On the efficiency of products
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by SpockPQ
Note à mes très chers lecteurs : puisque cet article est destiné à un lectorat très vaste (soit le e-monde au complet), je me suis permis de l’écrire directement en anglais. Une version française sera publiée un de ces jours! 😛
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During the Christmas vacation, I had the time to find the equations describing the efficiency of weapons, houses, food and health packs. This efficiency (E) is defined as the total influence points procured by the product divided by the number of productivity units required making it. The efficiency is then normalized in such a way that food efficiency is equal to one (for all quality level). The higher this efficiency is, the more “bang” you have for your bucks!
The productivity units used as the basis to compare products can be seen as another reference currency like gold (both are "made" by admins after all…). For this analysis, the productivity units required to produce the raw materials are also included into the total amount of productivity units to make a product. More information about the productivity and influence formulae, used to find the efficiency formulae, can be found here:
http://wiki.erepublik.com/index.php/Productivity_formula
http://wiki.erepublik.com/index.php/Military_formulas
So now, here are the efficiency formulae:
Foo😛
E = 1, for all Q
Houses: E = (30*Q - u)*u / (500*Q)
Weapons : E = (30*Q - 10*u)*u / (200*Q)
Health Packs with weapons : E = 90*(1 + 0.3*Q - 0.1*u) / (0.5/c + 180*Q/u)
Health Packs without weapons : E = 90*c/0.5
where :
E is the efficiency of the product
u is the number of use (number of shots for weapons and number of days for houses)
Q is the quality factor of the company
c is the market equivalent cost of one productivity unit
In order to compare the health pack (sold in gold) with other products, one must convert gold into productivity units. I considered that one productivity unit cost about 0.0011 gold (according to current prices and wages). Therefore, a health pack corresponds to about 455 productivity units.
Here are the results for some typical products:
Food (all Q) : E = 1.000
Q1 Weapon : E = 0.100
Q2 Weapon (3s/30fp): E = 0.225
Q3 Weapon (4s/50fp): E = 0.333
Q4 Weapon (6s/60fp): E = 0.450
Q5 Weapon (5s/100fp): E = 0.500
Q5 Weapon (7s/80fp): E = 0.560
Health pack without weapon: E = 0.198
Health pack with Q5(5s/100fp) weapon: E = 0.284
Q1 House (15d/7.5h): E = 0.450
Q5 House (50d/50h): E = 2.000
Q5 House (75d/37.5h): E = 2.250
The number of productivity units required to produce a weapon scales with the quality factor of the company (Q), while the total influence multiplier of the weapon (fire power x number of shots) scales with Q^2. This explains why the efficiency is roughly proportional to Q. This means that admins, in their great wisdom, designed the game mechanics so that Q1 weapons are totally useless since you have more bang for your bucks using health packs! Therefore, making Q1 weapons is like burning money in a wood stove.
Other interesting things:
- A fight made using food only (no weapon) requires 90 productivity units (grain + baking). Using this magic number, the efficiency of products, and the cost of productivity units, one can estimate the cost of fights using each product.
- Two third of productivity units required to make products are for making the raw materials. Therefore, in an economy that is perfectly balanced, two third of workers would work for raw material companies;
- For weapons, the product customization that maximizes marginal efficiency is u = 1.5*Q;
- For houses, the product customization that maximizes marginal efficiency is u = 15*Q;
If you find this article interesting, please vote it. Thank you!
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Comments
Le e-monde! 😁 ambiteux 😛
voté.
Cool
\o/
Nice article, give a good basis for comparison. I disagree with your optimal product customizations however, although it is mathematicly correct it ignores the other limitations in the game and ultimately results in undesirible products.
For example we're laying the smack down fighting call it 45 hits in a day- with my choice of weapon ( Q5 100/5) your basic health gives you 30 hits, my choice of Home (Q5 50/50) gives another 5 hits and you slam back 10 health packs... net result 90x your base damage consuming 2700 prod in 300 food, 225 productivity from 1 day in the home, 8100 productivity in 9 weapons, plus 10 health packs (call it 4550 productivity using your figures)- total consumed 15575 productivity.
To do the same 90x base damage with your 'optimized' customizations takes 50 fights using 7weapons and 16.25 health packs. Resources consumed 2700 prod in food, 6300 in weapons, 150 productivity from the home plus 7393.75 from the health packs- total consumed 16543.75 productivity.
In my books thats about a 6% loss in efficiency using your customizations plus a little over 3 gold leaving the game rather than curculating in our economy... doesen't sound very efficient to me.
Actually, I think my method gives the same result as yours. It's only a matter of interpretation!
The Q5(7s/80fp) weapon is only more efficient than "regular" Q5 5s/100fp if you DON'T plan to use health packs.
The correct interpretation is the following :
It is noteworthy that using a Q5 house is very efficient way to fight (E >=2.000) Then, fighting with food only without weapon is the most efficient way to go (E=1). However, if you reach the maximum number of fights with food and still need more influence in the battle, using some Q5(7s/80fp) weapons is then the most efficient way to fight (of course, you have to think about this BEFORE fighting...). Then, if all your hits use Q5(7s/80fp) and you still need more influence that day, replace some Q5(7s/80fp, E = 0.560) with Q5(5s/100fp,E = 0.500). Then, if you are using only Q5(5s/100fp) and you still need more influence, use health pack with Q5(5s/100fp) with an efficiency of E = 0.284. Indeed, the Q5(5s/1000) is the most efficient weapon to use with health packs according to the formulae. Moreover, using health pack without weapon is not an option.
Therefore, the Q5(7s/80fp) is the best theoretical solution for "moderate" fights (more influence than food only but less influence than the health pack limit). In practice, Q3 and Q4 could also be interesting solution for these "moderate" fights considering the cost of ownership of Q5 weapons company. However, Q1 and Q2 weapons should absolutely be avoided.
Let me also comment about the point that using health pack removes gold from our economy.
Actually, fighting with products (food and weapons) removes productivity units from our economy. As I said, gold and productivity units are the two reference currencies in this game. If we use one more than the other, the relative value of these two reference currencies will change (we will have gold inflation or deflation). But there is notting bad about that.
I think the most important thing is to make sure that you fight efficiently, no matter if you use either gold or productivity units. Using Q1 weapons is the dumbest thing to do.
Other comments about gold inflation/deflation...
If the price of productivity units becomes too high with respect to gold, peopoe will start to use productivity boosters to "convert" gold into productivity units. This will reduce the price of productivity units with respect to gold.
On the other hand, if the price of productivity units becomes too low, using health packs will become relatively "more expensive" with respect to our daily wages and the low price of productivity units will make them more attractive. Demand will increase and the price of productivity units will increase.
To be clear my point of contention is not the formula but your statement under other interesting things that:
"- The optimal product customization for weapons is u = 1.5*Q;
- The optimal product customization for houses is u = 15*Q;"
The only case where these are true are as follows:
For the house someone looking to do between 2.25 to 3.75 times their base damage daily, for the weapon someone looking to do between 30-63x their base damage daily.
I think it is a poor choice to advise the public to optimize production for these scenereos, the first is virtually nonexistant, the second describes a niche market.
I agree that if you are using weapons less than Q5 and you're not completing a mission your wasting resources.
Good catch on the gold leaving the game comment- it brings to light my personal view that gold is the more scarce of the two as I don't support the purchasing of gold. This situation is reversed if you support the purchase of gold in which case it would be preferable to use health packs since you can alway buy an unlimited amount of gold. In actual fact gold has a zero productivity cost and therefore infinate efficiency.
This is an outstanding analysis and the comments actually add to the value delivered by this article.
o7
Vanquizor :
- I agree that the word "optimal" may indeed be misleading in the current context. In order to clarify things, I changed the wording of these sentences for the following : "the product customization that maximizes the marginal efficiency E". Actually, these two maxima are obtained for dE/du = 0, and thus gives the maximum MARGINAL efficiency. For weapons with odd values of Q, it is indeed impossible to get this maximal efficiency as "u" would not be an integer. And it is also true that this optimal efficiency for houses corresponds to a niche market.
I think that the main idea people should keep in mind is to avoid to make Q1 and Q2 houses and weapons as their efficiency is too low.