I'm thinking the 'number ranges' are making combat too random...

I don't think it quite works this way.

The first roll is the 'To hit' against the dodge counter. If you score a hit then the next roll is the damage against the armour.

Thanks for the clarification.  I was focusing mainly on the Damage roll in my discussion.

This is why I said Attack and Defense.  Substitute 'To Hit' and 'Dodge' for the first set of rolls, 'Damage' and 'Armor' for the second set of rolls. The reason I think there are 'competing' dice rolls, is because I remember Brad mentioning something to this effect.

Shields now block as well, plus there is that mysterious 'Resist' I see pop up every so often with 1.09n.

My point is the way the rolls are calculated now.  If it's linear, it's more random.  If a bell curve (multiple dice) is introduced, then you start seeing stronger 'middle' results, and extreme results are more rare.

This has been discussed before, a couple of months back.  I should probably use the forum search a little more often, but the probability discussion noted above still stands.

https://forums.elementalgame.com/392880/page/1/#2739732

I agree 100%. There was another thread about this shortly after the game was released, and (if I recall correctly) the overwhelming majority of posters were very against random distributions on dice rolls. At one point the devs posted that they agreed. I'm not sure if this is still in the works or not.

Actually, it has been said by one of the dev that they square the max value before making the roll, then they take the square root of the roll, which gives an average of ~70% and a lower standard deviation -thus, less randomness-.

I think lowering randomness any further is bad. Managing uncertainty and probabilities is part of ones' tactical skills, and should be part of this game as well.

No kidding? Is that in the current beta version?

Well THAT's an interesting way to do things... and explains the 70% comment in the thread I just edited into my post above.  Something happened to the formulas in the last couple of patches that have made attacks over a certain threshold very powerful, and I'm trying to understand what exactly happened.

As an example: Before one of the fairly recent patches, my longbowmen used to cause damage around 1/3 of the time versus 'typical' early midgame targets, so bowmen needed defenders in front of them.  Now, longbows are my weapon of choice, as I can bring down those same 'typical' targets in one or two shots in one turn, so a single Bowman can take on 3-4 targets before the enemy makes it into Melee range.  Plus, I'm seeing a fair number of 1 shot 1 kills against some 'tougher' targets (around 8 def) using said bows. 

Before, Stat boosts to Strength were not as big, due to the limited number of character points you had to work with, and those other stats you spent points on (pre 1.09n). 

Now, boosting your Strength over 20 doesn't take long at all, which may be messing with the attack/damage rolls.  However, even my 10 STR guys are seeing these results, albiet just a little less often.

I'm seeing the same in Melee with the bigger (9+ attack) weapons, but of course then the counterattacks come into play, so it's not as 'obvious'.

I still think 2Dn or 3Dn (perhaps with the squaring) might not be such a bad thing.  I'll do some calculating/playing around with the probabilities and get back with you.

OK, I'm seeing a potential problem here... assuming the sqaring/square root situation.

Apparently, the 'die type' is squared, and THAT is the new attack die.  Then the result is square-rooted and compared to the defense roll, which was also squared/square rooted.

A simple chart for quick comparison:

Strength- Square

1 - 1

2 - 4

3- 9

4 - 16

5 -25

6 -36

7 - 49

8 - 64

9 - 81

10- 100

OK, lets assume you have a 10 attack versus a 6 defense.  Doesn't sound too scary, right?

10*10 = 100.  6*6 = 36

Average rolls would be 50.5/ sqrt to 7   Defense 18.5 sqrrt to 4. Note how the spread just changed.

OK, lets assume defender rolls max, attacker rolls average:

50.5/sqrrt to 7        Defense 36/sqrrt to 6

I think you'll see now that the 10 Attack has a 63% chance of ALWAYS beating the 6 Defense, regardless of what he rolls.  And if Damage works the same way, this is why we keep seeing 'similar' results on the damage output.

This gets worse as the ranges increase.  Using my 28 vs 12 example above... there is an 82% chance of 28 attack ALWAYS beating the 12 defense, regardless of what he rolls.

Now I'm wondering just exactly how damage is calculated, but this might explain those multiple 28's I was seeing with my bows before, and the 10-14 damage I've been seeing fairly consistently as of late.

Simply put, the Square/Square Root system heavily favors whomever has the higher value, with the difference changing things exponentially.  Once one value is 20% higher or more than the other, things skew very quickly.

Inverting the chart above:

Strength vs Lower Strength: Chance of always beating the 'lower' value, if he rolls max/avg.

1 - 99/99

2 - 95/97

3 - 90/95

4 - 83/91

5 - 74/87

6 - 63/81

7 - 50/74

8 - 35/67

9 - 18/59

10 - 0/49

It'd take longer than I'd like at the moment to calculate the final chance of beating the lower value, but doing a simple calculation of my 10 vs 6: Defense rolls 36: Attacker wins 63%.  Defense rolls 18.5 (avg): Attacker wins 81% of the time.  81% looks about right to me, from what I've seen (that's 4 out of every 5). 

As a comparison, if the defender had rolled average, using straight probability (no square/squareroot), the 10 vs 6 situation would result in the attacker always beating an average defense roll 64% of the time, instead of the 81% noted above...

It also explains why my ambushed Pioneers aren't able to do ANY damage anymore - before they might at least deal out a point or two of damage before they were snuffed.

2D'n' would only amplify this situation, not help it.  Rolling average more often WITH the square/squareroot system would simply make things worse.

Since the attack values I've seen are generally higher than the defense values in the combats I've been in, this does track with the results I've been seeing ingame.  If attack exceeds defense by a mere 30%, it looks like around 74% of the time the defense gets clobbered.

I think I'll try ubering the dex on one of my heroes to well over 20, strip off his armor, and I'll let you know what happens...

I've seen the resist TOO often. I have encountered with both Empire & Kingdom. Catapults, longbows, & dragon fire have been ineffective. These units don't appear to be anything special---13HP/2ATT/7DEF LVL 1. I did encounter the wife of Magnar 25HP/71ATT/44DEF. She was a real pain in the ass. A veteran company of archers only got resist. She took out 2 heroes, a squad of Draths, & a dragon before I killed her. Spells don't work on these "resisters" either. I have multiple shards--the air or fire tactical have no effect though I can freeze the more dangerous units but then it feels like I'm wasting mana.

I can use archers & dragon fire against a Fire Elemental & easily kill him--what does he have? 200+ HP? how does that make sense?

Have you figured out what the resist is? How it's derived? My units have been able to block but not resist.

I want the exponential factors in attack and defense though so that dodge can be more valuable to a given strategy. How great would it be to have an entire army of hard to hit heroes wipe out another player's heavily armed soldiers. Makes my day.

Actually, that doesn't give you the average sqrt-ed roll. 

Assuming the system rounds down (but the numbers stay roughly the same if it doesn't), P(X=n in [1,N-1]) = (2N+1)/(N^2), with N the max value.

The average is then N^2-1 = 2N/3-1/2+5/(6N) ~ 2N/3 for large N. It's close enough at high values (but deviates a lot at lower values), but the most important point is, the higher values are the most likely, the most likely of all being N-1.

For for an attack value of 10, 9 is the most likely results (if the system rounds down), or 10 if the system rounds up.

It think it's a good thing though. It makes combat dangerous .

Well, Dodge is broken for now apparently (see relevant thread), so it simply comes down to Attack Strength versus Defense (armor) for now, guys and gals.

So, for now, if you want to wade through enemy units without taking damage, you'll need uber armor!

I'm sure they will fix Dodge soon (not this week though, with it being Thanksgiving and all).

So, if I NOW understand combat mechanics correctly, it's accuracy versus dodge (dex modifies both), then attack strength versus defense (strength modifies attack).

Here's part of another post, where Derek lists how stats are SUPPOSED to work for 1.1.

Strength- Modifies damage

Dexterity- Modifies dodge

Constitution- Modifies hit points

Intelligence- Modifies spell resistance, boosts some spells, required for Champions to cast some spells

Charisma- Sovereigns Charisma modifies Champion recruit costs.  Champions and the Sovereign give a prestige boost to the city they are in.

  That leaves us with the following formulas:

Attack (which is damage) = Weapon Attack + ((Strength - 10)/2)

Defense (which is damage absorb) = Armor Defense

Accuracy = 15 + (Level * 2)

Dodge = Dexterity / 2

Hit Points = 10 + ( (Constitution / 5) * (2 * Level) )

Back to the discussion at hand.  At first I though results are too random, but re-evaluating recent battles, I am seeing what appears to be the square/squareroot at work.

One way to mitigate this was suggested in another thread: i.e. adding a value to all attack and defense factors, to help reduce the percentage of difference in factors.  As an example, if you add 10 to all factors, a 10 attack becomes 20, and a 6 attack becomes 16.  That puts the values within 20% of each other (instead of 40%), thus mitigating the square/squareroot 'skew' a bit.

I'll try to analyze 2D6 versus 2D10 soon, to evaluate how much that will smooth things out, random-ness wise.

BTW, 23 base attack factors for a cedar longbow currently seems a bit much for most situations... the best Sword I've found so far only gives 15 attack. That's a topic for another thread, though...

Rather than add it to damage, why not separate damage from the attack roll completely? Either add it as a weapon stat or else have a fixed roll modified by strength. I'd prefer the weapon stat approach since having someone be just as deadly with a dagger as they are with a claymore seems a bit ludicrous, but whatever works.

So you'd go -

D(attack) vs D(dodge) to check for hit

D(attack) vs D(defence) to check for wound

If both rolls succeed

D(damage) + Strength damage.

You still have the same random factor in whether you hit in the first place, but by lowering the damage to a more reasonable level it prevents some of the more extreme outcomes. Your dagger armed combat specialist might be able to hit their target every turn, but if the most they can do is 1 - 3 damage + strength it'll take a long time to carve up a dragon, unless they have godlike strength of course.

It seems a little off to have two near identical rolls for dodge and defence, but I'm thinking you have some room for differentiation there by playing with spell and weapon abilities. Dragon breath or similar affects which ignore armour would still have the potential of being dodged, and of course you could add on hit effects which trigger if you hit, even if you bounce off the armour. As a nice bonus, this also nicely differentiates dodge vs defence, since you'd have to worry about both for a combat focused hero.

It took me a couple of reads to understand what you are trying to convey, Archonsod.  As it stands now, (if I AM understanding this correctly), you have an Accuracy vs Dodge roll, followed by a Strength vs Defense roll. 

If I grasp your concept correctly, the second roll would simply determine penetration of the armor, with the third (Damage) roll being a set value (DWeapon Strength, plus strength bonus).

Hmmm... interesting.

Anyways, I got a little off track in my probability discussion.  I think that Weapon/attack strength versus defense hasn't been adequately thought out.  It seems to me that as more powerful creatures/units come online, defense strengths became disproportionatly huge, which has required weapon strengths to be similarly huge.  So if you have the 'necessary' equipment to be effective against said huge defense strengths, anything with even a 25% lower defense strength becomes a pushover, unless it has a LOT of hit points.

This would track with some things Brad said about the development of the game.  Several groups were involved in the initial design, and apparently they weren't exactly on the same page.  A good example of this is city building costs versus weapons costs, and how slowly your cities initially produce gold versus the huge caches in the goody huts.  Standard levels weren't quite adhered to in this case, and subsequent patches have been slowly cleaning up the mess.

I'm sure the developer guys are evaluating combat values at the moment (note the recent reduction for bows).  What I'd suggest is that we establish some Norms, that all creatures and units must follow regarding attack & defense.  Then all weapons, defenses, and creatures would have to meet these norms.

As an example: Say the 'average' weapon attack strength chosen is 6.  This means that the average defense strength would also be 6.  So an attack of 12 should be considered huge, and 18 would be legendary/rare.  Everything in the game has to be designed against this scale (i.e. you'd better have a REALLY good reason for something with a 12, and 18 would be seen maybe once or twice in game, that's it.

BTW, my reasoning for 12 being strong versus 6 being average is that the high value has around 87% chance of winning under square/square root, so Full Plate only having double the value of leather actually means it is 87% effective against a strength 6 attack, versus the leather's 50% or so effectiveness.

Also, using the 18 'uber rare' max versus the 6 average, the 6 only has around a 5% chance of beating the 18.  A 1 in 20 chance of your average dude having a chance of damaging that Lord Dragon with the 18 defense sounds about right to me.  If said Dragon also had a 18 Dodge versus a 6 Accuracy, that 1 in 20 becomes a 1 in 40, i.e. probably NOT going to happen, and even if it does, said dragon has better than a 95% chance of hitting you back, with likely a LOT more damage in return!

Same for armor.  Say 6 is a full leather suit/tough hide, 9 is a full chain suit/armored hide, and 12 is full plate/rock hard hide.  That 'Armor of Azor' suit might grant you a 15 with some other defense bonuses in play as well.  Only the biggest baddest dragon in the game gets to be eligible for an 18 defense.

These values mentioned above assume resonable application of stats.  So that 18 attack would involve a high Strength characteristic along with an appropriate, artifact level sword.

Stat bonuses to these values would be targeted as a balance/mitigator to the low and high values, say avg. 3 to the above values (10/4=2.5, round up to 3), with 6 involving a rather high str/dex (say 24).  That way, everyone gets at least a 3 attack/defense from stats (unless they have less than 10 in a stat), even if they are unarmed - no D-zero rolls allowed.  This becomes more important with the square/squareroot in play.

So that 6 'average' attack becomes a 9 with an average strength.  The average leather armed unit would need to be close/equal that 9, with perhaps a higher minimum armor value as well, say defense starting at 2 instead of 0.  I actually like the 9 avg attack versus 8 avg defense, as that 1 point difference means, in an average situation, damage happens more often than not.  I'm talking about the damage roll here, not the 'to hit' roll.  Perhaps the 'average accuracy versus average dodge' should be 9 versus 8 as well, so again hits happen more often than not (allowing successful penetration of both dodge and defense/armor to happen around half the time).

Note that Leather Greaves, Helm, Armbands & Cuirass could each be worth 1.5 instead of 2, to get to that '6' average.  The game uses decimals anyways, so as long as all armors are adjusted similarly, it's all good.

Higher base numbers could be used, but the point is that 'Average' needs to be adhered to strictly, especially with square/squareroot in play.  The farther values get away from the average, the more skewed combat results are going to be.  Auto-kills get boring after a while, you know!  And a 2 attack versus a 36 defense is just pointless, no matter HOW many times you try...

Yup, that'll teach me for writing late at night You've pretty much got it though; rather than using the difference between the attack and defence roll as the damage we have a separate roll or fixed result for the damage.

 Where it becomes interesting is you keep the current D 0 - attack or defence roll, but it only determines a hit. What I like about this is it's magnitude rather than actual number that becomes important. Attack 30 is much more useful vs Defence 15 than Attack 100 is vs Defence 90.

 The problem at the moment is the little numbers the player sees. If you have twice the attack (i.e. 30 vs 15) then the damage done is going to range from 1 - 30 depending on the difference in rolls. Improving your attack simply makes this range wider; which is where the disconnect comes in. An attack 100 dragon should slaughter a defence 1 peasant, however in the current (or at least pre-sqrt system) the dragon can always roll a 2 while the peasant rolls a 1, and do a whole 1 damage. It's unlikely, but we're more likely to remember that than the multiple times we saw the dragon do in excess of 50 damage to said peasant. Furthermore, even if the dragon slaughters the peasant, the numbers we see can vary between whatever hitpoints the peasant has up to the 100 attack of the dragon, which enhances our perception of it being completely random (particularly when we see our dragon dish out 98 damage to a golem and only 25 damage to a cloth wearing peasant).

Fixing damage to say strength + smaller randomiser does a couple of things. Firstly, it gives you a fixed minimum and maximum damage. If our dragon has strength 40 and D10 claws, then while it will still occasionally miss the peasant, when it does hit we're always going to see a number between 40 - 50 damage. Psychologically we like it because it's more consistent. Secondly, it adds an important element of predictability. If that peasant only has 20 hitpoints then we know the dragon will always kill him in one hit, but we still have the possibility of a rare miss occurring (and conversely, the peasant can still hit and wound the dragon too on an outside chance). The simple fact we see a much tighter damage range will reduce the impression of randomness too.

 Finally it gives another area to play with which is always good. You can stick a high attack value on weapons alongside a low damage value so they hit more often for less, or reverse it to hit less but make sure they feel it when you do. You can add a little variation against weapons with the same attack modifier by adjusting the damage too.

The actual damage roll and strength modifier would need testing and balancing of course, as long as it consistently returns a small variance in the damage it should work. Really it's just a roundabout way to achieve similar results you're getting by reducing the average number. The main difference however is this allows you to retain the large variety in the attack and defence values, which allows for more room to play with and presents a good illusion of variety (the problem with averaging on six is people will see most units with six defence as being pretty similar. On the other hand a unit with 98 defence will 'feel' different to a unit with 80 defence, even though there's not necessarily a significant difference between the two; again, depends on the magnitude rather than the actual number).

I agree it is as much about perception of how the fight transpires as it is the actual values that show on the screen.

The random factor has value in that it allows for that "If I can just hit him this time, I can win!" when at the outset of that fight, it was rather obvious that I should lose. It adds excitement value. You can never have enough excitement value in a game, even if it is only once in a blue moon that the obvious outcome is contradicted.

Another idea, on how to positively affect how the whole battle is perceived, might be to represent a Death blow the same as we see the "Miss" (now "blocked") attempt.

If 2 opponents face off, say the Dragon vs peasant scenario as mentioned above, instead of putting up a 50 point hit when it is obvious the Peasant is toast, even if a 2 floats up, why not put up "Death" "Dead" or "He's Toast" for that matter.

A bunch of random death notices would be hilarious. What could be better than watching, "Damn that must Hurt" float up from a collapsing corpse on the battle field instead of the final "1 and done".

One way the interface could show you what just happened, if your attack failed, would be as follows:

Dodge wins vs Accuracy: "Miss" appears

Defense wins vs Strength: "No Damage" appears

That way, you'd know if the Dodge skill was responsible for the miss.

Reminds me of bookworm adventures - "whomped", "crushed" "obliterated" are all common overkill words - in that game you actually get a bonus for the overkill.  But any of those combined with the flying backwards animation would give you more emersion and an epic feel - particularly if they only happened on significant overkill.

Re the volatility you could just split the attack up into 3 swings per attack, with the chance to hit /dodge being as now, the damage calculation being as now and hitpoints 3 times higher, or divide the damage by 3.  It would then be possible to have a single counterswing in the attack.  This might normally go Attack, Attack, defender, Attack.  but might vary in some circumstances (e.g. Defender, attack, attack attack for spear vs cavalry, or attack attack attack defender for sword vs battleaxe)  For display you could have Miss, -7, blocked float up or just the total.  Battle of westnoth just gets by with number of strikes, probability to hit and fixed damage,

Quadratic! not exponential. Quadratic and exponential are both super-linear, but exponential is a special type of super-linear progress that is particular bad, so please don't use when you only mean quadratic or other polynomial growths

Linear - Quadratic - Exponential

1 - 1 - 1

2 - 4 - 4

3 - 9 - 8

4 - 16 - 16

5 - 25 - 32

6 - 36 - 64

7 - 49 - 128

8 - 64 - 256

9 - 81 - 512

10 - 100 - 1024

And this using a weak exponential growth. A powerful 10-based would have ended at 10 million.

Apologies, Mr Math Wizard, for using the incorrect term.  My statistical analysis still stands though, until you post your own mathematical calculations and show otherwise.

I don't usually point out other peoples word errors in such a blunt fashion.  I might have posted "Don't you mean quadratic instead of exponential?" and explained the difference.  I haven't had a math class in several decades, so getting the terminology wrong occasionally is going to happen.

as a short term fix, how about changing the random number generator itself to follow a normal distribution, or weigh it to the centre through some other means?

Your analysis still stands. If it was wrong I would have said so

My post was no critique of you specifically, I have just seen this mistake several times on the forum, and thought it might be about time to go into the details and explain the difference. It can be hard for some to see if they have never had math, and I tried to make it readable to everyone, not just you.

I _was_ being pedantic, I know, but the difference is actually slightly important to 4X games. Most things are never truely exponential in growth, most are merely quadratic (which itself is pretty bad). But one strategy stands out: city spam. City spam is often the winning strategy in the end because it effects an exponential growth in faction power unless curtailed by game mechanics (2 cities produce 2 settlers giving you 4 cities producing 4 settlers, etc.).