Upgrading math re continuing old serial vs new serial

[unmerged(3221)]

There have been a few questions lately about whether or not it's better to continue letting an old series run or whether you should start a new run. The general answer is that if you are going to build 5 or 6 more in a serial run, then start a new run while cancelling the old run. That's because both the old and the new run benefit from gearing, and when gearing benefits start to converge, the 2 step process of building the old and then upgrading it becomes more expensive.

The math to do this is straight forward as long as you can see the daily upgrade % in the statistics folder [an early version of Arma lost this]. You then need to collect the data from an existing serial run: when an old run produces a division, look at the completion time for a new model. After getting the relevant data, it's simple math.

Examples [not sure how well the spreadsheet will fit into the forum]:

Armor2 vs Armor3 for SOV. 1940.
Upgrade = 1.74% daily upgrade progress. 100/1.74 = 57.4 rounded to 58 days at 14.88 IC daily. Upgrade cost is 863.04 IC*days.
Armor-2 costs 14.88 and is built in 93 days = 1488 IC*days.
new Armor 3 costs 19.2 for 148 days or 2841.6 IC*days

UPGRADE COST	863.04    
ARMOR-2 build cost 37 gearing	1488  
old run net	2351.04
new Armor-3 build in IC*days	2841.6
savings from continuing old run:	490.56

Next compare that with starting a new serial run using 95% for 2nd new division, 90% for 3rd, etc.

first	2841.6	490.56
second	2699.52	348.48
third	2557.44	206.4
four	2415.36	64.32
fifth is cheaper	2273.28	-77.76

The only reason to continue an old serial run of Armor-2 would be to benefit from twice obsolete upgrading such as Armor 2 to Armor 4. You have two model price savings. I also looked at Germany PZ div and the math was essentially the same: the 5th model of a new Armor3 run was cheaper than continuing an old Armor2 run.

I also looked at infantry using the USA as an example with full hawk, full free market, and fully drafted parameters. Infantry costs the same for all models.

% daily	7.39	
IC daily	2.24	
# days	13.53	
days rounded	14.00	
IC*days for upgrade	31.41	
INF 39 build	86.40	
NET COST	117.81	
new 1941 build	154.80	
savings	  36.99	  difference =
gearing 2nd	147.06	29.25
gearing 3rd	139.32	21.51
gearing 4th	131.58	13.77
gearing 5th	123.84	6.03
gearing 6th	116.10	(1.71)
6+ of new series is cheaper

When gearing progress starts to equalize, one of the prime benefit of keeping an old series going is lost [it's cheaper]. So why would you even try to keep an old serial run going?
== It's cheaper at the beginning.
== You can get units on the field in time for key dates.
== It takes time to research new models and even more time to gear a new model. Obsolete divisions on the map can fight and be upgraded while newer models still being produced have zero combat capability.

 

[bbasgen]

Good work on finding a new twist to an old subject. I've been doing this in practice for a long time, though not quite as efficient. Sometimes, I cancel an old serial when it has just produced a unit and new technology is available. Other times, I'll let the serial run out for 3-4 more times if it is close to the finish.

 

[CharonJr]

Yes, very nice work, did you figure in the added upgrade time from going full central planning into your calculations ?

CharonJr

 

[ForzaA]

I'm not sure I'm following, so let's do a fact check

You're saying that it is the 5th armour to be built that would be cheaper with the new serial replacing the old?
..That means you're still paying significantly more in total, since numbers 1-4 were more expensive?


If that reading is correct, how many more armour would have to be produced to "cancel out" the initial penalty (about 1100 IC*days)? this depends, I guess, on where your gearing cap is... but it can't be much beyond number 6.. let's say that one has a 200 IC*day saving compared to the old run... that would mean you would need at least *10* units (five before the produced unit is cheaper, plus five to recoup "startup" costs) in the run before you'd save anything?
..But then, a new model would surely be available?

 

[bbasgen]

..That means you're still paying significantly more in total, since numbers 1-4 were more expensive?

No, all his numbers are based on the net cost. This makes sense intuitively, because all this really says is that once the new units catch up on the gearing bonuses, they are generally cheaper per unit, thus reducing total cost. The absence of this kind of truism would mean a strategy of producing old units throughout the game.

In game play, I think the conclusion of maximizing efficiency is to continue an old serial *and* start a new serial of the new unit. Expire the old serial after several more units are produced, by which time the new serial will be caught up in gearing.

 

[Makarion]

How would you run the calculations when building a series of LArm 2, who get upgraded to (LArm3 >) Arm3? Especially with doctrinal effects reducing the cost of LArm by a different amount to Arm, it gets a touch tricky.

 

[unmerged(90249)]

Nice demonstration, but :

1) the 01/01/1936 I can start a loop of 17 TAC that will be ready by 01/09/1939 or so. It's when I need them , not 6 month later.

2) Even lvl 1 , a unit when fighting gain experience, experience that is kept after upgrading.

3) IC wise, it will be better to have a long loop (let say 17 TAC) instead of 2 middle loops (10 and 7). It allow more flexibility for what you have to build.

4) lvl 1 is disponible in 1936, lvl 2 or better will be disponible later. Building an early loop and by so using only a small amount of IC is to be compared with building several loops of up to date model that I will need tomorrow (and not in 3 years). Upgrade may be done at any moment.

Those 4 points are , I believe, true before 01/09/1939; in war time they may be not so true as priority are often to have a lot of something right now (preferable to have it the day before 'right now').

Another point is the difference btw lvl 1 and lvl 2 ; or lvl 2 and lvl 3 is not that great (but for some very specific units); also when you check the cost in time and IC to upgrade ART lvl 1(or is it lvl2 ?) to ART 1939 ( that is an easy exemple) or INT lvl 1 up to INT 1941 ( that can be done by Germany in jully 1939), and compare those cost to the cost for upgrading a bunch of lvl 1 tp lvl 2 and the same bunch + those you build as lvl 2 after to have cancel the first build upgrading to lvl 3 I am far to be sure your method is the winner.

If you quantify in more the rounding problem, the time you as player will spend by canceling and recreating loops (with the right amount of units in); the AI deciding to play a-historical and by so making your swiss clock ticking the wrong way; I do nto see what is to gain with it, but to claim that building L-ARM 1936 in 1956 is wrong (yes it is obviously).


Mathematically speaking, if we use your results we get an hyperbole (spelling?) f(x) = 1 / x; so assuming we have the month of the year as axis X, the best your data can do for us will be to tell us when the last unit of a build of an early model must be build (assuming it is superior or equal to 5, if less than 5 it would still be beneficial to continue the serie).

 

[ForzaA]

No, all his numbers are based on the net cost. This makes sense intuitively, because all this really says is that once the new units catch up on the gearing bonuses, they are generally cheaper per unit, thus reducing total cost. The absence of this kind of truism would mean a strategy of producing old units throughout the game.

Yes and no... That's why I'm asking.

I mean, yes, I see the new units becoming cheaper.. But what I *see* is just that the marginal cost (the cost of a specific unit, ie. "unit #3 of the modern serial" vs. "#3 produced with the old serial after the new unit is invented") is cheaper after #5, what I don't see is the TOTAL cost for #1 through to #5.. Hence I'm asking *where* that is, if it is anywhere.

(do I remember my gearing %ages wrong maybe?)

 

[CharonJr]

With +25% to upgrade time AND cost for full central planning even the 2nd new unit should already be even to upgrading an old unit (unless CP is already factored in the numbers of the original post).

CharonJr

 

[bbasgen]

I mean, yes, I see the new units becoming cheaper.. But what I *see* is just that the marginal cost (the cost of a specific unit, ie. "unit #3 of the modern serial" vs. "#3 produced with the old serial after the new unit is invented") is cheaper after #5, what I don't see is the TOTAL cost for #1 through to #5.. Hence I'm asking *where* that is, if it is anywhere.

I can't speak to John's numbers, but just looking at the game system: eventually the gearing bonuses of a new and old serial will equalize. Considering that an old serial has a *constant* cost to upgrade, while the gearing bonus is only a temporary advantage, it follows that an old serial stops making sense at a certain point. The question is simply: at what point. John has attempted to make that answer, though he hasn't fully expressed his work yet.

ericB: you make good points, but don't forget that IC you dedicate to upgrades. THat constitutes the *real* cost (total IC days) of having those units, and not being able to have new or multiple serial runs, for example.

 

[unmerged(3221)]

1) re starting a TAC 1 run: I should have emphasized more that this was basically a one model comparison. I did include one line about that idea:

The only reason to continue an old serial run of Armor-2 would be to benefit from twice obsolete upgrading such as Armor 2 to Armor 4. You have two model price savings.

The longer that you can put off upgrading really old models, plus any model price differences, mean that old serial runs remain viable when you get 2 or more model price diffentials. That would apply to your TAC 1 serial build or an armor 2 build that continues a very long time. I usually hold off upgrading my starting TAC 1 until I get to the 1940 TAC 4 model, and immediately starting a long serial run of the much cheaper TAC 1 is a very efficient idea [though I am personally more of a build factories guy].

2) Any questions about central planning or army slider changes are irrelevant. Whether you are building or upgrading, you use the same parameters. If you get one of the last four hawk moves while you building a long serial run, that is applied immediately to any builds and to any upgrades.
2.1) Note that my two examples were full central [SOV] vs full free market with full hawk: those are pretty extreme examples.
2.2) The only time that central planning or hawk moves or army slider changes could be relevant would be a timing change: should I upgrade in 1939, 1940, or 1941 to save a little more IC?

3) I did not analyze any "recoup" idea and I don't see why anyone should. You could look at average costs for the old serial run vs average costs for the new model run, but why would you do that? You already know that around the 5th or 6th model of a new run, you are better off, so at that point you can drop the old model run if you have not already done that, and you can continue the new model run for a very long time if you have a fetish about recouping.

4) Light armor divisions are not a good candidate for IC efficiency. If you build or start with a tankette, you get only one obsolete model upgrading benefit by waiting until you research the improved light tank division before upgrading your tankette to a basic light armor division. Then you have to pay TWO full time upgrades: from basic light armor division to improved light armor and then from improved light armor to basic medium armor [armor3].
4.1) While improved light armor div are cheaper than armor3, so it's armor2. Both upgrade to the same model. The benefit of an armor2 run is that it's useful if you keep it going a very long time since you can get 2x or 3x obsolete upgrades, plus you can start an armor2 run very early while most countries have to research the 1939 light armor division.
4.2) I separately analyzed the question of whether it's cheaper to keep any starting tankettes or to sell them off in 1936. I contrasted that with starting an armor2 series and found it was still cheaper with supplies and the 3 upgrades to keep them than to get rid of them. But that comparison did not include building them due to the two full time upgrades that you need: keep them but do not build tankette light armor divisions if you are concerned about IC efficiency.

 

[CharonJr]

Hmm, maybe I am overlooking something, but shouldn't have the +25% cost and time have an influence on when the "break even" unit would be produced ?

Unless I am wrong the IC cost for building a Arm-3 unit would stay the same as would the production costs for a Arm-2, but the upgrade IC-days would be higher under full CP than under full FM.

I fail to see how this can be irrelevant, but I might be missing something here.

CharonJr

 

[unmerged(90249)]

I can't speak to John's numbers, but just looking at the game system: eventually the gearing bonuses of a new and old serial will equalize. Considering that an old serial has a *constant* cost to upgrade, while the gearing bonus is only a temporary advantage, it follows that an old serial stops making sense at a certain point. The question is simply: at what point. John has attempted to make that answer, though he hasn't fully expressed his work yet.

ericB: you make good points, but don't forget that IC you dedicate to upgrades. THat constitutes the *real* cost (total IC days) of having those units, and not being able to have new or multiple serial runs, for example.

The problem is we shall differenciate btw unit that have important difference btw lvl and those who do not have so much difference.

One trivial exemple is anti-air brigade

# 0 - Basic (1937)
model = {
cost = 5
buildtime = 45
manpower = 5
defensiveness = 1
hardattack = 1
airattack = 5
airdefence = 4
maxspeed = -1
supplyconsumption = 0.3
upgrade_time_factor = 0.5
upgrade_cost_factor = 1.0
}

# 1 - Improved (1941)
model = {
cost = 6
buildtime = 45
manpower = 5
defensiveness = 1
hardattack = 1
airattack = 8
airdefence = 6
supplyconsumption = 0.35
upgrade_time_factor = 0.5
upgrade_cost_factor = 1.0
}

obviosuly, lvl 1 have a speed penality that lvl 2 or better do not have. So your model willsimply apply because an early build make only sense if the need is desesperate and it will be better to stop the early build as soon as there is not economical advantage.

On the other hand SP ART :

# 0 - Early
model = {
cost = 6
buildtime = 70
manpower = 5
defensiveness = 3
toughness = 3
softness = -5
softattack = 5
hardattack = 2
supplyconsumption = 1.3
fuelconsumption = 2
upgrade_time_factor = 0.5
upgrade_cost_factor = 1.0
}
# 1 - Basic
model = {
cost = 7
buildtime = 70
manpower = 5
defensiveness = 4
toughness = 4
softness = -6
softattack = 7
hardattack = 2
supplyconsumption = 1.4
fuelconsumption = 2
upgrade_time_factor = 0.5
upgrade_cost_factor = 1.0
}

the values are not so better. So I do believe a long loop started in early 1939 will be more efficient that several started late 1940 to have all my mobile units (ARM MOT or MEC) having an efficient brigade. Upgrade will mater less than the sheer force of the number (anyway I can have SPART lvl 1 and decide to upgrade only when lvl 4 is reached, basically 1944).

What I am trying to say, with a poor english I do agree, is that your demonstration is just fine, but is let say in 2D. Basically to be fully accurate we shall use X dimensions, and cross more variables. futhermore I do not believe basic arythmetic is fitting here, I do believe some models close to those used in micro economic model (such as those created by Cohen in the early 80') should be used.

Allow me an raw exemple :

the discussion raged 3 years ago about IC whoring. Efficient or not.

Kanikatlan came with numbers , proving from his point of view that IC whoring where not efficient, because the return on investment was 5 years long.

I challenged not the numbers, but the way they were used. Because if you invest 5 IC to have a new one after 1 year, it mean 50 IC will generate 10 new IC after a year (50 IC is a value that every major can invest in IC whoring while producing still somehting else if not GER can put almost 120 IC in IC whoring). Those new 10 IC will not yield a ROI after 5 years, but quite earlier if you also invest them in IC whoring (and by so freeing 10 of the old IC pool for somehting else), so the ROI is not only the result of what you produce, but the sum of it + what the new investment you can do with those new IC + what the new investment you can do with those new IC + ... + a delta (delta tending to 0 without reaching it) ...... In mathematic it's called a suite.

Sorry to be smart ass, but what I do love with P'dox games since 2001, it's this capacity to use the theorical knowledge I gained 30 years ago instead of using brute force.

 

[ForzaA]

3) I did not analyze any "recoup" idea and I don't see why anyone should. You could look at average costs for the old serial run vs average costs for the new model run, but why would you do that? You already know that around the 5th or 6th model of a new run, you are better off, so at that point you can drop the old model run if you have not already done that, and you can continue the new model run for a very long time if you have a fetish about recouping.

Simple: because in the end it's about getting the most tanks on the battlefield for the least amount of IC*days.

Yes, if you can support two armour runs only temporarily, then it makes sense to keep the old one only until the new one "caught up" in terms of gearing.. Otherwise, you should only drop and replace the old run if you plan to build 10(guess)+ armour on that run still, since only then will the TOTAL cost for your armour be lower.

 

[Darlor]

As a nit picker, I must point out that everyone is ignoring the cost of supplies to support units during upgrade in these calculations. These supplies also cost IC. This may indeed be too small to really affect the break points but I have not done the calculations yet to see.

 

[unmerged(3221)]

Hmm, maybe I am overlooking something, but shouldn't have the +25% cost and time have an influence on when the "break even" unit would be produced ?

Unless I am wrong the IC cost for building a Arm-3 unit would stay the same as would the production costs for a Arm-2, but the upgrade IC-days would be higher under full CP than under full FM.

I fail to see how this can be irrelevant, but I might be missing something here.

CharonJr

You are comparing 2 different countries. I was trying to answer the question others have raised about whether or not to continue an old serial run or start a new one. How do you do that between countries?

If the SOV have an old serial run going with full central planning, it's completely absolutely irrelevant to see what the math for a new model series is for the USA with full free market:

BECAUSE THE USA DOES NOT GET A CHANCE TO UGPRADE THE SOVIET ARMOR DIVISION.

Both countries obviously have separate parameters for upgrades, land doctrine effects, ministers, etc that affect unit production and upgrading. Each has it's own math for the old model series and then for the new model series. Each step in the production and upgrade process already includes the math for the various effects such as upgrading costs on the sliders. They are automatically included if you are using in game data which is what I have been using. I was not using the general model costs given in your \db\units folders, I use in game data as I described above including how I gathered the data.

 

[unmerged(3221)]

As a nit picker, I must point out that everyone is ignoring the cost of supplies to support units during upgrade in these calculations. These supplies also cost IC. This may indeed be too small to really affect the break points but I have not done the calculations yet to see.

It turns out to be too small to be relevant which is why I did not include it. Using the armor 2 upgrade example above, which is for 58 days at a supply cost of 2.2 supplies a day, that's 127.6 supplies during the upgrade. At 5 supplies per IC, that's only a net difference of 25.52 IC*days. Including supplies the break even point is still the 5th model:

contrasted with gearing Armor-3		with supplies
first	2841.6	516.08
second	2699.52	374
third	2557.44	231.92
four	2415.36	89.84
fifth is cheaper	2273.28	-52.24

25 IC*days is about 1% of the total costs.

 

[unmerged(3221)]

Simple: because in the end it's about getting the most tanks on the battlefield for the least amount of IC*days.

Yes, if you can support two armour runs only temporarily, then it makes sense to keep the old one only until the new one "caught up" in terms of gearing.. Otherwise, you should only drop and replace the old run if you plan to build 10(guess)+ armour on that run still, since only then will the TOTAL cost for your armour be lower.

If you drop the old serial run and start a new serial run, by the 5th or 6th model you are already building cheaper tanks. How long you want to continue that improvement is up to you. The main reason that most players stop building units in long serial run are related to many factors including TC load, manpower, meeting key dates, need to build other kinds of units, etc

As Germany I start Barbarossa with either 16 or 17 Pz div which includes a long Armor 2 serial run, but the most important thing is to have X upgraded PZ div on the field when you need them, not some mathematical balance point. If my armor2 serial run finishes in time for me to have enough upgraded PZ for Barbarossa, then I do not build any new Armor 3, which seems to agree with your point about continuing an old serial run. But the reason that I do that is deciding when I have enough PZ div, not some abstract mathematical break even point.

BTW the balancing point that you are looking for would be about the 8th division of a new model run for the new series. The average cost of the new model run with production of the 8th new model is about the same as the cost of continuing the old run [with full standing army], or around the 7th new model if you are not yet at full standing army.

Net Armor2 cost with supplies	2376.56		
contrasted with gearing Armor-3		with supplies	
first	2841.6	516.08	[U]average[/U]
second	2699.52	374	
third	2557.44	231.92	
four	2415.36	89.84	
fifth is cheaper	2273.28	-52.24	[U]2,557.44[/U]
6th	2131.2		[U]2,486.40[/U]
7th 	2131.2		[U]2,435.66[/U]
8th	2131.2		[U]2,397.60[/U]

 

[unmerged(90249)]

in real, 6 ARM is the right amount for GER from 1939 up to 1941. An additional 6 doing good for Barbarossa.

So one loop starting in 1936, and another starting in 1939 but with ARM 1941

Fact is we are using a given time frame (1936/1956) and not an infinite time; with well know important date (01/09/1939 for exemple).

We must be ready in time instead of be ready early (waste of supplies) or be ready later, so unless that is also quantify calculation are not really usefull but to understand the theory.

 

[ForzaA]

If you drop the old serial run and start a new serial run, by the 5th or 6th model you are already building cheaper tanks.

Just saying that you aren't since by DOING the switchover, you "lost" IC*days.

..But yeah, in the end it's not so much about the exact cost of each armour, but more about the when and where (though it was you starting the thread on costs )