How Trade Works (with formulae)

Sir Arkatreides · Aug 10, 2013

Trade in EU4 is a massive improvement from EU3 and a sheer joy once you understand the basics. However at first it can be a bit overwhelming and I am writing this to make the mathematics behind it clearer. This is not supposed to the a strategy guide. I am not telling what to do, just how it works

Throughout, definitons in bold are ingame terms, defintions in italic are my own terms.

Throughout, I am taking as examples the values from Portugal at the start of the demo [at some point I plan to redo all the examples with 1444 starting in the full game].

Province Level
Each province provides two important things to the trade node it belongs to, Trade Value and Trade Power.

Trade Value.

Trade Value = Current Price * Goods Produced + Local Trade Value Bonuses
- Every Province produces a trade good which has a Current Price. That current price is determined by the Base Price (ranging from 1 to 3 ) and supply and demand.
  Current Price = Base Price * Demand / Supply.
- Good Produced= 1+Base Tax/100+Local Production Modifiers
- Local Trade Value Bonuses: e.g. Trade Depot: +1
- Local Production Modifiers: e.g. Workshop: +20%
e.g. Porto has Wine @ 3.12 (wine base Price is 3), Base Tax = 10, no Local Production Modifiers, no Local Trade Value Bonuses
=> Goods Produced = 1 + 10/100 + 0= 1.1
=> Trade value = 3.12 * 1.1 + 0 = 3.44

Click to expand...

Note that this is the 'yearly' trade value. Trade Value also directly contributes to the monthly income: Production Income = Trade Value * (1+Production Efficiency) / 12
where Production Efficiency is a national modifier.

e.g. for Porto, Production Efficiency is 20%, so this yields a monthly Production income of 3.44 * 1.2 / 10 = 0.34

Click to expand...
Trade Power
Trade Power = (Base Trade Power + Local Trade Power Bonuses ) * Provincial Trade Power Modifier
- Base Trade Power = 1 for land province, 1.5 for Coastal Province
- Provincial Trade Power Modifier= 1 + Local Trade Power Modifiers + 2*Mercantilism
- Local Trade Power Modifiers: e.g. Trade Depot: +25%
- Local Trade Power Bonuses: e.g. Marketplace: +1, Important Centre of Trade: +5
e.g. Porto is Coastal(1.5) has a Dock (+0.25), Market Place (+1), and 10% Mercantilism
=> Trade Power = (1.5+0.25+1) * ( 1+ 2*0.1) = 2.75 * 1.2 = 3.3

Click to expand...

These are the basics on a province level

Trade Node Level
At Trade Node Level, things start becoming a bit more complicated.

Trade Node Value = Incoming + Local+ Outgoing
- Local = Sum( Trade Value for all Provinces in the Trade Node) / 12
  
  Local Trade in Sevilla = 4.43 (of which 0.28 (3.44/12) comes from Porto)
  
  Click to expand...
- Incoming = Sum( Boosted Outgoing of immediate UPSTREAM nodes )
  Boosted Outgoing = Outgoing * Boost
  Boost works as follows: the more nations that steer trade forward the greater the Boost is. If only one nation is steering trade, Boost = 20%; the second nation increases this by 10%, 3rd: 6.6%, 4th: 5%, 5th: 4% for a maximum of 45.6% (Note in the demo these bonuses were halved). It doesn't seem to matter which countries contribute to the boost and no specific bonus to any country. Also note that you only get a Boost bonus if a merchant is present. Boost can be very powerful, e.g. rooting the trade around Africa (Zanzibar->Cape of Good Hope->Congo->Ivory Coast->Mauritanian Coast->Sevilla) with a Merchant at each node (and assuming no/negligible local trade collecting) gives a an output of 1.2^5 = 2.49 for every trade value generated at the Gulf of Aden. This becomes 1.3^5 = 3.71 if two nations are steering (and 1.456^5 = 6.54 if 5 nations were steering).
- Outgoing is a bit more complex and we need to understand a bit more how Trade Power Share works before we know how to calculate Outgoing.
e.g. for Sevilla, Incoming = 2.29, Local = 4.43 = 6.72

Click to expand...
Trade Power Share (TPS) = Nation Trade Power/Sum( all Nations Trade Power )
Nation Trade Power = ( Trade Power (from all owned provinces )+ Trade Power from Light Ships + 5 (Capital Present) + 2 (Merchant Present ) ) * ( 1 + Trade Power Modifiers ) / ( 1+ No Capital Penalty) + Transferred from Downstream (see later)
- Trade Power from Light Ships = (Sum of all Light Ships trade power) * ( 1 + Leader Manoeuver * 0.05 )
  e.g. Portugal has Trade Power of ( 53.7 (sum of all the Provinces in the Sevilla node) + 2 (Merchant) + 5 (Captial) ) * ( 1 + 0.495 (from Modifiers) ) = 90.7
  
  Every Light Ship boots the Trade Power by 3 to 6 (depending on tech level) which can be further modified by Fleet Leader stats - a 5% boost for each point in their Manouever skill. Ships thus contributes a much larger factor than a Merchant to the Trade Power of the Node. However adding ships to a node has a diminishing returns effect as unlike owning/adding more provinces has a diminishing returns effect. In fact ships have the largest impact in nodes that you nation is not very powerful in. E.g. imagine, Trade Value of a node is 10, your Trade power is 5, Trade power of other nations is 95. This means you currently get 0.5 Trade (raw) out of this node. Having a ship will make it go to 10*8/103 = 0.78, a 55% increase. The additional 0.28 might well warrant the monthy cost of having a ship. Now imagine same Trade value, but your trade power already is 50, other nations 50. Currently you get 5 Trade out of the node. Having a ship will give you 10*53/103 = 5.14, a mere 3% increase and the 0.14 is likely not worth the effort.
  
  Click to expand...
- Trade Power Modifiers = Trade Efficiency+Prestige effects + Stability Effects
  
  e.g. Portugal has Trade Power of ( 53.7 (sum of all the Provinces in the Sevilla node) + 2 (Merchant) + 5 (Captial) ) * ( 1 + 0.495 (from Modifiers) ) = 90.7
  => Portugal Trade Power Share = 90.7/215.2 = 42%
  
  Click to expand...
  
  No Capital Penalty = 1 if collecting from a Node that does not have the nations capital present, 0 otherwise
Now that we have the TPS, depending on what the merchant placed does, three things can happen:
- Transfer Trade Power Upstream: => 20% of the Trade Power (not TPS) is added as a bonus to the Trade Power of the node Upstream. That's all. Nothing more happens.
- Transfer Trade Power (Downstream): A country that choses to Transfer Trade Power moves TPS * (Incoming+Local) to a downstream node. The total of this for all nations transferring will be the Outgoing value of the trade node
  
  e.g. the total outgoing Trade in Sevilla is -2.80. This is because 42% of trade power pulls trade forward. 0.42*6.72=2.8.
  
  Click to expand...
  
  Once we know how much Outgoing there is, we can work out the net trade left in the node for collecting purposes
  Net Trade Node Value = Incoming + Local + Outgoing
  
  e.g. the Net local trade in Sevilla is 2.29 (Incoming) + 4.43 (Local) - 2.80 (outgoing) = 3.92
  
  Click to expand...
- Collect Trade: Monthly Trade income = CTPS * ( 1 + Income )
  - CTPS (Collecting Trade Power Share) = Nation Trade Power/Sum( all Collecting Nations Trade Power )
    (Annoyingly the ingame tool tips don't differentiate between CTPS and TPS, which can make things confusing ...
    Income = 0.1 (Merchant Present) + Trade Efficiency
  e.g. in Sevilla, only Portugal, Granada and Morocco collect trade. Portugal has 90.7 trade power, Granada 13.5, Morocco 9.3 for a total of 113.5. That means Portugal's CTPS 90.7/113.5 = 79.9%. The total net trade in Sevilla is 3.92 => Portugal's share is 0.799 * 3.92 = 3.13.
  Actual income = 3.13 * (1+0.1 (Merchant) + 0.25 (Trade Efficiency) ) = 4.22
  
  Click to expand...
SIMPLIFIED (made up) EXAMPLE, no modifiers:
Bordeaux Node, Incoming Trade Value = 5, Local Trade Value = 5
Portugal: Trade Power = 40, Transfer Upstream
France: Trade Power = 10, Collect
Spain: Trade Power = 20, Collect
England: Trade Power = 30, Transfer Downstream

=> Total Trade Power = 100

=> Portugal, 20% * 40 = 8 Trade Power added to Upstream (Sevilla) Node
=> England, TPS = 30% => 3 Trade Value Transferred Downstream to London Node (Boosted by 20% to 3.6)

=> Net Local Trade Value = 5 + 5 - 3 = 7
=> Spain CTPS = 20/50 = 40% => collect 2.8
=> France CTPS = 30/50 = 60% => collect 4.2

Click to expand...
If the downstream node has multiple upstream nodes, then the percentage of outgoing trade being routed this way is determined by the Trade Power Share (see below) of the steering nations, modified by their Steering Power

Edit:

18Aug13 - 1.1 Added info about collecting from non-capital node penalty, steering boost
17Aug13 - 1.0 Complete rewrite to clarify a few points

Zarine · Aug 10, 2013

Collect doesn't take in the outgoing, and there are still things missing about trade in it...
It's much more complex than that.

Sir Arkatreides · Aug 10, 2013

Zarine said:
Collect doesn't take in the outgoing, and there are still things missing about trade in it...
It's much more complex than that.

You need to factor in outgoing before collect (i.e. outgoing is subtracted first, then whatever remains in the node gets shared amongst the collecting nations). I put in some actual numbers from the Demo to make it clearer - you can verify these numbers yourself.

Zarine · Aug 10, 2013

Sir Arkatreides said:
You need to factor in outgoing before collect (i.e. outgoing is subtracted first, then whatever remains in the node gets shared amongst the collecting nations). I put in some actual numbers from the Demo to make it clearer - you can verify these numbers yourself.

Ok, I get it...
I do my math on collecting on incoming + local counting all trade power
You do your math on incoming + local + outgoing couting only collecting trade power.

You method seems weird as increasing your power as a collector will reduce the outgoing.
I mean, if I hold 40% of the trade power (which is instant to get), I do 40% * (incoming + local) and I have my share (* my bonuses ofc).

Anyway, we end up with same values.

SomethingSharp · Aug 10, 2013

What about the increase in value for steered trade? Like if you look at Sevilla, there is 2.85 outgoing, but Bordeaux has 3.50 incoming (0 from North America so it's all coming from Sevilla). If you hover over the little box that says 3.50 next to Sevilla, it says:

100.00% of power sends trade in this direction
42.40% of power is being used to draw trade on
Armagnac increases value by 10.00%
Auvergne increases value by 5.00%
Bourbonnais increases value by 3.30%
Brittany increases value by 2.50%
Nevers increases value by 2.20%

3.50/2.85 = 1.228, and the sum of the above percentages is 22.8%, which matches.

What I can't seem to figure out is what determines how much each country increases the outgoing trade value. All of those countries have a merchant drawing trade forward but their trade power appears to be the same. Maybe some of those minors have ideas that give them a bit of an edge - maybe that's what the "% bonus to trade steering" ideas do? Dunno, maybe we'll have to wait for the full game to figure this one out.

Any thoughts?

Skrytwitch · Aug 10, 2013

Thanks for the breakdown; it cleared a few things up pretty well for me! However, how do trade steering bonus fit into all of this? Are they a bonus to trade power in foreign nodes or something?

MajorHeartfire · Aug 10, 2013

Very interesting write-up. Thanks for the help!

Sir Arkatreides · Aug 10, 2013

SomethingSharp said:
What about the increase in value for steered trade? Like if you look at Sevilla, there is 2.85 outgoing, but Bordeaux has 3.50 incoming (0 from North America so it's all coming from Sevilla). If you hover over the little box that says 3.50 next to Sevilla, it says:

100.00% of power sends trade in this direction
42.40% of power is being used to draw trade on
Armagnac increases value by 10.00%
Auvergne increases value by 5.00%
Bourbonnais increases value by 3.30%
Brittany increases value by 2.50%
Nevers increases value by 2.20%

3.50/2.85 = 1.228, and the sum of the above percentages is 22.8%, which matches.

What I can't seem to figure out is what determines how much each country increases the outgoing trade value. All of those countries have a merchant drawing trade forward but their trade power appears to be the same. Maybe some of those minors have ideas that give them a bit of an edge - maybe that's what the "% bonus to trade steering" ideas do? Dunno, maybe we'll have to wait for the full game to figure this one out.

Any thoughts?

This is not totally clear to me either -BUT the percentages are always the same, irrespective of node and country. I.e. the top one always is 10%, then 5%, 3.3%, 2.5%, 2% etc.

Now my guess is that all the countries steering away trade are ranked and then allocated to those percentages.
Would require a bit more extensive testing but that seems to be the pattern.

Sir Arkatreides · Aug 11, 2013

Updated with a few more details

repent · Aug 11, 2013

What effect do the navies have and does simply "patrolling" rather than actually assigning ships to a route help at all?

Also, is it better to assign fleets to protect a route you are steering trade along or is it better to assign them to a node from which you are collecting in your territory?

Sir Arkatreides · Aug 11, 2013

repent said:
What effect do the navies have and does simply "patrolling" rather than actually assigning ships to a route help at all?

Also, is it better to assign fleets to protect a route you are steering trade along or is it better to assign them to a node from which you are collecting in your territory?

You need to assign navies to a trade node or the boost effect won't happen. Patrolling is good to get rid of pirates but won't do anything to your trade.

Whether to assign fleets to a steering node or collecting node depends on the node. E.g. for Portugal in the Demo there is no point putting the fleet to the Mauritanian node as already 100% of the trade flows downstream (neither is putting a merchant there - you should remove him at the start and place him somewhere else).

On the other hand if you play venice then it makes a lot of sense to assign your fleet to Alexandria. That node has 3 outflows, and you want to push as much trade as you can your direction.

repent · Aug 11, 2013

Sir Arkatreides said:
You need to assign navies to a trade node or the boost effect won't happen. Patrolling is good to get rid of pirates but won't do anything to your trade.

Whether to assign fleets to a steering node or collecting node depends on the node. E.g. for Portugal in the Demo there is no point putting the fleet to the Mauritanian node as already 100% of the trade flows downstream (neither is putting a merchant there - you should remove him at the start and place him somewhere else).

On the other hand if you play venice then it makes a lot of sense to assign your fleet to Alexandria. That node has 3 outflows, and you want to push as much trade as you can your direction.

Thanks, makes sense. Does the fleet size assigned to the node have an effect?

Tiaexz · Aug 11, 2013

repent said:
Thanks, makes sense. Does the fleet size assigned to the node have an effect?

Each Barque for example is 3 power. So 10 Barques would be 30 power.

Sir Arkatreides · Aug 11, 2013

Tiaexz said:
Each Barque for example is 3 power. So 10 Barques would be 30 power.

Also, this is further modified by the Manoeuver Skill of the attached leader, e.g. a Manoeuver 4 Leader would increase this by 4*5% = 20% to 36 Power.

Pyriel · Aug 11, 2013

Tiaexz said:
Each Barque for example is 3 power. So 10 Barques would be 30 power.

I accually didn't know this.. that light ships help with trade.

Heatth · Aug 11, 2013

Sir Arkatreides said:
Also, this is further modified by the Manoeuver Skill of the attached leader, e.g. a Manoeuver 4 Leader would increase this by 4*5% = 20% to 36 Power.

Wait, really? I did not know that. This is useful information, thanks

Diomedes · Aug 11, 2013

Great stuff all around!! Thanks for posting this.

Lord Canterbury · Aug 11, 2013

Thanks for this.

Do you fancy putting it onto the EU4 wiki as I'm sure many will be looking for help on trade.

Or do you mind if I copy the info over?

jeppev · Aug 11, 2013

Feel like expanding on your post with regards to the "modfiers" in trade nodes, as it is an interresting writeup =)

Trade node modificers:
Trade Efficiency-multiplier (200% capped) + Prestige-multiplier + 0.5 x Trade Efficiency-multiplier (not 200% capped) + Global Trade Power-multiplier
Trade to income conversion:
Trade efficiency-multiplier(max 200% capped) + Global Trade Income Modifier

Notice Trade Efficency is appearing twice in the trade node modifiers!? If someone would please confirm this is I would be thrilled, because it could just be bugged on my end.

The above numbers I have gather from tooltips ingame by hovering above numbers in tradesnodes, trade screens etc.. During that proces I also neglected to uncover any tooltip showing any reference to effect of the Trade Steering-multiplier. So I am I thinking Trade Steering might be bugged or just not working as I think it does (should increase your power when trying to transfering trade a node?).

Feel free to give me your input on the above if you think I missed something =)

arctus · Aug 11, 2013

Sir Arkatreides said:
Trade in EU4 is a massive improvement from EU3 and a sheer joy once you understand the basics. However at first it can be a bit overwhelming.

Hopefully the following will make it clearer on how it works. I am taking as examples the values from Portugal at the start of the demo.

Province Level
Every Province produces a good which has a Price. That price is determined by supply and demand though it's not exactly clear how the value is reached.
e.g. Porto has Wine @ 3.12

Trade Value = Price * (1+Local Production Modifier)
where Location Production Modifier = Goods Produced - 1
and Good Produced= 1+Base Tax/100

e.g. for Porto, Base Tax = 10, Good Produced = 1.1, Local Production Modifier = 0.1 => Trade value = 3.12 * (1+0.10) = 3.44
Note that this is the 'yearly' trade value. Trade Value also directly contributes to the monthly income: Production Income = Trade Value * (1+Production Efficiency)

Also every Province has a Trade Power value.
e.g. Porto = (0.25 (Dock) + 1 (Market Place)+1.5 (Coastal) )* (1+0.2 (Mercantilism) ) = 3.3

These are the basics on a province level

Trade Node Level
For each trade node, we first look at all the provinces that are part of that trade node and sum all the Trade Values and divide by 12 (to get the monthly trade value)
e.g. the 3.44 Trade Value from Porto contributes 3.44/12 = 0.28 to the Sevilla Local trade

Local = Sum( Trade Value ) / 12
e.g. Local Trade in Sevilla = 4.43

The total value of the Trade Node is made up of Incoming (trade diverted from further upstream) and Local.
Total trade = 2.29 (Incoming) + 4.43 (Local) = 6.72

The Trade Power of a nation in the Trade Node is determined by

Trade Power = ( Sum( Province Trade Power ) + Merchants + Other Modifiers (e.g. capital) ) * ( 1 + Modifiers )
e.g. Portugal has Trade Power of ( 53.7 (sum of all the Provinces in the Sevilla node) + 2 (Merchant) + 5 (Captial) ) * ( 1 + 0.495 (from Modifiers) ) = 90.7
An important factor here are the number of Light Ships assigned to the trade route. Every Light Ship boots the Trade Power by 3 (which can be further modified by Fleet Leader stats) so contributes a much larger factor than a Merchant to the Trade Power of the Node.

Trade Power Share = Trade Power/Sum of Trade Power of all nations
e.g. Portugal Trade Power Share = 90.7/215.2 = 42%

Next two things happen:

Transfer Trade Power: A country that choses to Transfer Trade Power moves Trade Power Share * (Incoming+Local) to a downstream node. The total of this will be the Outgoing value of the trade node
e.g. the total outgoing Trade in Sevilla is -2.80. This is because 42% of trade power pulls trade forward. 0.42*6.72=2.8.

Collect Trade: We now take the net local Trade Node Value = Incoming + Local + Outgoing.
e.g. the Net local trade in Sevilla is 2.29 (Incoming) + 4.43 (Local) - 2.80 (outgoing) = 3.92
All the countries that collect trade will take a share out of this Local Trade Value according to their share
Collect Trade Power Share = Trade Power/Sum of Trade Power of all nations collecting
e.g. in Sevilla, only Portugal, Granada and Morocco collect trade. Portugal has 90.7 trade power, Granada 13.5, Morocco 9.3 for a total of 113.5. That means Portugal takes 90.7/113.5 = 79.9% of the share of the node. The total net trade in Sevilla is 3.92 => Portugal's share is 0.799 * 3.92 = 3.13.
Trade Collected = Collect Trade Power Share * (Incoming + Local + Outgoing ) * (1+Modifiers)
e.g. Actual income = 3.13 * (1+0.1 (Merchant) + 0.25 (Trade Efficiency) ) = 4.22

in which way does a fleet commander influence the trade trade power of light ships?

How Trade Works (with formulae)

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