coaster in the game, this multiplier is 1. The only exception currently in the game is the Vertical Spinning Coaster, which has an intensity multiplier of 0.

Velocity
The intensity contribution from velocity is determined only by the maximum velocity in km/h on the ride, clamped between 0 to 200 for the purposes of calculations. The formula is cubic, clamped between 0 to 100 (However the formula itself will never give an intensity contribution larger than 20), and is shown below.

$$I_{V_{max}} = M_{V_{max}} (-1.5229*10^{-6} {V_{max}}^3 + 4.13621*10^{-4} {V_{max}}^2 + 0.0825171 V_{max} -0.86501 )$$ Where:


 * Vmax is the maximum velocity in km/h on the ride.
 * MVmax is the intensity multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For every coaster currently in the game, this multiplier is 1.

Nausea
The Nausea rating of a coaster behaves much like the intensity of a coaster with slightly fewer parts. In total, the nausea rating is determined by the following:


 * Base Nausea factor
 * G-forces
 * Lateral G-time
 * Inversions
 * Drops

These factors are calculated separately using relevant secondary stats of the coaster and are then added together to give the coaster's nausea rating. If this rating is negative, it is set to 0. Coasters also have a nausea multiplier, which is multiplied with the calculated nausea rating to obtain the final value. The nausea multiplier by default is 1, and it is not known whether any of the coasters carry a different nausea multiplier. How each factor is calculated will be detailed in each subsection below.

Base Nausea
Each coaster has a base nausea factor defined in code, which defines a starting nausea for the coaster. For every type of coaster currently in the game except three, this value is 0. The coasters that has a non-zero base nausea are the Spinning Coaster & Inverting Spinning Coaster which carry +8 nausea, as well as the Vertical Spinning Coaster which has +10 nausea. A table detailing the base nausea for each coaster can be found below.

G-Forces
In order to obtain the nausea contribution from G-forces, all maximum G-forces (max positive and negative vertical G-forces, max positive and negative lateral G-forces as well as max positive and negative longitudinal G-forces) are compared by their absolute values and the largest one is selected to be used for calculating the nausea contribution from G-forces. The formula to calculate the nausea contribution is cubic, is clamped between 0 to 100, and is shown below.

$$N_{G_{max}} = M_{G_{max}} (0.0429946 {G_{max}}^3 - 0.332419 {G_{max}}^2 + 4.41168 G_{max} - 4.12226)$$ Where:


 * Gmax is the maximum G-force on the ride.
 * MGmax is the nausea multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost all coasters currently in the game, this multiplier is 1, with the exception being the Vertical Spinning Coaster, which has a multiplier of 2.

Lateral G-time
Lateral G-time is a currently unresearched secondary stat which is used to calculate the nausea contribution from lateral G-time. It is assumed to be the equivalent of airtime for lateral G-forces. To obtain the nausea contribution from lateral G-time, a quadratic formula is used which is clamped between 0 to 100. The formula used is shown below.

$$N_{T_{latG}} = M_{T_{latG}} (0.00284722 {T_{latG}}^2 + 0.521528 T_{latG})$$

Where:


 * TlatG is the lateral G-time on the ride.
 * MTlatG is the nausea multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For all coasters currently in the game, this multiplier is 1.

Inversions
In order to obtain the nausea contribution from inversions, the number of inversions on the ride is clamped between 0 to 14. This value is then used in a cubic formula, clamped between 0 to 100, which is shown below.

$$N_{i_{}} = M_{i_{}} (-0.0124008 {i_{}}^3 + 0.228175 {i_{}}^2 + 2.09325 i_{})$$

Where:


 * i is the modified number of inversions on the ride.
 * Mi is the nausea multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For all coasters currently in the game, this multiplier is 1.

Drops
In order to obtain the nausea contribution from drops, the number of drops is used as is. This value is then used in a quadratic formula, clamped between 0 to 100, which is shown below.

$$N_{D_{}} = M_{D_{}} (0.0134278 {D_{}}^2 + 0.464136 D_{} - 0.0475921)$$

Where:


 * D is the number of drops on the ride.
 * MD is the nausea multiplier, unique to each coaster.

This function has been graphed, as seen in the picture to the right.

Below follows a table detailing the multiplier (M). For almost all coasters currently in the game, this multiplier is 1. The exception is the Vertical Spinning Coaster, for which this multiplier is 1.5