Great People Points: Focus in one city, or distribute across many?

[Vol]

While playing some recent games, I became curious about whether or not it mattered if I concentrated all of my Great People Point production in one city or not. Assume that you have a finite number of points you can generate across your empire, you can either focus all of them (specialists and wonders) in one city, or across a few cities (say your three best cities).

If the points required to generate a Great Person were constant (always 100), this would not be an issue. In the long run, the points would always generate the same number of great leaders. However, the points required is not constant. Each Great Person costs 100 more Great People points to generate than the last.

As I'm sure we've all seen, cities with a single specialist (+3 GPP/turn) steadily accumulate points, however the capital may be generating many Great People in the meantime, and thus raising the bar, faster than the smaller city can catch up. Basically, any city that cannot produce 100 Great People Points in the time it takes for the biggest cities to generate another Great Person will never produce one.

So I built a simple simulator, so I could explore the dynamics. These are the assumptions/parameters I used:
- Three cities, with a finite number of Great People Points distributed across them. For simplicity, I chose 30 Great People Points to distribute.
- I defined a parameter, d, which describes the distribution of those points. Basically, its the ratio of the the points in one city to the others.

For example:
If d = 1, the cities have 10, 10, 10.
If d = 2, the cities have 15, 7.5, 7.5.
If d = 3, the cities have 18, 6, 6.
If d = 10, the cities have 25, 2.5, 2.5.
As d approaches infinity, the cities have 30, 0, 0.
If d is larger, you have one city that has much more Great People Points production than the other cities.

If d = 0.5, the cities have 6, 12, 12.
If d = 0.1, the cities have 1.428, 14.28, 14.28.
As d approaches 0, the cities have 0, 15, 15.
If d is smaller, you have one city that has fewer Great People Points than the other cities.

- I ran the simulation and measured the number of turns required to generate 20 Great People, and then normalized the data about d = 1.

Here is the result:

Please note the use of a logarithmic x-axis, and the y-axis is zoomed in. Lower is better, as this denotes fewer turns required to generate the same number of Great People.

Some observations to make:
- No distribution of Great People Points can help you or harm you by more than about 8%.
- The sporadic behavior is caused by cases where cities are unable to "catch-up" to the increasing point total required to generate a Great Person.
- At around d < 0.2, the city with less Great People points is never able to generate a Great Person, as the required total number of points increases faster than the city can accumulate points. Thus, beyond this point, it is better to use those Great People Points to speed up the other cities.
- At round d > 10, the same thing happens in reverse. The other two cities are now never able to generate a Great Person since the primary city is outpacing them and moving the required total faster than they can generate points. At this point, it is better to focus on the one city.
- Both extremes approach asymptotic limits
- There is a dangerous break-point near d = 10 where the primary city gains one more Great People Point and now the required total points is outpacing the other cities, reducing Civ-wide Great People production by 16%.

This case assumed that there were no boosts to Great People Point production. Most boosts are empire-wide (Parthenon, Philosophical, Pacificist), and thus the d value is unchanged (all numbers get bigger, but the ratios stay the same, you have 60 points to distribute instead of 30).

However, the National Epic boosts Great People Points by 100% in just one city. Let's see how that impacts the distribution of points:

We basically see the exact same behavior, but it has been "tilted" and moved to the left by 2x with the impact of the National Epic's 100% multiplier.

Now we see some more interesting, and expected, behavior:
- The total difference in points (from having no Great People Points in the city with the National Epic, to having all Great People Points in a city with the National Epic) is a factor of 2 (60% to 120%).
- Individual break-points relating to cities being unable to catch up to the pace still has an effect of about 10%.
- Focusing all of your Great People Points in one city is the way to go
- The big jump-point where no other city can produce a Great Person due to the run-away primary city now occurs at d = 4. That is, the primary city is generating 20 points (40 with National Epic), and the other two cities are generating 5 points. It takes 2.5 turns to generate 100 points for the primary city, and 20 turns to generate 100 points for the other cities at that point.

In summary, in the reasonable range of d, there is a potential to increase your Great People production by 20% to 30% if you focus your Specialists and Wonders in one city with the National Epic. Other cities will be able to produce Great People, up until a point. If you get many Wonders and Specialists in your National Epic city, you may gain no Great People from having a single specialist or wonder in another city.

As with most other game systems in Civ4, its all about specialization. Having jack-of-all-trades cities is significantly less efficient.

 

[Vol]

A little more detail on cities trying to catch-up to a pace-setting primary city.

Here's an example off of the National Epic curve, where d = 5.25 and within the scope of a game, the other cities are never able to generate a Great Person.


Now, the required number of points goes with the square root of turns, while the accumulated points for any city goes linearly with turns, so there is always some point in time where a city will generate a Great Person. Its just that with a sufficiently fast primary city, this point in time may exceed the 400 turn limit of the game.

Here's an example of d = 2.0 (primary city has 15 points [30 with National Epic], the two secondary cities have 7.5 points).

Here we see that the secondary cities produce 4 Great People, and the primary city produces 16 Great People. Even this relatively slight difference in raw Great People Point production (15 vs. 7.5) has a large effect.

 

[CiverDan]

There is one flaw I immediately see in your analysis. The number of additional GPP required for the next GP increases by 100 only until 1000. After that +200 GPP are required until 3000 GPP are reached, Then 300 additional points are required, etc.

0-1000: +100 GPP
1000-3000: +200 GPP
3000-6000: +300 GPP

You get the idea.

Note that the number of initial GPP required, and thus the initial increases and the breakpoints every 10 GP generated can be higher or lower based on game length. an Epic game has ~150% of the turns of a normal game, so 150 GPP required for the first GP.

 

[Vol]

Intriguing, I never knew that, as its not spelled out anywhere.

I don't think that really changes any results or conclusions, and in fact, it might make the effect even more pronounced in favor of focusing on one city.

 

[Aminor]

Thanks for the analysis and explanation. And also the note the constructive criticism it needs some adjustment.

I had been giving this some thought without clear resolution so far. I did realize the good potential for some GP points to never be effective in lesser cities... but the specialists/improvements are typically for the other benefits than the GP points. So far, GP generation has remained one of the auto-pilot areas for me in the game and thus incidental to the fact that I typically have just a few large, high production cities which are the most likely sites for GP point related construction.

The whole question of GP point distribution also involves the special aspect of what kind of GP one wants next so a GP dominant city which is also heavily religious or scientific etc. will tend to result in more GP of a specific type than may be desirable. But this is perhaps more the result of not paying attention to this aspect of the game.

 

[DaveMcW]

Another flaw is that you don't have a finite number (30) of GPP to distribute. This would be true if wonders were the only source of GPP.

But with Caste System, or many improvements, you have vitually unlimited empire-wide GPP production through specialists. Increasing GPP in one city does not decrease it in another city.

Your analysis is most applicable to Great Engineer and Great Prophet points, which can't be increased using Caste System. Still, Forge and Factory (9 Engineer GPP) is almost as good as every great wonder (10 Engineer GPP) or the Iron Works (10 Engineer GPP).

 

[Vol]

Aye, its not meant to be an end-all simulation of everything that can happen in Civ4... for that you need, uh... Civ4!

This was put together to understand some simple cases, to get a feel for the trends and behaviors. I figured maybe someone else might get a kick out of it, so I posted it. Use it for what it is, but certainly don't expect it to provide solve the problem for every case in Civ4.

I hope to put up some updated plots with the increased GPP requirements tomorrow.

 

[KrikkitTwo]

Actually an improved model might have a 'base GPP' for each city (specialists which are basically available on a equal per city basis.) as well as a 'bonus GPP' (Wonders which are limited)

Perhaps an analysis of adding an additional GPP to the 'max city' when it is already X greater than the others

 

[LeSphinx]

Woo! Good threat but I have to stop to work in order to analyse it to understand every thing.

LeSphinx

 

[Specialj]

Nice Job done. That absolutely clarifies some concepts behind Great People Point.

 

[nklatt]

This is a great start for this issue! What about taking into account WoundedKnight's suggestion to have individual cities focus on generating specific Great People types?

Ugh, getting into Civ IV is great - I now need to brush up on both probabilities for analyzing combat and numerical analysis for this!

 

[Heroes]

Your analysis is great, at least for its intensive use of math!
However, it seems to me that there is a true question: how to increase GPP? You have 2 ways: hire specialists and build wonders. To build wonders, a city needs high production, but specialists generally reduce production. This is a dilemma. What's the best compromise? I am still wondering.

 

[Vol]

OK, here's an update of the above four plots with the increased number of GPP required after 1000. As expected, this factor makes it even harder for cities generating few GPP to produce a Great Person if another city is consisently upping the requirement by 200 GPPs.









I have also generated an animation of the timeline plots as d increases, with the National Epic in the primary city. This helps visualize the impact of cities just barely able to generate a great person or not. Note that there's not a lot of difference in total number of Great People generated.

Right Click and Save As here for the animation (2.8 MB, zipped).

Again, this assumes finite number of points to distribute, but its interesting given the assumptions.

Now let me take a whack at analyzing some of these other questions that have come up.

 

[AU_Armageddon]

Whenever I get a philo leader I look for the opportunity for a GP strat. This concept has had me curious too and I have tried both types a number of times. From my experience, one city is no doubt whatsoever the fastest and easiest way of producing the most GP, but if you have the right layout for spreading early wonders and high food prevalence nearby distributing can be more effective, but slower harder game with more mm.

If I see a place with LOTS of flood-plains or fish etc that can be one of first couple cities, I go with the one city GPs. Pyramids and Parthenon are the musts (anywhere) and you set the target city up to get Great Libary. I focus on getting Mercantilism, Ankor Wat (philosophy is must for civic anyway), and later Statue of Liberty. Sistene Chappel as bonus as well.

Many GP get pumped back into target city to make it super city, and it also is of course your science city. You don't need any others cos it will make many hundreds by itself.

With Representation (immediately from Pyramids), Beurocracy if it is your capital, or else Free Speech if not, and all target city tiles are cottages, and caste system, mercantilism, and philosophy and above wonders and a high food city you have a early classical age GPP of usually 200+ and the bonuses stack up including +3 Science + 1 hammer (priests) + 2 CP on top of what each specialist already produces. 250% GP in your city in your target jumping to 350% as soon as you research Philosophy.

If you have a lot of cities (like 25+) and a generally high food terrain, distributing your GPP can be worth it with careful monitoring. You can maintain the GPP production for much longer if you add Statue of Liberty to the mix as next goal and with caste system, can add (with food allowance) often 3+ specialists per city to the exisiting 2 free ones, all getting 250% for 40-100 GP production in every single city. If its 25 cities, just the civic science BONUS alone is over 400 accross your empire. I often find myself going all priests in bursts for the production on top.

These are maybe more important strats for me than most people cos I prefer to play with tech trading turned off most of the time so the science discoveries are vital (on emporer they have been to keep ahead with tech trading off, but getting the early wonders is much harder so I mostly have to forego any real GP strat since they suck unless you go all the way). But even with tech trading allowed as default it's still nice mega-bonus and just plain fun way to play.

 

[Vol]

OK, new analysis.

Lets say we have built some Wonders at the capital, that in total generate 4 Great Prophet points, 4 Great Artist points, and 2 Great Engineer points. This seems to be a relatively common distribution in many of my games. Since I'm mainly doing this analysis for my benefit, that's what I'll assume. If you play differently... feel free to do your own analysis!

So 10 GPP/turn in the Capitol from Wonders that were built for the primary effect of the Wonder, and the GPP was just bonus. Now, let's say we've decided we want two types of Great People more than anything else: Prophets and Engineers. (Just as an example).

Let's also say we have a secondary city that has also built a Wonder (say, giving 2 Great Merchant points), and that city can support 3 specialists. The capitol can support 3 specialists as well, and the National Epic has been built there. Finally, lets say we have another town which can support 2 specialists but has no Wonders.

How do we go about getting the most Prophets and Engineers over the next 200 turns, assuming we've already generated 2 great people so far in the game?

I ran each possible permutation (48 cases), with 1000 Monte Carlo runs each (since the type of Great Person you get is random).


In this scenario, the Capital generates 9 Great People, the secondary city generates 1 Great Person, and the other city is unable to generate any Great People. The secondary city is no slouch, with 1 Wonder and 3 Specialists, generating 11 GPP/turn (2 + 3*3), but this can "only" generate 2200 Great People points in 200 turns. The other city is running 2 Specialists for 6 GPP/turn, but still is unable to generate a Great Person over 200 turns (since it generates 600 in that time, but the requirement reaches 1400).

For getting the most Great Prophets (average of ~6.9), making all Specialists into Priests is the obvious answer. This setup still generates 1 Great Engineer on average.

For getting the most Great Engineers (average of ~6.1), making all Specialists into Engineers is the obvious answer. This setup generates nearly 2 Great Prophets on average.

However, if we look at the sum of Great Engineers and Great Prophets (basically, trying to drown out the Artist and Merchant points from our Wonders), the total variation is small (~0.2). If neither Engineers or Prophets are valued more than the other, the selection of Specialists should be based on their raw benefits, not the GPPs they generate.

Since the total number of points in each city is constant for all cases, all cases generate 10 Great People within the 200 turns. However, it appears that very consistently, you will get 2 Great People who are not Prophets or Engineers. This is typically Artists from the Capital and Merchants from the Secondary city, due to their Wonders.

In summary, this further emphasizes that generating a few GPP in your cities just won't do much for you, and should not be a consideration when adding Specialists or Wonders to your other cities. GPP should really only enter into the decision making process for the Capital and perhaps one other city. The rest of the time, just worry about the benefits of the Specialists and Wonders, and don't concern yourself with trying to accumulate GPPs there.

 

[Vol]

So my next thought was... does it ever make sense to not have Specialists in cities with different kinds of Wonders? Basically, since the Capital has a variety of points, perhaps instead of producing more "random" Great People there, we should generate no extra points there, allowing the other cities to generate the exact Great People we want.

Here are all permutations (12) where we do not have any extra Specialists in the Capital:


Now the Capital generates 5 Great People (vs. 9 with 3 Specialists), the Secondary city generates 2 (vs. 1) and the other city generates 1 (vs. 0).

The maximum number of Prophets is 4.7 (vs. 7.0), the maximum number of Engineers is 3.6 (vs. 6.1), and the sum averages to 5.7 (vs. 8.0). And the total number of Great People goes down 2 (from 10).

So trying to focus on producing the desired Great People in cities less cluttered with Wonder GPPs is rarely something worth doing. If your whole game hinges on completing a Wonder first, slowing down the Capital's GPPs and hiring many Engineers (although its rarely possible to hire more than 1 until Factories) might be a smart move. The rest of the time, just loading up your National Epic and most Wonder-filled city with extra Specialists is better in the long run, even if you randomly get some Great People that are less useful.

 

[eg577]

Awesome post.

Question: If you vary the number of great leaders, e.g. from 20 to 30 in the graphs of the first type, how does this middle region vary? Do the valleys shift left and right? It would be nice to find that given some d-neighborhood, say between d=9.0 and d=10.0, that there is an optimum choice of d that is somewhat insensitive to the number of great leaders in question.

 

[Vol]

How about this:

"As the number of turns increases from 0 to 400, how does the d at which the other cities no longer contribute (that is, an end to the sporadic peaks/valleys) vary?"

I think that would answer the basic question in a more straight-forward (for me) manner.

 

[Vol]

[Please scroll up and read the updated, previously "reserved" posts if you have not already seen them.]

Alright, here's a look at an interesting question.

Depending on the number of turns remaining (or that we care about), if we have many Great People Points being generated in the National Epic city compared to the other cities, the other cities will never generate a Great Person.

Here's the result:

Please note that the d ratio is calculated prior to the National Epic multiplier.

For example, if you have generated 2 Great People already, and are concerned about the next 250 turns, you should determine if your National Epic City's raw GPP output is more than 2.75 higher than your next highest city. So if the that city is generating 12 GPP (24 GPP/turn after National Epic multiplier), and the next highest city is generating 4 GPP (floor(12/2.75)), then that city will not generate a Great Person in the next 250 turns. If the city has 5 GPP/turn, it will.

Further example, you have generated 6 Great People already and think you'll have the game wrapped up in 100 turns, for better or worse. The d ratio of interest is ~1.3. That is, if your best city (after National Epic), is generating 32 GPP/turn, any city generating less than 12 GPP/turn will not contribute any Great People.

This of course assumes all cities are at 0 accumulated points at the beginning of the measured period.

In summary, if you have generated few Great People, and have a robust city with say, 4 Wonders, and 2 Specialists, and the National Epic, and have 200 turns to go, you'll need cities with 6 GPP/turn or greater (2 Specialists) for them to have an impact. But that impact will be in the form of a single Great Person, compared to many from the primary city.

Add more Wonders to the primary city, and the other cities will have to keep up (at the rate of increase * 1/d). Otherwise, cities with 2 Specialists are worthwhile for Great People generation.

 

[Luhh]

Great job Vol. Very thourough analysis, that comes up with a clear answer.

This begs the question if civIV should be tweaked so that a GP produced in one city increases the cap for 150 in that city, but only say... 50 in the others. This would make it a bit more useful to have more than one city.

I guess though that even with this change it wouldn't be a good idea with many GP cities, and two would probably be the max, with one city still generating the most of them.