Equation for Morale Makes No Sense!

[Voice of Reason]

I really like SC2, but I find it difficult to extract strategy-critical details from the manual. The worst problem so far is the equation for morale (p. 35), and it is difficult to make effective plans without knowing how morale is determined. I hope someone knowledgeable (ideally, the game designer) can clarify this. Here's the problem:

The equation contains 3 variables: old morale (I'll call it 'M'; range is generally 0-100), unit strength ('Str', range 1-10), and unit supply ('Sply', range 0-10). Here's the equation, as I understand it:

new morale = 0.75*M + (Str-0.75*M) * (0.1*Sply) * (0.01*M).

The first term is fine: in the absence of supply, morale decays exponentially, losing a quarter of its value for every turn out of supply. But the second term is impossible. The reason is that Str and M are of different orders of magnitude (Str ~ 0.1M); thus this second term will almost ALWAYS be negative and Sply > 0 would actually cause morale to drop FASTER than Sply = 0. Obviously, that does not happen. One solution would be to multiply Str by 10 (or divide M by 10). That removes the overt absurdity, but the equation remains pretty damn silly. This is because--as far as I can tell--10*Str can still be less than 0.75*M under reasonable conditions, and under those conditions, supply would still act to ACCELERATE morale loss, because (10*Str - 0.75) < 0.

I can't figure this out. Please advise.

[Cap]

Originally posted by Voice of Reason:

I really like SC2, but I find it difficult to extract strategy-critical details from the manual. The worst problem so far is the equation for morale (p. 35), and it is difficult to make effective plans without knowing how morale is determined. I hope someone knowledgeable (ideally, the game designer) can clarify this. Here's the problem:

The equation contains 3 variables: old morale (I'll call it 'M'; range is generally 0-100), unit strength ('Str', range 1-10), and unit supply ('Sply', range 0-10). Here's the equation, as I understand it:

new morale = 0.75*M + (Str-0.75*M) * (0.1*Sply) * (0.01*M).

The first term is fine: in the absence of supply, morale decays exponentially, losing a quarter of its value for every turn out of supply. But the second term is impossible. The reason is that Str and M are of different orders of magnitude (Str ~ 0.1M); thus this second term will almost ALWAYS be negative and Sply > 0 would actually cause morale to drop FASTER than Sply = 0. Obviously, that does not happen. One solution would be to multiply Str by 10 (or divide M by 10). That removes the overt absurdity, but the equation remains pretty damn silly. This is because--as far as I can tell--10*Str can still be less than 0.75*M under reasonable conditions, and under those conditions, supply would still act to ACCELERATE morale loss, because (10*Str - 0.75) < 0.

I can't figure this out. Please advise.

I'm on my 6th Rum & coke and I still don't know what the F&^% your babbling about!

Speak English so I can understand what point your trying to make

[pzgndr]

The new patch makes one change to this:

- fixed a bug where unit morale never increased once it reached 0%, in this case units will start their turn with a minimum of 10%

It's interesting to compare Hubert's SC2 formula with what Clash of Steel had:

MORALE: = Morale * 70%

MORALE: = Morale + (Efficiency - OldMorale) * Supply / 10

STRENGTH: = (Strength + Terrain Defense Bonus) * Morale/100

The key concept is that units at high strength and in good supply should see morale and readiness increase. Those at low strength and/or in poor supply should see a decrease.

[TaoJah]

Originally posted by Cap:

I'm on my 6th Rum & coke and I still don't know what the F&^% your babbling about!

Speak English so I can understand what point your trying to make

If this is your only contribution to this topic, then perhaps these forums aren't for you. Go to www.flame.me or something.

To the OP : the manual is indeed wrong, you got to multiply STR with 10 in the formula as you said.

- - - - - - - - - - -

Normal Strength units

- - - - - - - - - - -

These are the results for a unit with old morale at 80 (feel free to correct any errors I made).

Old Morale = 80, STR = 10 & SPL = 10 gives new morale 92 (+ 15%)

Old Morale = 80, STR = 10 & SPL = 9 gives new morale 88,8 (+ 11%)

Old Morale = 80, STR = 10 & SPL = 8 gives new morale 85,6 (+ 7%)

Old Morale = 80, STR = 10 & SPL = 7 gives new morale 82,4 (+ 3%)

Old Morale = 80, STR = 10 & SPL = 6 gives new morale 79,4 (- 1%)

Old Morale = 80, STR = 9 & SPL = 10 gives new morale 84 (+ 5%)

Old Morale = 80, STR = 8 & SPL = 10 gives new morale 76 (- 5%)

Old Morale = 80, STR = 9 & SPL = 9 gives new morale 81,6 (+ 2%)

Old Morale = 80, STR = 9 & SPL = 8 gives new morale 79,2 (- 1%)

Old Morale = 80, STR = 8 & SPL = 9 gives new morale 74,4 (- 7%)

Old Morale = 80, STR = 8 & SPL = 8 gives new morale 72,8 (- 9%)

So...

As you can see, this means that is impossible to to improve morale with STR 8 or lower.

This is why I go to great lenghts to keep my units at STR 9 or higher.

Silly ? I don't know... Note that the loss in morale with STR 8 isn't THAT big either, -5% with SPL 10, -7% with SPL 9.

- - - - - - - - - - -

Elite reinforcements.

- - - - - - - - - - -

It's intresting to see that this firmula gives nice straight results for a unit with STR 11.

Old Morale = 80, STR = 11 & SPL = 10 gives new morale 100 (+ 25%)

Old Morale = 80, STR = 11 & SPL = 9 gives new morale 96 (+ 20%)

Old Morale = 80, STR = 11 & SPL = 8 gives new morale 92 (+ 15%)

Old Morale = 80, STR = 11 & SPL = 7 gives new morale 88 (+ 10%)

Old Morale = 80, STR = 11 & SPL = 6 gives new morale 84 (+ 5%)

Old Morale = 80, STR = 11 & SPL = 5 gives new morale 80 (+ 0%)

Old Morale = 80, STR = 11 & SPL = 4 gives new morale 76 (- 5%)

Say you got a tank with morale 80, SPL 10 and you can pick between two options : attack now or give elite reinforcements and attack the next turn. Let's say in both cases you lose one point of STR with every attack.

Option 1.

Turn 1 : attack a unit.

At the start of turn 2 : Old Morale = 80, STR = 9 & SPL = 10 gives new morale 84.

At the start of turn 3 : Old Morale = 84, STR = 8 & SPL = 10 gives new morale 77.28.

At the start of turn 4 : Old Morale = 77.28, STR = 7 & SPL = 10 gives new morale 67.26.

At the start of turn 5 : Old Morale = 67.25, STR = 6 & SPL = 10 gives new morale 63,59.

At the start of turn 6 : Old Morale = 63.59, STR = 5 & SPL = 10 gives new morale 49,15.

This means you can attack 5 times in a row (turn 1 to turn 5), before your morale drops under the 50% line.

Option 2.

Turn 1 : strengthen to 11.

At the start of turn 2 : Old Morale = 80, STR = 11 & SPL = 10 gives new morale 100.

At the start of turn 3 : Old Morale = 100, STR = 10 & SPL = 10 gives new morale 100.

At the start of turn 4 : Old Morale = 100, STR = 9 & SPL = 10 gives new morale 90.

At the start of turn 5 : Old Morale = 90, STR = 8 & SPL = 10 gives new morale 78,75.

At the start of turn 6 : Old Morale = 78,75, STR = 7 & SPL = 10 gives new morale 67,67.

At the start of turn 7 : Old Morale = 67.67, STR = 6 & SPL = 10 gives new morale 57,01.

At the start of turn 8 : Old Morale = 57.01, STR = 6 & SPL = 10 gives new morale 46,88.

This means you can attack 6 times in a row (turn 2 to turn 7), before your morale drops under the 50% line.

So...

As you can see, with one turn in elite reinforcements, you can do one more attack before your morale drops too low AND those 6 attacks will do ALOT more damage then the attacks of the first option.

This is why I try to get elite reinforcements as soon as I can get them : you lose a turn at the start of your offence, but that is neutralised by the fact that you gain TWO extra attack turns at the end of your offence, before you got to restrength.

[ August 28, 2006, 01:11 AM: Message edited by: TaoJah ]

[Liam]

I had issues with this in SC2, slow regaining of morale after a long weary battle that or low strength units being introduced that need time to max out

minor hopping is a good compensator

[Voice of Reason]

Thanks for the clarification and advice. I still think it's strange that if your unit's strength is far enough below its morale level, having a higher supply actually hurts you, i.e., makes your morale drop faster than if you were out of supply. Intuitively, it seems to me that being in supply should always help, but I suppose the conditions under which it hurts are relatively rare and short-lasting.

[TaoJah]

Originally posted by Voice of Reason:

I still think it's strange that if your unit's strength is far enough below its morale level, having a higher supply actually hurts you

That's indeed odd.

But to have this happen, the unit has got to be at a strength lower then 3/4th the moral. That's kinda hard to do in the game since moral falls if STR lowers.

Besides, the effects aren't that big as these numbers show... (old morale always 80)

Old Morale = 80, STR 5, SPL 10 gives 52 new morale

Old Morale = 80, STR 5, SPL 9 gives 52.8 new morale

Old Morale = 80, STR 5, SPL 8 gives 53.6 new morale

Old Morale = 80, STR 5, SPL 7 gives 54.4 new morale

Old Morale = 80, STR 4, SPL 10 gives 44 new morale

Old Morale = 80, STR 4, SPL 9 gives 45.6 new morale

Old Morale = 80, STR 4, SPL 8 gives 47.2 new morale

Old Morale = 80, STR 4, SPL 7 gives 48.8 new morale

Weird, indeed, but not game-breaking IMHO.

[ August 28, 2006, 01:11 AM: Message edited by: TaoJah ]

[Liam]

I have a UK fighter 4 tiles away from London, at Strength 4 in a game. Morale is 20%, not certian what the supply is can't be all bad. Probably 6-7

I have a German corps on the border with USSR, strength 4, morale was down to about 15% I think or close to it. Was odd to see it fall so so low

some oddities.. I find it's to be cautious with strength for too many turns. Regardless of Supply

My Units in Egypt I notice suffer vastly in morale readiness they're worth a bucket of spit unless they can sit out of War for enough turns to build up. Comming in at lower strength than 10, and without HQ, and with just a few points of low supply really means the pits. 30-35% till many turns of building up

Originally posted by TaoJah:

</font><blockquote>quote:</font><hr />Originally posted by Voice of Reason:

I still think it's strange that if your unit's strength is far enough below its morale level, having a higher supply actually hurts you

That's indeed odd.

But to have this happen, the unit has got to be at a strength lower then 3/4th the moral. That's kinda hard to do in the game since moral falls if STR lowers.

Besides, the effects aren't that big as these numbers show... (old morale always 80)

STR 5, SPL 10 gives 52 new morale

STR 5, SPL 9 gives 52.8 new morale

STR 5, SPL 8 gives 53.6 new morale

STR 5, SPL 7 gives 54.4 new morale

STR 4, SPL 10 gives 44 new morale

STR 4, SPL 9 gives 45.6 new morale

STR 4, SPL 8 gives 47.2 new morale

STR 4, SPL 7 gives 48.8 new morale

Weird, indeed, but not game-breaking IMHO. </font>

[Hubert Cater]

Yes, sorry for the confusion as the Morale formula is indeed incorrect and you can multiply strength by 10, as Taojah indicated, to get the right calculations.

For the analysis, using an old morale of always 80 is actually not entirely correct as old morale changes each time a new calculation is performed.

For example, the STR 5 and SPL decreasing over time example would look something like the following (in game):

Strength Supply MoraleOld MoraleNew

---5------10-------80-------52

---5------9--------52-------44

---5------8--------44-------39

---5------7--------39-------35

[ August 22, 2006, 06:25 AM: Message edited by: Hubert Cater ]

[Liam]

That clears up a lot of confusion, math obviously isn't my strongpoint, when it comes to Strategic Command I rarely want to crunch #s I try to avoid it altogether.. I will be much more cautious.. BTW: Hubert is it true that placing a unit on a city increases it's Morale much faster regardless of other factrs? It seems to I'll run a hotseat to test

Originally posted by Hubert Cater:

Yes, sorry for the confusion as the Morale formula is indeed incorrect and you can multiply strength by 10, as Taojah indicated, to get the right calculations.

For the analysis, using an old morale of always 80 is actually not entirely correct as old morale changes each time a new calculation is performed.

For example, the STR 5 and SPL decreasing over time example would look something like the following (in game):

Strength Supply MoraleOld MoraleNew

---5------10-------80-------52

---5------9--------52-------44

---5------8--------44-------39

---5------7--------39-------35

[Hubert Cater]

No, the only thing I can think of is that it might have the better supply if in a city, i.e. a supply value = 10

[TaoJah]

Originally posted by Hubert Cater:

For the analysis, using an old morale of always 80 is actually not entirely correct as old morale changes each time a new calculation is performed.

True, true. I was just pointing out the effect of STR and SPL on one unit at a given time, not over a series of time. Obviously, when you want to make a time-series, you got to change the Old Morale.

[TaoJah]

Originally posted by Hubert Cater:

For the analysis, using an old morale of always 80 is actually not entirely correct as old morale changes each time a new calculation is performed.

True, true. I was just pointing out the effect of STR and SPL on one unit at a given time, not over a series of time. Obviously, when you want to make a time-series, you got to change the Old Morale, like I did in option 1 and 2 of my first post.

By the way : when is your morale calculated ? At the beginning of your turn or at the end of your turn ? Or is it calculated twice ?

[ August 28, 2006, 01:13 AM: Message edited by: TaoJah ]

[Hubert Cater]

Unit Morale is calculated for all units at the beginning of each turn

[TaoJah]

Originally posted by Hubert Cater:

Unit Morale is calculated for all units at the beginning of each turn

So twice ?

Weird, weird...

[Hubert Cater]

Once per turn as the supply situation can change after each player's turn

[TaoJah]

Originally posted by Hubert Cater:

Once per turn as the supply situation can change after each player's turn

<nods>

Thanks for clearing that up.

I got to check out what this means for my theory that it's better to take elite upgrades and attack then not take them, as posted above. If the game changes the morale after my turn and again after his turn, that may or may not change the theory.

We live to learn

[ August 30, 2006, 10:10 AM: Message edited by: TaoJah ]