Some more calcs

[couerdelion]

I’ve been doing some calculations along the lines that Blake did and looked at two groups of cities. It's quite opportune for me because I am at the stage in the game where I have choices between

a) Using specialists
b) Choice of scientist/merchants

My first test was to determine if certain specialist were beneficial or not and compared one city with a science multiplier of +25% (library) and no gold multiplier with another with a science multiplier of +25% and a gold multiplier of +25%.(library and market). Commerce in group 1 and 2 are both 100 (including trade routes but before multiplier).

For simplicity, I have assumed that the specialist is at the expense of a tile producing 2 food and 3 gold. I admit that those sorts or tiles are rather rare but wanted to be neutral with regards to the commerce generated by the specialist (3).

My final constraint was that there should be a “target” level of gold – a realistic assumption given that this is a very real constraint in the game (gold>=0) and that, over the long term, the investments in science and culture are based on what we can afford. In this test, my target gold is 90 fixed to allow a proportion of science:gold 60%:40%.

Without specialists, I have

Science = 100*60%*125% + 100*60%*125% = 150
Gold = 100*40% + 100*40%*125% = 90

Adding 10 scientist in group 1 cities will take 30 off commerce for that group and add 30 to science.

Science = (70*60%+30)*125% + 100*60%*125% = 165
Gold = 70*40% + 100*40%*125% = 78

Since we require gold of 90, we have to set the investment proportions. For sake of argument, I will assume I can set any value (not just multiples of 10%) and find that the proportion should be 53.8%. This gives us science of 151.9 (a small gain).

If I now return the scientist to working the tiles in this 1st group of cities and add 10 scientists to the 2nd group, I find a more interesting result. To generate the same gold, I need to set an science investment of 52.0% which gives us science of 148.0!!!. Moving 30 commerce in the 2nd group to 30 science has resulted in a net loss to science investment!!! It seems strange that there is a gain from the lesser developed cities and a loss from those more advance.

The explanation for this is similar to those given to explain real life trade benefits in two regions even if one region is at least as productive in producing all goods. My switch to scientist has been a switch from gold to science (with investment at 60:40 each scientist moves 1.2 from gold to science). With my science/gold multipliers, I benefit by moving to produce gold in cities that are “relatively” more efficient in gold and science in those that are “relatively” efficient in science. In the previous case, there was a switch to science from gold in those cities that were better at producing gold. To balance the books, more gold has to be produced in the other group of cities, which are better at producing science.

This means that, using these assumptions, for each scientist in group 2, there will need to be one scientist in group 1 just to break even. By the same logic, for each merchant in group 1, a merchant is needed in group 2 to break even.

The situation becomes more beneficial if we have 10 scientists in the 1st group and 10 merchants in the 2nd. Here we can adjust the science investment to 67% and make a net gain of 4.2 science with no loss of gold.

It is worth bearing in mind that this example is more important for indicating which specialists will be more beneficial in certain cities.

Areas for further investigation
1) Whether specialists are more useful that tile workers
2) Examples with several different groups of cities

[Cort Haus]

This seems to tally with what I've been seeing with spies in the AI cities in end-game.

As we know, the AI is no slouch at research during the end-game, and it likes to specialise. I believe the RL economic term is the Law of Comparative Advantage.

The AI was running 10 specialists in both its Oxford and Wall St cities (it was PHI btw), including 6 scientists in Oxford and 6 merchants in Wall St. I don't have numbers, offhand, but generally it's cities with specialists were matching my cities with laboratories. I'm wondering whether specialists in specialised cities is better than cottages (for non-FIN civs), especially post-biology.

[Cort Haus]

I should have added above that the AI in question was spewing Great Leaders - especially scientists which it was burning for new tech or Golden Ages.

[couerdelion]

To appoint or not to appoint

I’ve never yet played much beyond 600AD so I don’t have any clear answer about the sorts of multipliers you get with specialised cities or multi-purpose ones. It’s something I need to figure out before I start on those national wonders because it might be important in deciding where they should be built.

Your second point is really asking whether or not there is a marginal benefit from employing a specialist rather than a tile-worker and naturally the answer is that it depends on the situation. Simply put, taking a worker from a very productive tile (say 1/2/7) is almost always going to be counter-productive. But what about a 2/0/2 coastal tile or a 1/1/2 plains by river with cottage.

If the city is short of food then the tiles are probably the only alternative. This would presumably be a general rule of mine that you should not force someone to work as a specialist unless you can feed them. I can’t even think of a situation in which this might be done for a short period.

In the case of the coastal tile, let’s assume that you have a city size 15 and no surplus food with a specialist. Let’s also assume first that the city has no comparative advantage.

If the tile is worked you get 2 commerce and will grow in 13 turns and then appoint a specialist. The specialist is worth 3 commerce plus 3GP points.

Accumulated commerce/GP with tile worked (or with specialist)

10 turns - 20/0 (30/30)
20 turns - 61/21 (60/60)
30 turns - 111/51 (90/90)

It certainly seems that, if growth is not constrained by happiness or health reasons then the tile worker seems preferable. It even seems to confirm my initial feelings that specialists seem good for only one thing and that is to control population growth.

Bear in mind that the GP point advantage for the early selection of the specialist is merely a matter of timing and means you get a GP 13 turns earlier. I have assumed that this timing difference will not materially change my opinion here unless the specialist were to discover for you a technology are a very important time.

If I were to apply the same comparison to the cottage then the city takes 25 turns to grow but the commerce difference is neutral by turn 11 anyway. Of course, you then get into a situation where you spend 25 turns with an underfed specialist and 50 turns before the next one comes along so there is a bigger long term difference in GP points but the net long term gold is hugely in favour of working the cottage tile.

The biggest caveat here is that I have ignored the impact of comparative advantage. I’ll think about it for my next instalment.