Tech Progression Formula?

[Stone Mill]

OK... I've been playing for a while, but I'm embarassed to say this question eludes me...

When trading tech with human players, you often exchange for even value (research points). However, I have a hard time (maybe I'm too lazy) figuring out the Tech Progression Formula for tech cost.

In the research queue, your current level is displayed, along with the cost to reach next level. But the cost researched to get to those levels are not displayed.

For example, if I were to trade 4 levels of ship construction, could I calculate how much value (research points) I have already spent, based on the cost displayed to reach the next level?

Or is there a spreadsheet available that shows the costs? As always, I appreciate any advice!

[Andrés]

LC level cost
L level you want to research

Low tech cost - LC*L
Mid tech cost - LC*(L^2)/2
High tech cost - LC*(L^2)

[geoschmo]

Andrés, you can display the square symbol. Instead of "L^2" you can have it print as L². The command is Alt+0178. http://forum.shrapnelgames.com/images/icons/icon7.gif

Geoschmo

[Ed Kolis]

Note that on medium tech cost the first level is still L instead of L/2, though...

[geoschmo]

Originally posted by Ed Kolis:
Note that on medium tech cost the first level is still L instead of L/2, though...<font size="2" face="Verdana, Helvetica, sans-serif">True, perhaps the formula for mid tech should be:
Mid tech cost - LC*int[(L²)/2] , or something to that effect. http://forum.shrapnelgames.com/images/icons/icon12.gif

Geo

[Stone Mill]

Thanks for the help.

I tried to run through an example to apply the formulas.
I presume LC = The cost to get to level 1.

Mid-Tech(Medium) Cost

Repair (LC = 10,000)

Level 1: 10,000 * (1 * 1) = 10,000
Level 2: 10,000 * (2 * 2)/2 = 20,000
Level 3: 10,000 * (3 * 3)/2 = 45,000

High-Tech Cost

Repair (LC = 10,000)

Level 1: 10,000 * (1 * 1) = 10,000
Level 2: 10,000 * (2 * 2) = 40,000
Level 3: 10,000 * (3 * 3) = 90,000

Sound ok?

[ July 22, 2002, 18:34: Message edited by: Stone Mill ]

[geoschmo]

No Stone Mill, not 3 times 3, 3 to the power of 2. Is exponential, not multipled. And the exponent is always 2, that doesn't go up with the level. Only the base goes up with the level.

EDIT: Oh, crud. ROFL! I guess 3 * 3 is 3². Sorry Stone Mill. I guess you do have it right afterall. http://forum.shrapnelgames.com/images/icons/icon10.gif

Geo

[ July 22, 2002, 19:29: Message edited by: geoschmo ]

[DavidG]

Well thanks for confusing the heck out of me!! http://forum.shrapnelgames.com/images/icons/confused.gif I just added a feature to my modding program that tells you the total tech cost for an item but I had a different formula. After half an hour of head scratching I realized they gave the same results. Just to confuse you back here is what I used http://forum.shrapnelgames.com/images/icons/icon7.gif

Low cost - each level adds Cost x 1.
(5000, 10000, 15000, 20000, ...)

Medium cost
level 2 cost twice level 1, then each level thereafter adds (Level - 0.5) x Cost.
(5000, 10000, 22500, 40000, ...)

High cost
each level adds (Level - 0.5) x Cost x 2.
'(5000, 20000, 45000, 80000, ...)

[ July 22, 2002, 23:05: Message edited by: DavidG ]

[Baron Munchausen]

Those formulas were posted by PvK, and he was just describing what he saw without thinking very much about the underlying math. I don't think PvK is a mathematician or even a programmer. I think the new formulas posted in this thread are cleaner and probably closer to the truth of what's going on in the game code. Just goes to show you that there are many ways to describe the same thing. http://forum.shrapnelgames.com/images/icons/icon7.gif

[jimbob]

Alright, even more basic question:
If I want to trade with someone, say level 6 propulsion for level 2 sensors, what do I enter in the trade fields? Here's what I think I should do...

Give
propulsion
propulsion
propulsion
propulsion
propulsion
propulsion

Want
sensors
sensors

Is that what I offer?

[Grandpa Kim]

Jimbob, that will work in some but not all situations.

If you have only 6 levels of propulsion, thats what the other player will receive.

If you have 12 levels and he has 5, he will receive levels 6, 7, 8, 9, 10 and 11 !! You are giving him 6 levels that he doesn't have.

Best to know exactly what each other has before making the trade.

I once made this trade with the AI. Can't remember what I gave, but he gave me two levels of fighters. Like this:

fighters
fighters

I only received one level because that was all he had! (Naturally I had to declare war and wipe him out. http://forum.shrapnelgames.com/images/icons/icon12.gif )

[jimbob]

If you have 12 levels and he has 5, he will receive levels 6, 7, 8, 9, 10 and 11 !! You are giving him 6 levels that he doesn't have. <font size="2" face="Verdana, Helvetica, sans-serif">I think I got it... one more question. Suppose I have level 5 Existentialism and he has level 1 Existentialism, and then I offer:

Existentialism
Existentialism

Will he get levels 2 & 3? Or will he get all the way up to level 5 (even though I only 'gave' two levels in the trade)? It seems he should just get levels 2 & 3. But if he had level 2 to start, he would get levels 3 & 4.

Yes?

[geoschmo]

Yes. It appears you have it now Jimbob.

[DirectorTsaarx]

Originally posted by Baron Munchausen:
Those formulas were posted by PvK, and he was just describing what he saw without thinking very much about the underlying math. I don't think PvK is a mathematician or even a programmer. I think the new formulas posted in this thread are cleaner and probably closer to the truth of what's going on in the game code. Just goes to show you that there are many ways to describe the same thing. http://forum.shrapnelgames.com/images/icons/icon7.gif <font size="2" face="Verdana, Helvetica, sans-serif">Well, DavidG's formulas are mathematically equivalent to Andrés' formulas (yeah, I'm a geek; I did a quick arithmetic proof). DavidG's formulas are just the recursive form (i.e., the total cost is the previous level's cost plus the difference calculated from his formulae), while Andrés' formulas are the absolute form (i.e., you just need to know the level cost and the level being researched to find the total cost).

For those who are interested, the proof involves taking the "absolute" formula for level "L" and subtracting the formula for level "L-1", then reducing algebraically to come up with the difference between each level.

Full proof follows:

Low tech cost: absolute formula is LC*L

LC*L - LC*(L-1) = LC*L - LC*L + LC = LC

Therefore, the difference in cost for each level is equal to the level cost.

-----------------------------------
Medium tech cost: absolute formula is LC*(L²/2)

LC*(L²/2) - LC*[(L-1)²/2] = LC*[L²/2 - (L²/2 - 2L/2 + 1/2)] = LC*[2L/2 - 1/2] = LC*(L - 0.5)

Therefore, the difference in cost for each level is equal to the level cost times "Level - 0.5"

-----------------------------------
High tech cost: absolute formula is LC*(L²)

LC*(L²) - LC*(L-1)² = LC*[L² - (L² - 2*L + 1)] = LC*(2L - 1) = 2*LC*(L - 1/2)

Therefore, the difference in cost for each level is equal to the level cost times 2, times "Level - 0.5"

[ July 23, 2002, 17:18: Message edited by: DirectorTsaarx ]

[geoschmo]

Awesome work DirectorT. Really! http://forum.shrapnelgames.com/images/icons/shock.gif

I am a bit of a math dweeb myself, but not at your level apparently. I did test a few levels of DavidG's method (Can't bring myself to call it a "formula" http://forum.shrapnelgames.com/images/icons/icon12.gif ) and I did see that it worked for every one I tested. So I assumed it would be correct forever. I figured there was a way to mathematically prove it, but my brain started hurting when I tried, so I quit. http://forum.shrapnelgames.com/images/icons/icon7.gif

Geoschmo

[E. Albright]

Originally posted by geoschmo:
I figured there was a way to mathematically prove it, but my brain started hurting when I tried, so I quit. http://forum.shrapnelgames.com/images/icons/icon7.gif <font size="2" face="Verdana, Helvetica, sans-serif">Well, if you really were curious (and I certainly hope you're not), my semi-versed eye wants to say that proving this should probably involve mathmatical induction, and the principle thereof. 'Course, the Last "math" course I took was Analysis of Algorithms, and said principle was my main tool therein...

E. Albright

"When all you have is a hammer, everthing starts to look like a nail."

[Stone Mill]

Well, I did learn one thing... how to successfully bait math geeks. And to think how many of you were passed on the starring role in "A Beautiful Mind."

http://forum.shrapnelgames.com/images/icons/icon12.gif

Well, needless to say I found this info valuable, but as a pragmatist I bailed out mentally when arithmetic proofs popped up. OUCH! http://forum.shrapnelgames.com/images/icons/blush.gif

What I'm trying to say is thanks, especially to Andres, for his quick response.

I think most PBW players will find this info quite pertinent. It should limit the amount of stumbling around when figuring out trade values.