Garrison Effects

[Willie McBride]

I just joined the Guild, so I don't have any priviledges, which is why I am posting here. However, I just did some Excel-based statistics upon the effect of Garrison size upon Public Order. I had been led to believe I could find such information on this forum, and although my quest was not fruitful, I decided that this was the proper place for any conclusions I might reach after studying Garrisons.

I used a fairly limited sample size of 26 cities (those West of and including my Capital, plus my two largest cities, which happened to be East of my Capital) and collected data on their individual Populations, Garrisons, and Public Order bonus due to Garrison. My hypothesis was that there would be a direct relationship between the ratio of Garrison to Population and the Public Order bonus. I quickly observed that the PO bonus levels off at 80%, so I eliminated both of the cities in my sample (regretably, also the smallest Populations) that had PO bonus of 80%.

I then graphed the remaining 24 data points on a scatter plot in Excel, with the Ratio of Garrison to Population on the X-axis and the Public Order bonus on the Y-axis. The result:

Y = 701.54 X - 2.6972 R-squared = 0.9928

Once again, we're seeing a pretty simple linear relationship, regardless of buildings present.
In case you're wondering, the Golden Ratio that optimizes Garrison size for Population is 0.114458477; for example, a Garrison of 1376 soldiers assures a Public Order Bonus of 80% in a city of 12000 Population without wasting a single fighting man.

[therother]

Y = 701.54 X - 2.6972 R-squared = 0.9928

That is in good agreement with the formula I concocted. There is a slight complication due to unit size scaling though. See here for details.

This information is also contained in the A short investigation of squalor Ludus Magna thread. You make a good point though - perhaps it should be a little more accessible...

PS Welcome to the Org. Glad to have you aboard!

[warbeetle]

I posted this on the totalwar.com forum and someone said you guys may be interested in such things! (Maybe I can add some stuff regarding the whole public order thing later):

I realized this the first time working in 1.1. BUT it seems to have not changed in 1.2.! It works without changes in different difficult settings! And maybe also with different unit sizes, but havn´t tested this right now!

How to plan garrisons
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Did anyone already notice this?

You can exactly count the numbers of men you need, to give a town the maximum effect of garrison(80%)

formula:

([number of soldiers] : ([Number population]:100) ) * 3,5 = %Garrisson influence

shorter:
(x:(y:100))*3.5=z

If you want the number of people a town can have with a special amount of soldiers at 80% garrison try this:

population= ((soldiers*3,5) : [80]%) *100

shorter:
y=((x*3,5):z)*100

Example:
1.Minimum:A town with 700 people Population needs exactly 160 Men for a garrison of 80%. This means you don´t need a second unit of 160 men until population gets over this number

2.Maximum:20 units 0f 240 peasants can give a town of 21900 people 80% garrisson

As a rule: have one unit of 160 men for every 700 people or one unit of 240 men for every 1050 people

[player1]

I don't know about this calc posted, by my own testing show, that in order to get 80% loyalty, you need to have number of soliders equal to 1/8 of city population size (large unit scale). Sometimes something smaller number is enough, but I gess that's because of some sort of rounding up effect.

[therother]

From this post:

This is rough and ready to be sure, but it gives you a reasonable guesstimate of the garrison bonus:

Garrison bonus ~= -2.8 + 701*(garrison strength/population)

So –2.8 + 701*(1600/30000) ~ 35%, which is about right

Health warning: this won't even be remotely accurate as the expression in the brackets approaches 1! I will try to simplify this ASAP.

These calculations only hold true for large units sizes. The game appears to scale the garrison effect according to the average size of the units in the game. So two units of Hastati have the same relatively effect from small to huge unit sizes. Ergo you need to scale appropriately. Multiple the result of the equation by the following factors to get the right result:

• 4 for small
• 2 for normal
• 0.5 for Huge

[therother]

Okay, far more accurate data for 80 men. Did it quickly, so some of it may be out, but I think it's pretty accurate.


This table contains a lot more data than it first appears. In the transition column, it tells you the point at which garrison changes from one % to another. So 5-10 tells you the point at which garrison percentage jumps from 5% to 10%. Therefore every point between 5601 and 9333 is 5%.

[ZZR Puig]

There is something odd happening here if the last table of population values is right.

If we apply the hypothesis of y=700·X to that data we could see a few things.

First of all, that the garrison bonus that appear on the city details is not a rounded value to the nearest 5% but to the lowest one. So it seems to be working by thresholds, so until the exact real value doesn't get over the 5% the value displayed is 0%. It's not very surprising that it works like this, if not, the first 5% would be twice as easy to reach than the others. If we instead suppose that the values correspond to 2.5%, 7.5%, 12.5%, ... the resulting behavior of the garrison ratio is not linear, so it's unlikely to be the real one.

The most strange thing we can see from that data table is that the previous formula gives exactly the right population threshold for half the data (10%, 20%, 30%, ..., 80%), but on the other half it overestimates the effect by 1% (6%, 16%, 26%, ..., 76%) if we use the population values shown on the table. I we agree that the behavior is linear the formula must be correct, as it gives the right value in more than 2 points. The 1% mismatch must be some effect related to the accuracy or rounding that the game is doing.

We could get the same results if we consider the values to be rounded to the nearest 5% and use the formula y=700·X - 2.5, which is very close to the other proposed solutions, but these previous formulae (701·X -2.8, ...) get slightly wrong values for the population thresholds posted on the previous table.

So, IMO, the only thing to solve at this stage is that 1%, but not the formula.

[therother]

Okay, presenting the data for 80 men a slightly different way:

[sunsmountain]

Right, i found the same data, so the exact formula becomes:

Y = 700*X, - 1 if the 2nd digit of Y is 5 (so it becomes 4)
always round Y down.

This 1% mismatch is very odd. It makes no sense at all. If we ignore it then 700*X gives good results. If you want to correct i dont suggest using -2.5%, i suggest using -0.5%. -2.5 screws it up too much. It'll be a bugger to explain to newbies anyway.

[MajorFreak]

ahhhhh...it's good to be back (finally remembered my hotmail password to get THIS forum's password. lol)

In case you're wondering, the Golden Ratio that optimizes Garrison size for Population is 0.114458477

That's wonderful, but hardly useful unless you're less than 16 squares from the capital. To make that formula useful we'll need the modifier for distance from capital, and since i'm no math wiz i'm hoping someone out there will provide this and make life simple for me. *g*

BTW, that's hilarious CA scaled garrison affect for unit size. lol.

[sunsmountain]

I don't think the public order bonus provided by garrison troops has anything to do with 'distance to capital', i'm pretty sure it is dependent ONLY on:

number of soldiers/population

I do not recommend using more than 5 garrison troops (if each unit has an upkeep of 100) at all. The only reason why you would want a large garrison is to maintain a Very High tax rate. The difference between low and very high tax rate is usually roughly equal to 500 denarii. If you use more than 5 troops you are spending more than you are gaining, which is not a good idea.

[A.Saturnus]

I don't think the public order bonus provided by garrison troops has anything to do with 'distance to capital', i'm pretty sure it is dependent ONLY on:

number of soldiers/population

I think what MajorFreak ment was that although garrison effect is not influenced by distance to capital, public order is. A garrison size of 0.114458477*population won't ensure a public order of 80%. What he may overlook though is that garrison effect is cut off at 80%. What McBride meant with "Golden Ratio" is how to get maximum possible garrison effect without wasting money for a garrison that doesn't have an effect. If that doesn't bring your public order in a yellow area, you need other means to improve it.
I'm not sure why you say 5 units is enough. If unrest is high, you surely want to maximize your garrison effect before using more expansive means like games.

[sunsmountain]

To make that formula useful we'll need the modifier for distance from capital,

And what i'm saying is that these formulaes are useful, are linear, and are not missing a modifier.

What he may overlook though is that garrison effect is cut off at 80%

Both garrison and distance to capital effects are capped or cut off at 80%. That way they can compensate each other, leading to larger garrisons further from the capital.

If that doesn't bring your public order in a yellow area, you need other means to improve it.

Whereas i would advise people to use other means before using garrisons to improve public order.

Distance to capital does influence public order, and games are more expensive than troops below a population of say, 12000. However that does not mean you should use troops to get a Very High tax rate or a high public order for large populations. That will simply end up costing you more than it's gaining you.

To maintain public order, you should (in order of being cost effective):
1. Install a governor if you have a spare: you're paying for them anyway!
2. Build temples.
3. Build arenas/execution squares/odeons.
4. Build health buildings and the level 5 market, though these only compensate the problems they generate themselves in terms of squalor, long term.
5. Lower the tax rate. Aim for 85% at high rate, or 75% at low/normal (to avoid the traits efficient taxman & poor assessor).
6. Use as much garrisons as you need if the population is below 16800.
7. Use Games/Races above 16800, where you mix and match. Obviously if you need 25% you can throw Monthly Games and use some troops, you don't need Daily Games in that case.

The main weapon you have to avoid these latter two is controlling the growth rate: Make sure it finishes on or slightly above 8% (total growth rate, see settlement details, and add up all the contributions to growth: farms, buildings, health, grain, etc.).

[A.Saturnus]

Ok, this thread is not for strategies to increase public order. I merely wanted to point out that MajorFreak made probably a mistake which lead him to think the 0.114458477 ratio is not usefull.
Something that would be on topic though is the question, what is cheaper, a maximal garrison or games. It should depend on population size, but for which size are, say peasants, more expansive than games?