I have managed to figure out how manpower is calculated in Victoria (see Manpower Calculations Revealed). I believe that there are errors in the Manpower Calculations. The errors appear to have been introduced in patches 1.01 and 1.02. The specific changes that caused the errors are:
Manpower cap is now reduced by the amount of troops you already have deployed. (1.01)
Ships no longer cost manpower to build. (1.02)
I’ll discuss the calculations for the manpower cap first. Since ships no longer cost manpower, it makes sense that ships shouldn’t affect the manpower cap. However, the number of ships does affect the manpower cap. This is easily observed by disbanded some ship, advancing the game two days and observing the change in the manpower cap. I suspect that this was overlooked when the changes were made for 1.02.
In addition, I believe that the change made for 1.01, to reduce the manpower cap by the troops deployed, is mathematically flawed. I determined that the manpower Cap is calculated by the formula:
Cap = Soldiers * (.25 + .75*Slider) – Troops
Where: Soldiers = Total soldiers population in 1000s.
Slider = Defense Spending Slider percentage setting (0-100%).
Troops = Amount of troops deployed.
I believe that the correct formula should be:
Cap = (Soldiers – Troops) * (.25 + .75*Slider)
Both formulas give the same results when the defense slider is at 100%. However, for values less than 100%, the first equation gives lower values. It also results in more negative values.
Let me illustrate why I believe that the first equation is wrong. Assume that a country has 20,000 soldiers and no troops deployed. Let’s calculate the manpower cap at 100% and 0% defense slider settings using both equations. In this case both equations give the same results: 20 at 100% and 5 at 0%.
Now, let’s assume that the country builds two infantry divisions. At full strength these two divisions have a troop deployed value of 20. Also the number of soldiers in 1000s is 20. One can interpret this situation as having all the soldiers deployed in the two divisions and there being no manpower left over. The manpower cap should be zero. Let’s now see what values two equations produce. At 100% defense spending both equations give the expected value of 0. However, at 0% defense spending only the second equation gives 0. The first equation, which is how Victoria works now, gives a value of –15. This is clearly wrong.
I’ll give one last example. Let now assume 40,000 soldiers and 20 troops deployed. The second equation gives values of 20 at 100% and 5 at 0%. This is the same as with 20,000 soldiers and no troops deployed. This makes sense since you have the same number of undeployed soldiers in both cases. The first equation gives values of 20 at 100% and -10 at 0%. This is really strange because depending on the defense slider setting the manpower can be either positive or negative. This illustrates why you often lose all your manpower when you lower your defense spending.
I’ll now look at the calculation for the “monthly increase in manpower”. The formula for this is:
Increase = .5 * Slider * Cap / 12 [or 0 whichever is greater]
Notice that this equation depends upon the value of the manpower cap that in turn depends upon the defense spending slider. This makes the increase a function of the square of the slider value. This mean that for slider setting less than 100% that the increase is smaller than it would be with a linear equation. I believe that prior to 1.01 that the increase varied linearly with the slider value. In addition, the error in the calculation of the cap value results in even lower values for the increase.
I believe that correct equation should be:
Increase = .5 * Slider * (Soldiers–Troops) / 12 [or 0 whichever is greater]
Both equations produce the same values for slider values of 100% and 0%. However the first equation results in lower increases for slider settings between 0% and 100%.
To illustrate this let’s assume we have 24,000 soldiers and no troops deployed. Let’s calculate the increase at a 50% defense slider setting using both equations. The first equation gives a value of .31 troops per month and the second equation .5. The increase is 1 with slider at 100%. Thus second equation gives an increase at a 50% slider setting that is one half of the value at 100%. It makes sense that half the spending should result in one half the increase.
Finally, I’ll look at the calculations for defense spending. The formula for this is:
Spending = Slider * (.5*Officers + .25*Soldiers)
Where: Officers = Total officer population in 1000s.
I believe that this formula should be changed to:
Spending = Slider * (.5*Officers + .25*(Soldiers-Troops))
Note: the term (Soldiers-Troops) should have a minimum value of 0 and not be allowed to be negative in this equation.
The first equation is not outright wrong. However, in my opinion, if your manpower cap is reduced by the amount of troops you already have deployed, your cost should also be lowered. After all you already pay maintenance for troops. Why should you have to pay for them twice? The defense spending cost should only be for those soldiers that contribute to manpower (i.e. Soldiers-Troops).
If you are going to fix the manpower calculations you might want to take the opportunity to make some changes in the way they work. Since this is a bug-reporting forum, I’ll post my suggestions later in the general forum. Watch for them tomorrow or the next day.
George
Manpower cap is now reduced by the amount of troops you already have deployed. (1.01)
Ships no longer cost manpower to build. (1.02)
I’ll discuss the calculations for the manpower cap first. Since ships no longer cost manpower, it makes sense that ships shouldn’t affect the manpower cap. However, the number of ships does affect the manpower cap. This is easily observed by disbanded some ship, advancing the game two days and observing the change in the manpower cap. I suspect that this was overlooked when the changes were made for 1.02.
In addition, I believe that the change made for 1.01, to reduce the manpower cap by the troops deployed, is mathematically flawed. I determined that the manpower Cap is calculated by the formula:
Cap = Soldiers * (.25 + .75*Slider) – Troops
Where: Soldiers = Total soldiers population in 1000s.
Slider = Defense Spending Slider percentage setting (0-100%).
Troops = Amount of troops deployed.
I believe that the correct formula should be:
Cap = (Soldiers – Troops) * (.25 + .75*Slider)
Both formulas give the same results when the defense slider is at 100%. However, for values less than 100%, the first equation gives lower values. It also results in more negative values.
Let me illustrate why I believe that the first equation is wrong. Assume that a country has 20,000 soldiers and no troops deployed. Let’s calculate the manpower cap at 100% and 0% defense slider settings using both equations. In this case both equations give the same results: 20 at 100% and 5 at 0%.
Now, let’s assume that the country builds two infantry divisions. At full strength these two divisions have a troop deployed value of 20. Also the number of soldiers in 1000s is 20. One can interpret this situation as having all the soldiers deployed in the two divisions and there being no manpower left over. The manpower cap should be zero. Let’s now see what values two equations produce. At 100% defense spending both equations give the expected value of 0. However, at 0% defense spending only the second equation gives 0. The first equation, which is how Victoria works now, gives a value of –15. This is clearly wrong.
I’ll give one last example. Let now assume 40,000 soldiers and 20 troops deployed. The second equation gives values of 20 at 100% and 5 at 0%. This is the same as with 20,000 soldiers and no troops deployed. This makes sense since you have the same number of undeployed soldiers in both cases. The first equation gives values of 20 at 100% and -10 at 0%. This is really strange because depending on the defense slider setting the manpower can be either positive or negative. This illustrates why you often lose all your manpower when you lower your defense spending.
I’ll now look at the calculation for the “monthly increase in manpower”. The formula for this is:
Increase = .5 * Slider * Cap / 12 [or 0 whichever is greater]
Notice that this equation depends upon the value of the manpower cap that in turn depends upon the defense spending slider. This makes the increase a function of the square of the slider value. This mean that for slider setting less than 100% that the increase is smaller than it would be with a linear equation. I believe that prior to 1.01 that the increase varied linearly with the slider value. In addition, the error in the calculation of the cap value results in even lower values for the increase.
I believe that correct equation should be:
Increase = .5 * Slider * (Soldiers–Troops) / 12 [or 0 whichever is greater]
Both equations produce the same values for slider values of 100% and 0%. However the first equation results in lower increases for slider settings between 0% and 100%.
To illustrate this let’s assume we have 24,000 soldiers and no troops deployed. Let’s calculate the increase at a 50% defense slider setting using both equations. The first equation gives a value of .31 troops per month and the second equation .5. The increase is 1 with slider at 100%. Thus second equation gives an increase at a 50% slider setting that is one half of the value at 100%. It makes sense that half the spending should result in one half the increase.
Finally, I’ll look at the calculations for defense spending. The formula for this is:
Spending = Slider * (.5*Officers + .25*Soldiers)
Where: Officers = Total officer population in 1000s.
I believe that this formula should be changed to:
Spending = Slider * (.5*Officers + .25*(Soldiers-Troops))
Note: the term (Soldiers-Troops) should have a minimum value of 0 and not be allowed to be negative in this equation.
The first equation is not outright wrong. However, in my opinion, if your manpower cap is reduced by the amount of troops you already have deployed, your cost should also be lowered. After all you already pay maintenance for troops. Why should you have to pay for them twice? The defense spending cost should only be for those soldiers that contribute to manpower (i.e. Soldiers-Troops).
If you are going to fix the manpower calculations you might want to take the opportunity to make some changes in the way they work. Since this is a bug-reporting forum, I’ll post my suggestions later in the general forum. Watch for them tomorrow or the next day.
George
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