Here you can find information about how OpenTTD calculates in-game figures.

You always wanted to know how the station-rating was built up? How goods-distribution works? Here you can find it!

Company rating

Each part of the company rating is a linear function, i.e. earning 50% of the target for a component will give 50% of the points allocated for that component. Where components involve monetary amounts, these are converted to the currency of the current game; internally these amounts are stored as the pound amount. Where components involve times and the game uses wallclock timekeeping, these are converted to minutes at the rate of 12 minutes per year, one minute per month, and 2 seconds per day.

Station rating

This section shows the factors that affect the station rating. All calculations are done separately for each cargo type.

Divide the total rating points by 255 to get the percent rating. The maximum possible rating is 100%.

Every 2.5 days (5 seconds or 185 ticks), station ratings are computed; ratings can't change by more than 2 points (0.78%) per cycle, except due to items under "Event". Events give an instant, temporary boost (or penalty) to ratings of nearby stations. The rating will gradually return to normal, following the 2 points every 2.5 days or 5 seconds rule.

The amount of cargo that can be transported from an industry is fully reliant on the station rating. This means that if there is exactly one station serving an industry, on ticks when the industry produces cargo, exactly station rating % of the cargo will be moved to the station. So if the amount of cargo transported from an industry is low, it is probably because the station rating is low, too.

Note: The exact formula can be seen under "UpdateStationRating()" in station_cmd.cpp. This uses some values calculated in "LoadUnloadVehicle()" in economy.cpp.

Note: If the rating is less than 50%, the station starts losing cargo.

Note: If the amount of cargo waiting is greater than 4096 units (or 4,096,000 liters), the station also starts losing cargo. There is a hard cap of 32,768 units of cargo that can be waiting at a station. Any more than that completely disappears every few days. [6]

Cargo delivery to stations

Goods are distributed to stations according to their rating.

If there is only one station around, then a percentage of available goods equal to the station's rating is distributed to it every 2.5 days (5 seconds).

If multiple stations are present, then goods are divided between them based on rating. If there are stations belonging to more than one company, then goods are first divided between companies according to the best station of each company: the proportion of goods allocated to a company C is equal to the best station rating of C over the sum of all best station ratings for all companies. Note that this will be equal to 100% if all stations belong to one company. Then each company's allocation is subdivided among its stations. A station S belonging to C receives a fraction of C's company allocation equal to the rating of S over the sum of the ratings of all stations belonging to C.

Local authority rating

Ratings limit some player actions; they start at +500 and can change based on some actions.

Currently you can exploit the game by planting about 200 trees within a town's influence radius. You may need to clear an area first, in order to have somewhere to plant them, but planting 200 will raise even a minimum rating of -1000 to 220. If your rating is Mediocre or lower, planting 30 trees will approximately wipe out the rating penalty from building one station, depending on the size of the station and how forested the area was. Planting trees while at a rating of Very Good or better has no effect.

Every month (or minute), the ratings for all companies automatically change:

• Rating goes up by 5 if it is less than 200.
• Rating goes up by 12 for each station that has transferred cargo in the last 50 days (100 seconds).
• Rating goes down by 15 for each station that has not transferred cargo in the last 50 days (100 seconds).

Example:
A company has a rating of -300, (Very Poor), 2 active stations and 1 inactive station at a town.
5pts + 2 * 12pts - 15pts = 14pts points gain per month.
(-200 - -300)pts / 14pts/mo = 8 months (or minutes) before the town will let the company build another station.

Code for town ratings is in town.h, town_cmd.c, tree_cmd.c, and road_cmd.c.

Passenger and Mail Generation

Towns and company headquarters generate passengers and mail, while oil rigs only generate passengers.

Town Passenger Generation

In each round of periodic processing (i.e. every 256 ticks), a random value 0<=X<=255 is generated for each house tile. If X isn't smaller than the population of the tile, no passengers are generated. Otherwise, X/8+1 passengers are generated (rounded down). If there is a recession going on, the number of generated passengers is halved, but this division gets rounded up instead of down. Mail generation happens in a similar manner, but with a new random value, and checking against the mail generation multiplier instead of the population. See the full list of default values for HouseProps: [7]

Company Headquarters

The Company Headquarters is a unique structure that generates passengers and mail depending on it's level which is dependent on the performance rating of the company. Higher level company HQs generate more passengers and mail, the output of the headquarters is evenly distributed over all four tiles on a per tile basis as per the following formulas:

Passengers: 256 / 4 tiles / (6 - company HQ Level (a value between 1 and 5) )

Mail: 196 / 4 tiles / (6 - company HQ Level (a value between 1 and 5) )

Industry production

Here is how the game determines how much cargo an industry produces per month. Production of raw materials happens 8 or 9 times per month. (It happens every 256 ticks. There are 74 ticks in a day, and 28 to 31 days in a month (date_type.h). This means that only about 9% of industries will produce 9 times in a 28-day February, but about 96% of industries will produce 9 times in a 31-day month like March.) The production will always be a multiple of 8 or 9, unless the industry changed production during that month.

This table lists possible starting productions governed by the smooth economy patch. These numbers are multiples of 8. When the game generates a new map, each industry produced 8 times and had no production changes in the December before the game started.

(To calculate this table, look under _origin_industry_specs in table/build_industry.h for the industry and its cargo. The sugar mine has CT_SUGAR, 11, so the production starts at 11. Apply the formula from DoCreateNewIndustry() in industry_cmd.cpp: multiply the production by a random integer from 128 to 383, then divide by 256, rounding down. So 11 becomes 5 to 16. Finally, multiply it by 8 to get 40 to 128.)

Production change

Each month the game randomly changes some industry productions.

Default / TTD-like Economy Rules

For 256x256 tile maps there is one change per month possible (only 1 industry changes). Number scales nicely with map size since the introduction of "Daily production changes" function in trunk (r14332).

• As with smooth economy, industries produce cargo 8 or 9 times per month.

However - productions are limited to 6 production levels: lowest, lower, normal (with a new game started or a new industry built), higher, 2x higher and the highest. Production changes between these levels are either a 50% decrease (half) or a 100% increase (double).

• Examples:
  • A Coal Mine: lowest (32 or 40 t per month), lower (64 or 72), normal (120 or 135), higher (240 or 270), 2x higher (480 or 540) and the highest (960 or 1080).
  • A Forest: lowest (32 or 64 t per month), lower (35 or 70), normal (78 or 117), higher (208 or 260), 2x higher (416 or 468) and the highest (832 or 936).
  • A Gold Mine: lowest (12 or 18 bags/month), lower (32 or 40), normal (56 or 63), higher (112 or 126), 2x higher (224 or 252) and the highest (448 or 504).

To make things simple, let's look what are the chances for 256x256 maps (max. 1 change per month = max. 1 industry per month changes production):

• The chance for a production change each month is:
  • 50% for only_decrease industry to decrease (currently only Temperate terrain Oil Wells) or
  • 50% for 1/3 chance (=16.7%) that other industry (non only_decrease) changes production.

• If a production change does occur (~16.7% chance per month):
  • For an industry that has poor or no service (less than 60% of its cargo is transported): 33% chance of increase, 67% chance of decrease.
  • For an industry that has good (greater than 60%) service: 67% chance of increase, 33% chance of decrease.
  • There is no bonus for excellent service with default economy.

• To calculate the chance for a particular change, i.e. 50% * 1/3 * 33% = 5.56%:
  • Poor service: 5.56% that 1 possible change per month is an increase and 11.12% that 1 possible change per month is a decrease.
  • Good service: 11.12% that 1 possible change per month is an increase and 5.56% that 1 possible change per month is a decrease.

Smooth Economy Rules

Out of Date
This article or section is outdated. Some of its content may no longer be accurate due to changes in the latest release. Please update this article.
Difficulty setting and Advanced setting have been replaced by Settings

Distinguish Smooth economy (advanced setting) and Steady economy (difficulty setting)

• The chance for a production change each month is 4.5%; in other words, an average of 4.5% of producing industries from the industry list change production.

• If a production change does occur:
  • For an only_decrease industry (currently only Temperate Oil Wells) 0% chance of increase, 100% chance of decrease.
  • For an industry that has poor or no service (less than 60% of its cargo is transported): 33% chance of increase, 67% chance of decrease.
  • For an industry that has good (greater than 60%) service: 67% chance of increase, 33% chance of decrease.
  • For an industry that has excellent (greater than 80%) service: 83% chance of increase, 17% chance of decrease.

• These two are multiplied together, i.e. 4.5% * 33% = 1.5%:
  • only_decrease industry: 0% chance to increase and 4.5% chance to decrease
  • Poor service: 1.5% chance to increase and 3.0% chance to decrease
  • Good service: 3.0% chance to increase and 1.5% chance to decrease
  • Excellent service: 3.75% chance to increase and 0.75% chance to decrease

• With the Smooth economy option enabled, production changes per month are between 3% and 23%
  • Industries with very low productions, (i.e. 12-40 tonnes per month) will have higher changes.
  • Primary industries produce cargo 8 or 9 times a month. Monthly production is an industries 'base value' multiplied by 8 or 9. For example, the base value for a coal mine is 15 tons, so the monthly production is 120 or 135 tons. This base value is capped at 255, so the maximum possible monthly production for any industry is 2040 or 2295. Ref

Special Cases

• Oil Rig passenger production is limited to 16 passengers per production event, meaning a maximum of 144 or 128 passengers per month. [8]
• Lumber Mill is technically not a producing industry and is classified as a secondary industry in the code. Four or five times a month, it will search outward in a 40 by 40 area in a spiral pattern looking for a fully-grown tree to cut down. If it finds one, the tile will be demolished and 45 tons of wood will be output. This means it has a maximum production of 225 or 180 tons of wood per month, solely dependent on the availability of trees.[9]
• Temperate climate banks never change production (except due to the 8 or 9 production events per month).

Examples

If a coal mine has 70% of its output transported, there is a 3% chance (4.5% * 67%) of a production increase from 3-23% and a 1.5% chance (4.5% * 33%) of a production decrease from 3-23% (but 13% on average).

(1 + (0.03 - 0.015) * 0.13) ^ 12 - 1 = 0.0237 or 2.37%

The coal mine will grow an average of 2.37% on average after the first year.
(1.0237 ^ 20) - 1 = 59.6% after twenty years
(1.0237 ^ 50) - 1 = 321.8% or 3.22x after fifty years
(1.0237 ^ 100) - 1 = 10.35x after one hundred years

For an industry with rating of more than 80%, there is a 3.75% chance of increase and 0.75% chance of decrease:
(1 + (0.0375 - 0.0075) * 0.13) ^ 12 - 1 = 0.0478 or 4.78%

The industry will grow approximately 4.78% on average after the first year.
(1.0478 ^ 20) - 1 = 2.54x after twenty years
(1.0478 ^ 50) - 1 = 10.32x after fifty years
(1.0478 ^ 100) - 1 = 106.62x after one hundred years

For an industry with the only_decrease flag set (currently Temperate Oil Wells), there is only a 4.5% chance of decrease:
(1 + (0 - 0.045) * 0.13) ^ 12 - 1 = (0.99415) ^ 12 -1 = -0.068 or -6.8%

The industry will shrink on average by approximately 6.8% after the first year.
(0.9320 ^ 20) = 24.46% of initial production after twenty years
(0.9320 ^ 50) = 2.96% of initial production after fifty years

ln(0.5) / ln(0.99415) = 118.1 months or 9.84 years is the half life of an only_decrease industry.
ln(8 / 48) / ln(0.99415) = 305.9 months or 25.4 years is the mean lifetime of a temperate Oil Wells (starting at 48 oil/month).
ln(8 / 152) / ln(0.99415) = 501.8 months or 41.8 years is the mean lifetime of a temperate Oil Wells (starting at 152 oil/month).

For good service, it takes 29.6 years on average to double; with excellent service, it takes 14.8 years. If in the game's time a day is 2 seconds, then the doubling time with good service is about 6 hours; with excellent service, the doubling time is about 3 hours. For production to go from near bottom of 100 to near maximum of 2040 or 2295 takes 130 years with good service and 65 years with excellent service.

However, in game you will find industries changing their production rate very randomly. It must be stressed the above examples are only true when observing many industries over the long-term; individual industries may greatly deviate from these averages. Statistically speaking, 6 out of 10 industries will not go from 100 to 2040-2295 even with the best service during 65 years. About 1 out of 9 industries will even lower their production when being served at 60-80% cargo transported for 50 years.

For more responsiveness from industries, adapt the number of wagons to industry production and service frequency (for the lowest production with good frequency, you should use two wagons). [Full Load] orders are usually used for such cargo trains.

Note: The exact formula can be seen under "ChangeIndustryProduction()" in industry_cmd.cpp.

Delivery payment rates

The amount you get paid for delivering cargo is based on 4 factors: the amount of cargo you deliver, the value of the cargo, the distance you deliver it, and how on-time you deliver it.

Initial cargo payment values are for delivering 100 pieces of cargo 1 tile. Payment goes up with inflation as the game progresses.

Late delivery penalties:

• For each day after the Early Delivery time that you deliver the cargo, you are penalized 0.4%.
• For each day after the Late Delivery time that you deliver the cargo, you are penalized an additional 0.4%.
• Maximum penalty is 88%, after which you are penalized further based on how long after the max penalty it takes for you to deliver the cargo.

Extremely late delivery penalty:

• The penalty is an additional factor of 31 / (x + 32) multiplied onto the existing payment, where x is the number of days in transit after the regular late delivery penalty reaches its maximum.
• This translates into another 50% reduction at 30 days past the maximum penalty, increasing to 75% at 92 days past the maximum penalty, and to 88% at 216 days past the maximum penalty.
• This penalty is effectively unbounded and can be found here: [10]

Examples (no inflation):
Deliver 200,000 liters of oil 20 squares in 10 days:
2 * £54 * 20 squares * 100% = £2160

Deliver 100 bags of mail 100 squares in 100 days:
£55 * 100 squares * (1 - 0.80*0.4 - 0.10*0.4) = £3520

HINT calculate easy:
Income = cargo units * cargo value * 0.4
Cargo value comes from the Y-axis on the specific transported goods graph in-game
measure your real delivery time in days and plot on x-axis This result will give you an easy estimation of your income with 5% deviation

• A useful rule of thumb is around 1-2x the transport speed. I.e. for a 200 km/h train, around 300 tiles distance is ideal. Well tuned train networks can push a little further, but any unexpected delays will destroy your value for long distance haulage.

• The exact formula is much more complicated and slightly more accurate, due to rounding error when converting from larger discrete values. See economy.cpp (GetTransportedGoodsIncome()) and Cargo income.

• Distance is measured between the name-labeled tiles of the stations, not from the industries or by vehicle distance traveled. It is computed by adding the differences in x and y tiles (manhattan distance), not straight-line distance.

• Time is measured as the total time the cargo is spent inside a vehicle, from the moment of loading to the moment of unloading. Cargo waiting at stations does not age. By default, all vehicles age their cargo at the same speed, but this may change with NewGRFs.

• Each cargo has a characteristic time at which payment is maximized, assuming you can keep it moving away from the source station at a constant speed. For a cargo with a "late delivery" penalty, this time is typically around 70 days or 2 minutes; for one without, this is typically around 130 days or 4 minutes.

Vehicle speeds

Internally OpenTTD works with a unit called "km-ish/h", which is equal to "mph*1.6". The conversion factor from km-ish/h to km/h is 1.00584, and the conversion factor from km-ish/h to mph is 1.6.

A tile is, for vehicle speed purposes 664.(216) km-ish, 668 km or 415 miles long. This is based on the following facts:

• A tile has 16 sub locations per X/Y axis.
• A vehicle has stores remainder of tile movement in a byte called subspeed, thus has 256 different values.
• The vehicle's (raw) speed is added to subspeed. The resulting number is divided by 256, the remainder is stored in subspeed and the vehicle is moved quotient sub locations forward. For trains and aircraft the raw speed is in km-ish/h, for road vehicles/ships in 0.5 km-ish/h. For trains and aircraft this step is done twice a tick, whereas ships and road vehicles do it once a tick.
• A day contains 74 ticks, and takes 24 hours.

Now assume a vehicle going 1 km-ish/hour: (1 * 16 * 256) / (74 * 2) * 24 = 664.(216).

The net result is that 100 km/hour is ~3.6 tiles/day (1.8 tiles/sec).

Aircraft

• By default aircraft fly at a quarter of their listed speed (this can be changed in advanced settings).
• Aircraft acceleration varies per aircraft, between 144 km-ish/h/day and 400 km-ish/h/day.
• Broken down planes fly at 320 km-ish/h.
• Airport taxi speed is 150 km-ish/h.

Road Vehicles

• Road vehicles accelerate at 37 km-ish/h/day.
• Road vehicles go around corners at half their max speed.
• Road vehicles accelerate an additional 74 km-ish/h/day downhill.
• When going uphill, road vehicles slow down 10% 4 times per tile. This balances out with acceleration at 34-ish km/h for all road vehicles.

(Note: This does not apply when using the improved road vehicle acceleration model.)

Ships

• Ships accelerate at 37 km-ish/h/day.
• A "stopped" ship resumes its last speed instantly.

Trains

(with the realistic train acceleration patch)

• Trains are not affected going up or down hills if they are powerful enough.
• Trains are limited to entering and exiting a depot and making 90° turns at 61 km/h.
• Trains can make one 45° turn or two 45° turns in opposite directions at a time without slowing down.
• When making two or more 45° turns in the same direction, the max speed is limited as follows:

"Curvature" means the average number of wagons of the train between turns. However, very sharp turns (curvatures 0 and 1) are not averaged out in longer trains.

• New rail types can specify custom maximum curve speeds in the same steps as the three default types in the table.
• Tilting trains can take curves about 20% faster than other trains (varies with some engines).
• Train acceleration and max speed are affected by engine power, maximum tractive effort (all engines and powered wagons combined), current speed, air drag, total train mass, and wagons/engines on slopes.
• Non maglev train Acceleration spreadsheet can be found on tt-forums: tt-forums
• Braking is twice acceleration except when entering a depot or a station.

See also: Realistic acceleration and Corners.

See ground_vehicle.cpp, aircraft_cmd.cpp, roadveh_cmd.cpp, ship_cmd.cpp, train_cmd.cpp, vechicle.cpp for code.

As of OpenTTD 1.6.1, given power in hp, max tractive effort in kN, total weight of the train in tonnes, the number train parts (engines and wagons), the air drag value of the first engine in the train (NewGRF setting, defaults to min(192,max(1,floor(2048/max_speed))), meaning faster trains are built more aerodynamically), the combined weight of any train parts (engines or wagons) currently on an up-slope, the combined weight of any train parts (engines or wagons) currently on a down-slope, the slope steepness (game setting [1-10], default 3), and the current speed of the train in km/h, the acceleration of a non-maglev train can be calculated as follows:

force = min((max_te * 1000), floor((power * 746) / (current_speed * 5/18))) [N]

slope_force = weight_on_upslope * slope_steepness * 100 - weight_on_downslope * slope_steepness * 100 [N]

axle_friction = total_weight * 10 [N]

rolling_friction = floor((current_speed + 512) * 15 / 512) * total_weight [N]

air_drag_coefficient = 14 * floor(air_drag_value * (1 + number_of_parts * 3/20)) / 1000

air_drag = floor(air_drag_coefficient * current_speed^2) [N]

acceleration = (force - (slope_force + axle_friction + rolling_friction + air_drag)) / (total_weight * 4) [256th of a km/h per half-tick]

Note: air_drag_coefficient is twice that if any part of the train is in a tunnel.

Given the same values, the equilibrium speed, e.g. the speed the train would eventually settle on if the same conditions continued indefinitely, can be calculated as follows [Assuming a constant rolling_friction (i.e. the speed stays below 512 km/h), and ignoring the flooring of force and air_drag to an integer value]:

p = (slope_force + axle_friction + rolling_friction) / air_drag_coefficient

q = (-power * 746 * 18/5) / air_drag_coefficient

C = (27/2*q + ((27/2*q)^2 + 27*p^3)^(1/2))^(1/3)

equilibrium = min(max_speed, p/C - C/3, max(0, max_te * 1000 / air_drag_coefficient - p)^(1/2))

Town growth

See Towns#town-growth.