[0rph3u5]

I can give at least one of my hand form time to time next year

my freding skills are more than basic and that's all I can do (no modelling or stuff like that)

[IPAndrews]

Ok back to the problem of calculating losses for each side in the war. I'm really struggling with this actually so I'm throwing it open to the general public to see if they can come up with any good equations. Remembering that FRED does not support fractions, only integer values. mmkay.

Here's what I have so far:

Raiders (Ship Str = 2, Ships = 500)
League (Ship Str = 3, Ships = 1500)
Narn (Ship Str = 5, Ships = 2000)
EA (Ship Str = 6, Ships = 2000)
Centauri (Ship Str = 8, Ships = 1500)
Minbari (Ship Str = 12, Ships = 1500)
Drakh (Ship Str = 14, Ships = 500)
Shadows (Ship Str = 16, Ships = 500)
Vorlons (Ship Str = 20, Ships = 500)

So I need to calculate the number of ship kills inflicted by team 1 on team 2 and vice-versa. I think the equation should take into account the following:

* The strength of the race's ships
* The number of the race's ships
* The strength of the enemy's ships
* The number of enemy ships
* The momentum of the campaign (varies: -10 to 10, -10 means team 1 in full retreat, 10 means team 2 in full retreat).

At the moment I have:

team1kills = (team1shipstr + momentum) * team1ships)
                    * 10
                    / ((team2shipstr - momentum) * team2ships)

Which means on day 1 (campaign momentum 0) the Vorlons would destroy 133 raider ships. The Raiders would destroy 0.75 (rounded down to 0) enemy ships.

Assuming the raiders did really well and managed to obtain a campaign momentum of 10. They could potentially destroy (500 * (3 + 10)) * 10 / 500 * (20 - 10)) = 13 ships!

So I think, what I have at the moment is rubbish. Anyone got any opinions?

[0rph3u5]

Raiders (Ship Str = 2, Ships = 500)
League (Ship Str = 3, Ships = 1500)
Narn (Ship Str = 5, Ships = 2000)
EA (Ship Str = 6, Ships = 2000)
Centauri (Ship Str = 8, Ships = 1500)
Minbari (Ship Str = 12, Ships = 1500)
Drakh (Ship Str = 14, Ships = 500)
Shadows (Ship Str = 16, Ships = 500)
Vorlons (Ship Str = 20, Ships = 500)

make the ships strengh like this
RAIDERS: 0.2
LEAGUE: 0.3
NARN: 0.5
EA: 0.6
CENTAURI: 0.8
MINABARI: 1.2
DRAKH: 1.4
SHADOWS: 1.6
VORLONS: 2.0

and try to integrate them into the formula via multiplication not by simply adding them to the momentum.... maybe you could exchange the teamxships and the teamxshpistr in the formula:

team1kill/10.000=
((team1ships/100 + momentum) * team1shipstr)
/((Team2ships/100 + momentum) * team2shipstr)=team1kills

(((5+10)*0.2)/(5+10)*2=0.1/10000=1000
(Raiders vs. Vorlons @ momentum 10)

(I'm not very helpful I know - 6 points (just enough for passing) in maths all over the years...)

[Megadoomer]

No floats support is going to make that problematic.

Do you want a faction like the raiders to ever be able to destroy a vessel of a much more powerful race?

How about for each race you work out how many ships you would want it to take of each other race to destroy it, and how many losses they would suffer, and reverse engineer the calculations. Then use a momentum factor to alter the result.

How are you deciding how many forces are engaged in a battle? Are you assuming all the fleets go up against each other? Or a portion is engaged in any battle?

You could factor in to the calculations a percentage each side would commit to a single attack, and have the proportion related to momentum?

Just some ideas, I'll give it some though and see if I can think of anything solid.

[IPAndrews]

No floats support is going to make that problematic.

Yes the lack of floating point/fractions is going to sink Megadoomer's maths straight away I think. Still I'll have a good think about what he's put and see if there's anything I can take away from it before I comment fully on that.

Do you want a faction like the raiders to ever be able to destroy a vessel of a much more powerful race?

hmm... Possibly not. Perhaps the best they should be able to achieve is to last a few days.

How about for each race you work out how many ships you would want it to take of each other race to destroy it, and how many losses they would suffer, and reverse engineer the calculations. Then use a momentum factor to alter the result.

You mean calculate how many ships it would take to destroy one enemy ship. So we have:

shipstodestroy1enemy = enemyshipstr / friendlyshipstr
enemiesdestroyed = friendlyships / sihpstodestroy1enemy

So in the case of Raiders vs Vorlons. 20 / 3 = 6. 500 / 6 = 83. Meaning the Raiders would destroy 83 out of a fleet of 500 ships! With no momentum modification applied. I could tweak the ship strengths of course. I wouldn't have a clue how to factor in the momentum modifier though. Aside from that it's an interesting idea.

How are you deciding how many forces are engaged in a battle? Are you assuming all the fleets go up against each other? Or a portion is engaged in any battle?

Yes I'm still in two minds as to whether this is a good idea. I think my original formula assumes that 10% of either side is in combat (I believe that's what the spurious * 10 does) although in reality it wasn't designed that was as such. I just stuck an arbitrary number in there to make the resulting numbers a bit bigger . There's no real elegance here I just want something that works.

I believe maybe only 25% of the forces on either side should be engaged at the start of a war. With the rest in reserve. There are issues:

1) As an army loses resources more and more of it needs to be engaged. ie: if an army is down to 50 ships against 2000 it doesn't make sense for the army with 50 to only commit 25% of it's force!

2) It I increase the amount of forces commited by an army because the enemy has more ships (as in the example above) that gives the army with less ships a slightly better than normal kill ratio against the other side because of those extra commited ships. I'm not sure if that's a good thing or a bad thing really.

3) Assuming we allow an army with less ships to commit more to battle, how many more? I need another :

[madaboutgames]

I would stick to 10% of forces in battle, this is more feesable and realistic as well as either side suffering huge losses making the war last only a few missions.  Like I explained in the pm i sent earlier some races loss ratio seems to work great but some other races don`t.  Do you think it would be better to keep all races starting ships and loss ratio almost the same maybe with a slight varient of 0.3.  This would still be fair as stronger races such as vorlons and Minbari will be quite hard to defeat during battle and would even the odds out of the variables for their losses.  If you fight a hard race its the battle result which should primarily direct the course of the war, this reflects the players results in their battles and how the final outcome should be expected to flow.

[IPAndrews]

I would stick to 10% of forces in battle

Well that's all fine and dandy but what about the issues I mentioned above about limiting the number of ships engaged . Do you think a side with only 100 ships left facing 10,000 would still only commit 10% of it's ships. Also can non-commited ships be destroyed? If not then you're never going to be able to destroy all of a race's ships because you only ever get to kill 10% of them every day.

, this is more feesable and realistic as well as either side suffering huge losses making the war last only a few missions. 

Well I think if a war between the raiders and the vorlons goes bad for the raiders it could conceivably be over in a few missions. Maybe 10 at the most.

Like I explained in the pm i sent earlier some races loss ratio seems to work great but some other races don`t.  Do you think it would be better to keep all races starting ships and loss ratio almost the same maybe with a slight varient of 0.3.

No floating point numbers dude  . So Orpheus's idea of making all ship strengths fractions ain't going to fly. Also the other idea of working out how many ships are needed to destroy an enemy ship. That won't fly either. Reason? Well Vorlon ship = 20. Raider ship = 3. 20/3 = 6 (rounded down). So 6 raider ships to kill 1 vorlon. Works yes? No. EA ship = 6. Narn ship = 5. Number of Narn ships needed to kill 1 EA ship = 6/5 = 1 (rounded down). Number of EA ships required to kill one Narn ship = 5/6 = 0! (rounded down). Nightmare! 

If you fight a hard race its the battle result which should primarily direct the course of the war, this reflects the players results in their battles and how the final outcome should be expected to flow.

That's what the momentum concept is there for. The player should have a major say in the momentum of a war. Maybe between -5 to +5 depending on mission success.

[Megadoomer]

Looking at it I think the way your doing ship strengths is wrong.

Initially I suggested that you work out what you wanted a standard battle outcomes to be in terms of ship losses and work out the ship strengths from that. Raider 1 Vorlon 100 might be more realistic.

How about instead of faction ship strengths, you have a faction-faction ratio.

e.g. A really simple case EA - Narn  have a 9:10 kill ratio. So if 100 Narns attack 100 EA Vessels all the narn die and 10 EA vessels survive.

Momentum could then improve the ratio so a fleet winning the war will lose less ships, and a fleet losing the war suffers heavy casualties, e.g. EA have +4 momentum lose only 50 ships to wipe out a 100 Narn or Narn have +5 momentum wipe out a 100 EA ships losing 55 ships.

I'll try and work out an integer based formula to do that for you.

Other ideas I've had are:
1) Divide faction strength and ship numbers into ship classes, so you have faction strength for each class.

e.g. The Vorlons and Raiders may both have 500 ships, but if thats 450 raider fighters, 40 light cruisers, and 10 cruisers, vs 1 planet killer, 99 Heavy cruisers, 150 transports and 350 fighters. Then 1 side already has a clear advantage. It might be reasonable for 20 raider fighters to kill 1 vorlon fighter, with about 16 losses, maybe 450 raider might kill a vorlon cruiser with maybe 1 or 2 survivors (possibly by all raming one point ), but the entire raider faction couldn't touch the planet killer.

2)With ship numbers, you could stick to a 10% ships in a battle, but have a 'battle of the line' cut off value, at which point all a factions ships are engaged so they can survive (100 ships maybe).

3)Alternate faction victory condition in which you capture/destroy a homeworld (gives the raiders and the league more chance as they haven't a central base).

4)Flee factor - a number of ships at which a faction attempts to flee a battle (assuming there not doing a battle of the line)

5)Getting really complicated by having a moral factor that affects how a faction responds to a losing was - being easier kill, committing more/less forces, running away, etc.

[IPAndrews]

e.g. A really simple case EA - Narn  have a 9:10 kill ratio. So if 100 Narns attack 100 EA Vessels all the narn die and 10 EA vessels survive.

Wouldn't this require me hard coding 9*9 different kill ratios? Can we not calculate kill ratios from the existing strength values. The kill ratio and strength values are conceptually trying to represent the same thing afterall?

I'll try and work out an integer based formula to do that for you.

Yeah do. If you can come up with something that works you get a special mention when the campaign is done . Oops gotta go for now. My time is so limited these days.

[Megadoomer]

Wouldn't this require me hard coding 9*9 different kill ratios? Can we not calculate kill ratios from the existing strength values. The kill ratio and strength values are conceptually trying to represent the same thing afterall?

I don't think the existing strength values are correct at the moment.

In many way I'm suggesting each faction has a strength value compared to the other ones. If only because it seems reasonable that raiders would have a reasonable chance to damage EA ships, but at the same time theres almost no way raiders could hurt the vorlons, but the EA might have a chance.

Still hard coding in that many factors doesn't sound appealing.

Yeah do. If you can come up with something that works you get a special mention when the campaign is done  .

Heres a formula (well several):

First decide Winning faction - faction with highest engagement score.

EngagementScore = (Ship Strength * Number of Ships)/Percentage of Fleet commited. [1]

Losing side loses set % of ships.

Total number of ships lost by loser = (No Of Ships Committed * Losers % Loses)/100

Total number of ships lost by winner = (No of Ships lost by Loser * Loser Ship Strength)/Winner Ship Strength.

So some examples using your current ship strengths (that could do with altering), 10% fleet usage, 10% of losers survive to flee and no momentum:

Raiders vs Vorlons:

Raiders Commit 10% of there ships.
Vorlons Commit 10% of there Ships
Raider Engagement Score =(500*2)/10  = 100
Vorlon Engagement Score =(500*20)/10  = 1000 Winner

Raiders loses = (50 * 90)/100 = 45 ships
Vorlons loses = (45 * 2)/20 = 4.5 = 4 ships

EA vs Vorlons

EA Commit 10% of there ships.
Vorlons Commit 10% of there Ships
Raider Engagement Score =(2000*6)/10  = 1200 Winner
Vorlon Engagement Score =(500*20)/10  = 1000

Vorlons loses = (50 * 90)/100 = 45 ships
EA loses = (45 * 20)/6 = 150 ships

Narn vs Centauri

Narn Commit 10% of there ships.
Centauri Commit 10% of there Ships
Narn Engagement Score =(2000*5)/10  = 1000
Centauri Engagement Score =(1500*8)/10  = 1200 Winner

Narn loses = (200 * 90)/100 = 180 ships
Centauri loses = (180 * 5)/8 = 112.5 = 112 ships

[1]This is where the momentum should be factored in - at best I'd think momentum should allow Narns to beat Centauri, but not allow Raiders to beat the Vorlons

[madaboutgames]

The main idea is a fair fight - LOL if you call raiders fighting the Vorlons fair LOL.

Any race should with a great deal of effort be able to win the war, even the raiders. If we make it so its impossible to win then whats the point in trying?

Like my survivor campaign LOL

[yubyub]

First decide Winning faction - faction with highest engagement score.

EngagementScore = (Ship Strength * Number of Ships)/Percentage of Fleet commited. [1]

Losing side loses set % of ships.

Total number of ships lost by loser = (No Of Ships Committed * Losers % Loses)/100

Total number of ships lost by winner = (No of Ships lost by Loser * Loser Ship Strength)/Winner Ship Strength

Couldn't we just set the momentum like

Total number of ships lost by loser = (No Of Ships Committed * Losers % Loses)/100 * ((10 - momentum) (-9 through +9) /10)

So a momentum of +1 decreases loses by 10%, a momentum of -1 increases loses by 10%?

Example: Raiders with +3 momentum

Raiders vs Vorlons:

Raiders Commit 10% of there ships.
Vorlons Commit 10% of there Ships
Raider Engagement Score =(500*2)/10  = 100
Vorlon Engagement Score =(500*20)/10  = 1000 Winner

Raiders loses = (50 * 90)/100 * ((10 - 3) /10) = 31 (rounded down) ships
Vorlons loses = (45 * 2)/20 = 4.5 = 4 ships

or Narn with +7 momentum

Narn vs Centauri

Narn Commit 10% of there ships.
Centauri Commit 10% of there Ships
Narn Engagement Score =(2000*5)/10  = 1000
Centauri Engagement Score =(1500*8)/10  = 1200 Winner

Narn loses = (200 * 90)/100 *((10 - 7) /10)  =  54 ships
Centauri loses = (180 * 5)/8 = 112.5 = 112 ships

Seems to work to me 

This system WOULD make momentum a powerful thing, enough to even out a raider vs vorlon fight, if I understand correctly.

[madaboutgames]

I agree, with the momentum as a big factor this could help even things out a  bit.  10% of forces in battle for all races is fine, but I suggest moving upto to 25% when the losing team has 20% of ships left (from start total).

[Megadoomer]

So a momentum of +1 decreases loses by 10%, a momentum of -1 increases loses by 10%?

The only problem there is that the momentum hasn't figured into the side that won. You would still want momentum to alter which side wins too. It would also make sense for only one side to have momentum at a time - or that negative momentum is just the same as saying the opponents have that amount of positive momentum.

I suppose you could change it so that the losing side has momentum*10% of their ships escape, i.e. if they had good momentum but they still lose it's like they got out of the fight before they got slaughtered.
And that the winner side suffers loses, reduced by a momentum*10%

So the formulas would be (assuming momentum goes from 0 to 10):

Total number of ships lost by loser = (No Of Ships Committed * 10 - (momentum))/10

Total number of ships lost by winner = (No of Ships lost by Loser * Loser Ship Strength*(10-momentum))/Winner Ship Strength*10

For example (again momentum still not factored into who wins or loses)

Narn with +7 momentum vs Centauri

Narn Commit 10% of there ships.
Centauri Commit 10% of there Ships
Narn Engagement Score =(2000*5)/10  = 1000
Centauri Engagement Score =(1500*8)/10  = 1200 Winner

Narn loses = (200 * (10-7))/10 = 60 ships
Centauri loses = (60 * 5*10)/8*10 = 37.5 = 37 ships

EA +4  vs Vorlons

EA Commit 10% of there ships.
Vorlons Commit 10% of there Ships
EA Engagement Score =(2000*6)/10  = 1200 Winner
Vorlon Engagement Score =(500*20)/10  = 1000

Vorlons loses = (50 * (10-0))/10 = 50 ships
EA loses = (50 * 20 * (10-4) )/6*10 = 100 ships

By having each faction having a momentum value, you could then potentially have things where you have a three way war, and thanks to victories against two sides vs a third, when those two side fight they both have postive momentum.

Other ideas this allows - scouting missions which if the player completes successfully, the players side know how many ships the enemy will commit, and so commits enough to win (more ships means higher engagement score).

*edit*

Thinking about momentum factoring in to the engagement score. You could either have it that momentum increase the effective tech level of ships in calculating the score, or makes a factions ships count for more:

eg:

EngagementScore = ((Ship Strength+momentum) * Number of Ships)/Percentage of Fleet commited

or

EngagementScore = (Ship Strength * (Number of Ships + (Number of Ships * momentum)/10))/Percentage of Fleet commited

e.g.

Narn with +7 momentum vs Centauri

Narn Engagement Score =(2000*(5+7))/10  = 2400 Winner
Centauri Engagement Score =(1500*8)/10  = 1200

or

Narn Engagement Score =((2000+(2000*7)/10)*5)/10  = 1700 Winner
Centauri Engagement Score =(1500*8)/10  = 1200

The Raiders still won't be able to win a battle with the vorlons even with a momentum of +10, but at least wouldn't ever lose any ships in the battle.

You could total up all the engagement scores to get an overall status of the campaign at each stage.

*/edit*

10% of forces in battle for all races is fine, but I suggest moving upto to 25% when the losing team has 20% of ships left (from start total).

I still like the idea of a battle of the line style affect, where when a faction is down to a % of their starting fleet they commit all their ships in a last ditch defence.

[IPAndrews]

Wow this is going to take me a little while to go through. It looks like you're having some success though. I'm going to have a go at implementing some of this stuff.

re: how much of their force a side should commit. Well in the interests of fairness if one side commits more forces the other side should do the same. Also I believe the amount commited should be related to territory. So if a race has their back against the wall they up the stakes. Until finally if their homeworld is under threat they throw the lot in.

I could do that using bands:

eg: (territory ranges -50 to 50 where -50 = players hw under threat & 50 = enemy hw under threat)

territory =< -10 or => 10  15% forces committed
territory =< -20 or => 20  20% forces committed
territory =< -30 or => 30  30% forces committed
territory =< -40 or => 40  40% forces committed
territory = -50 or 50         100% forces committed (homeworld defence)

[madaboutgames]

Think the banding system will be ideal for commiting forces

[yubyub]

The only problem there is that the momentum hasn't figured into the side that won. You would still want momentum to alter which side wins too. It would also make sense for only one side to have momentum at a time - or that negative momentum is just the same as saying the opponents have that amount of positive momentum.

That negative momentum is the same as the other sides positive momentum.  I just stuck that on the loser's side because it made sense at the time.

I suppose you could change it so that the losing side has momentum*10% of their ships escape, i.e. if they had good momentum but they still lose it's like they got out of the fight before they got slaughtered.
And that the winner side suffers loses, reduced by a momentum*10%

That is what I had intended.  Personally, I don't understand how being the winner really helps with losses (in the current equation it does, but to a small degree (of course I could be misinterpreting the formula)), and in the end, war is mostly about losses.  So, having momentum only help 'win' the battle would make it almost useless.  That is the simple beauty of factoring it in at the losses, it makes momentum a powerful thing.  However, having momentum at both areas wouldn't boost power to much would it?  I'll try that with both of our momentum at losses systems.



Basically, summed up before I go into math, the end result is that, IMO, the momentum system should be applied to losses the way I wrote, and to engagement score the way you* wrote.

Narn +7 vs Centauri
Narn Score: ((5+70)2000)/10=2400 winner
Centauri Score: ((8)1500)/10=1200
Narn Losses: (200 * 90)/100 *((10 - 7) /10)  =  54 ships
Centauri Losses = (180 * 5)/8 = 112.5 = 112 ships

This seemed to work.  The Narn's score was double that of the Centauri, so they lost half as many ships.
Let's try this in another situation.

EA +4 vs Vorlon
EA Score = ((6+4) * 2000)/10=2000 Winner
Vorlon Score = ((20)500)/10=1000
EA Losses = (63 * 20)/ 6 = 210
Vorlon Losses = (50 * 90)/100 * ((10 - (-4)) /10)= 63 

This doesn't work. Or does it?  The EA has 4 times the number of ships as the Vorlon, so divide the number of EA losses by 4 and you get... 52 rounded down.  So the system works.  The EA, while they had twice the Vorlon's score, lost 11% less ships per ship committed.  So the engagement scores could still use some tweakings, though that could be written off as the EA performing twice as well as the Vorlon's but getting crippled by their technological inferiority.  I'll think on it.

Now to try your system of losses. (Direct quote)

Narn with +7 momentum vs Centauri

Narn Commit 10% of there ships.
Centauri Commit 10% of there Ships
Narn Engagement Score =(2000*5)/10  = 1000
Centauri Engagement Score =(1500*8)/10  = 1200 Winner

Narn loses = (200 * (10-7))/10 = 60 ships
Centauri loses = (60 * 5*10)/8*10 = 37.5 = 37 ships

and

EA +4  vs Vorlons

EA Commit 10% of there ships.
Vorlons Commit 10% of there Ships
EA Engagement Score =(2000*6)/10  = 1200 Winner
Vorlon Engagement Score =(500*20)/10  = 1000

Vorlons loses = (50 * (10-0))/10 = 50 ships
EA loses = (50 * 20 * (10-4) )/6*10 = 100 ships

To the EA losses I then divide by 4 and get 20.  This shows that they lost 30% less ships per ship deployed then the Vorlons.  While momentum should be powerful, this is to powerful IMHO.  While I don't watch B5, I know enough to know that the Vorlons pwn the EA, and 30% better losses with such a low momentum is a bit rediculous.  However, I do applaud your work on the engagement scores, and the work on losses that I stole to make the base of my momentum system.  I think that a merger between our two systems, my losses and your engagement score, would work best.

Also, as one last note, I think the joint system would hold true for the banding system proposed by IPAndrews as well, but I need to try it.  I'll edit when I do.

*When I say you, I'm referring to Megadoomer

[Megadoomer]

EA +4 vs Vorlon
EA Score = ((6+4) * 2000)/10=2000 Winner
Vorlon Score = ((20)500)/10=1000
EA Losses = (63 * 20)/ 6 = 210
Vorlon Losses = (50 * 90)/100 * ((10 - (-4)) /10)= 63

This doesn't work. Or does it?

It doesn't work because both sides have managed to lose more ships that they committed. The problem arose because you applied a negative momentum to the vorlons.

Personally, I don't understand how being the winner really helps with losses (in the current equation it does, but to a small degree (of course I could be misinterpreting the formula)), and in the end, war is mostly about losses.

The basic principle behind my formula was this - trying to calculate losses for both sides independently is too complicated, especially when you start adding momentum in to both sides. As you've shown above trying to apply negative momentums messes up the calculation. So to simplify it I did the following:
- The losing side loses a fixed quantity of ships (which is a percentage of their commited ships). Momentum can help them win, or help them mitigate their loss accordingly. The base case is the worst case, they lose all their ships.
-The winning side them loses enough ships (based on the ratio of power levels) to have destroyed the number of ships the losing side lost. The better the momentum the less ship they lose achieving this.

To the EA losses I then divide by 4 and get 20.  This shows that they lost 30% less ships per ship deployed then the Vorlons.  While momentum should be powerful, this is to powerful IMHO.  While I don't watch B5, I know enough to know that the Vorlons pwn the EA, and 30% better losses with such a low momentum is a bit rediculous.

I agree with you the losses aren't correct, but then again I don't think the faction power levels are right. The problem is balancing realism, with gameplay so that factions have a chance to win. The way to do it would be to play around with numbers using the formula, until you achieved a series of values that worked. I'd still be inclined to have values that compare specific races, only because you would have greater option for balancing things out. Of course it also depends at which point in the B5 story you want it to be. The newest EA ships are powerful.

Think the banding system will be ideal for commiting forces 

So do I 

Well in the interests of fairness if one side commits more forces the other side should do the same.

And simplicity I supect  . Though it would still be cool to successfully complete a mission, and get your side the intel so they could attack an unexpecting enemy fleet with overwhelming forces.

Oh and you means yubyub

[yubyub]

You're right of course... 
Let's see what happens if I switch where I originally used a negative to having momentum apply to the winner there (i.e. to the side with the positive momentum).

EA +4 vs Vorlon
EA Score = ((6+4) * 2000)/10=2000 Winner
Vorlon Score = ((20)500)/10=1000
EA Losses = (63 * 20)/6 * ((10 - 4)/10) = 126
Vorlon Losses = (50 * 90)/100 =45

Now divide by 4 and you get 31 (rounded down).  Now it seems to work.  Vorlons lost 45 of 50 committed, and EA loses 126 of 200 commited.

Another example of applying momentum to the side with momentum. (already shown)

Narn +7 vs Centauri
Narn Score: ((5+7)2000)/10=2400 winner
Centauri Score: ((8)1500)/10=1200
Narn Losses: (200 * 90)/100 *((10 - 7) /10)  =  54 ships
Centauri Losses = (180 * 5)/8 = 112.5 = 112 ships

An another one trying to break my equation.

Shadows +6 vs Raiders
Shadows Engagement: (500 *(16+6))/10=1100 Winner
Raiders Engagement: (500*2)/10=100
Shadows Losses:(45*2)/16 * ((10 - 6)/10) = 2.25 rounded down to 2
Raiders Losses: (50*90)/100=45

Seems to work when it is always applied to the side who has the momentum.  But I'll make the person with the momentum be the loser this time.

Raiders +6 vs Vorlons
Raiders Engagement: (500 * (2 + 6))/10 = 400
Vorlon Engagement: (500 * 20)/10 = 1000 WINNER! (big surprise)
Raider Losses: (50 *90)/100 * ((10-6)/10) = 18
Vorlon Losses: (18 * 2)/20 = 1 (rounded down)

Ok NOW it works I think.  The ((10 - (momentum))/10) and the (score plus momentum) lines just need to be always added to the side with the positive momentum.  Momentum would go from 0 through 10 (at zero both of those lines are dropped, as a value of zero would break the equation nicely).  Is that possible to code?  If not have momentum go from 1 to 10, and have no zero used. (IE If one side has +1 momentum and the other side takes the momentum, then the other side immediately goes to at least +1 momentum).

Does this formula-equation thingy work now?  I must say, I've never had this much fun with math LOL.

edit: Above post shows why you should never do math in 3 equations on the same post on a forum while doing your math assignment.  To many numbers = confusion = stupid mistakes

[Megadoomer]

EA +4 vs Vorlon
EA Score = ((6+4) * 2000)/10=2000 Winner
Vorlon Score = ((20)500)/10=1000
EA Losses = (63 * 20)/6 * ((10 - 4)/10) = 126
Vorlon Losses = (50 * 90)/100 =45

You forgot to update the EA losses formula they only have to destroy 45 ships, not 63.

Narn +7 vs Centauri
Narn Score: ((5+7)2000)/10=2400 winner
Centauri Score: ((8)1500)/10=1200
Narn Losses: (200 * 90)/100 *((10 - 7) /10)  =  54 ships
Centauri Losses = (180 * 5)/8 = 112.5 = 112 ships

And here you don't narn losses from the number of ships destroyed but from the number they commit instead, which isn't the same as the above.

Having just checked the vorlon vs EA formula you used, yubyub, is actually identical to mine just rearranged:

winner losses = ((losser losses * loser strength)/winner strength) *((10-momentum)/10) = (losser losses * loser strength* (10-momentum))/(10*winner strength)

Except you are assuming a base of 10% of losing ships escape still, where I no longer do. It should be noted in the above a momentum of 10 results in no losses for which ever side has it, and a momentum of 0 doesn't cause a problem.

Er, sorry to point out your mistakes.