Sunday 12 April 2015

Game Design #37: The Better the Hit, the Better the Damage - Managed Probability & Modifiers

I'm surprised how little this gets used.

Most often to resolve firing, a "to hit" roll is made.  Let's say 4+ on a d6.
Then a "to damage" roll is made.  Let's say it's also a 4+ on a d6. Or perhaps it's a roll to "save" damage done. It's just terminology - the effect is the same.
A pretty common, 40K-esque mechanic. I think Warlord Games needs to offer me a job!

However there is NO connection between the accuracy of the hit, and the damage done.  

It's the same with "criticals" in space and naval games.  A shot hits, then there is a separate roll for critical hits.  There is seldom any connection between how good or accurate the shot was and the % chance of scoring a critical.

This does not make much sense.  A well aimed shot should do more damage, or have a proportionately higher chance to do damage.

I think I first noticed this with DP9's Silhouette system.  It's a little weird, but illustrates my point:

You roll 2d6 and pick the best one. (+/- ranged modifiers)
Your opponent rolls 2d6 and picks the best one too. (+/- defence modifiers)

Now you compare the difference (and this is the key word).  If the defender wins or ties, there is no effect. But if the attacker wins the difference is very important. 
Let's say the attacker rolled a 3, 5 and had a +2 modifier.  The best dice (5) plus the modifer (2) = 7   

The defender rolls a 2, 4 and has a +1 modifier. The best dice (3) plus the modifier (1) = 4

The difference between the rolls (7 - 3) is 3.  This is multiplied by the weapon's damage.  Let's say the damage is 4.  4 x 3 = 12.

As you can see, winning by a wide margin (say 3) does 12 damage.  Whereas hitting with only 1 to spare would do only 4 damage.  A better initial hit does proportionately more (or has a higher chance) to damage. 

That may have been a bit confusing.  Here's a simpler example.

We need to roll a 4+ to hit in our "Standard Rules"  example above.  But we rolled a 6 instead.  The difference is 2.   Now, since it was such a great shot - much better than what we needed to hit the target - it probably it more likely to hit something vital.

Let's add the difference (+2) to the "to damage" roll.   We needed 4+ to damage in our "Standard Rules", right?    Sure, but when we roll the dice, we add the +2 difference to the dice roll.  So a d6 roll of '2' would not damage a target normally.  But when we add our +2 bonus for our great initial shot, it would be a hit!

We've just linked the quality of the shot to the amount of damage done. 


It's common sense.    A easy, aimed shot at a point blank target is much likelier to inflict a deadly wound than a hopeful shot at long range.  The chance of a "headshot" when standing 1m from a target (with say a 80% hit chance)  would be much higher than a shot from 300 metres away (say a 10% hit chance).    In a space game, a starfighter which is skimming the Death Star's surface is likelier to hit a womp-rat sized hole than one firing from miles away.

It encourages sensible tactics.  If you have balanced your "to hit" roll, that is!  If you want to deliver the coup de grace, you may have to move close and set up a better probability shot to reliably do it.  Wargaming needs dice.  It needs that "uncertainty" - the chance of pulling off that one in a lifetime shot. However the probabilities should not be random.

Paul of Man Cave fame recently asked me once what I have against "exploding d6s" (I was probably ranting about Aeronef/Firestorm Armada at the time).  Those games are the antithesis of managed probability. I'm going to make an extreme example:

Let's say a game needs '6's to hit.  If you roll a 6 you get another roll until you fail to roll one.
Each weapon has the same range.  
Once a shot hits, you need a '6' to destroy the target.
There are no modifiers to either roll.

As you can see, there is no real decisions for the players to make. Simply move their units into the mutual range and roll dice madly, hoping for a d6. A random 17% chance.

As you can see, there is no effective way to "manage" your chances.  Just chug dice and pray for d6s, which are disproportionately valuable.  All you can hope for is to concentrate your forces, and hope your opponent spreads his units out and attacks your forces one at a time, allowing you a better ratio of rolls.   Since all weapon ranges are similar, speed has no effect, you can guarantee this - simply clump your ships together and move at the speed of the slowest ship.

We need uncertainty - otherwise we'd have the boredom of chess - i.e. whoever had the turn automatically kills an opponent within range or something similar - but it needs to have a way to manage this uncertainty.

Okay, here's an example of "dice to move."  This is something I have grudgingly become used to, but as a sport coach I find it jarring.  Kids don't suddenly run 100m in 10sec one day, then only 20m in 10sec the next (barring a broken leg).  It's about as sensible as dicing for the maximum possible range your weapon can shoot.  However time scales are flexible, and it does add "friction" to the game, and removes unrealistic precision.

Unpredictable Random
Every unit must roll a d20. The number it rolls on a d20 is the amount it can move.
(If you wanted to make it worse, the player must move that exact distance.)
Thus the player is at the mercy of a completely unpredictable dice, and can move anywhere from 1-20" per turn.  There is no way of making any plans, because you don't know with any degree of certainty what you or your opponent can do.

Predictable Random
Okay, let's replace that d20 with d6s.   4d6s would result in a move between 4-24" - the same 20 point spread. But due to the bell curve of the multiple dice, you can rely on a move of ~14".  Probably around 10-18" most times.   It's still unpredictable, but you at least have a guesstimate of what you can do, thus allowing him to plan ahead and formulate tactics instead of only reacting to dice results.   If you allowed the player to choose any distance up to the total, it would make it even more reliable. 

These have become a bit unfashionable of late. I think this is a reaction to some 90s rules, where there was a modifier for everything.
-1  captain ate baked beans this morning
+1 great Sports Illustrated issue this month
-2  hungover
-1 out of coffee
-1 undergarments too itchy
I agree they can be a problem. Too many modifiers are confusing, and negative modifiers are annoying (I mean, it annoys me if I roll a '6'  and I don't get a hit cos of that -3 modifier.  Buckets of Dice is a common trend (probably worth a post of its own) and it too has modifiers - only you simply add/remove dice rather than modifying the score of the dice.

However modifiers are important for determining tactics.  Infinity does a great job of this.  Let's say a soldier needs to roll a 10+ on a d20 to hit, and a 10+ on a d20 to wound.  Being in cover adds +3 to both rolls, which gives a strong incentive to stay in cover while not making it impossible to hit troops in cover.  Modifiers are important.  They help steer your players to play the game the way you want them - whether historically or otherwise. 


  1. Bear in mind that depending on how it's done, connecting the firing and the damage rolls will slow down play, because it makes rolling shots in batches harder.

    In games where each figure fires individually, it gets unwieldy fast unless we only have a few guys each.
    f.x. if I have 40 figures around the table, all firing, I'd rather not have to do separate damage rolls based on each figures hit roll.

    A reasonable middle-ground, I find, is where beating the hit roll by a fixed amount provides a damage bonus/bonus damage die or similar.

    There's a whole different conversation about how much variety you have in the firing roll and how that relates to the base damage.
    In some RPG's for example, most damage comes from the hit roll with a small bonus from hte weapon, which many wargames do it the other way around.

    Those things matter quite a bit as well.
    If, f.x., improving my hit roll chance will give me a 10% damage boost that's worthwhile but probably won't change how I play hugely.
    If improving my hit roll chance will give me a 50% damage boost, that's a pretty big deal and the game will probably revolve around it.

    A variant of it is that the ease of the shot acts as a cap on the damage that can be inflicted.
    Crossfire is kind of a rough example of this, where your firing dice depends on whether the target is in cover or not.
    Hence, with an easier shot, I can inflict more damage (and more reliably).

    Dragging an RPG into it again, Unknown Armies is a percentile roll against your fighting skill.
    If the roll is equal or under your skill, you do damage equal to the dice roll.

    Nice topic. There's a LOT of possibilities out there.

    1. I like the Unknown Armies method you mentioned. It seems like a good way to reduce the amount/times dice are rolled while still giving you a "higher is better" system.

  2. Strange Aeons links to hit and damage rolls exactly as you describe - the amount the succeed the To Hit by is a positive modifier on the To Wound roll.

    However Ivan's point is a good one, it does slow down play. It works in SA because as a 30s Pulp skirmish game you are only firing a 1-3 shots per turn per character, and on usually has only 3-4 characters. Overall I think it is absolutely worth it.

  3. As usual, I don't offer any useful solutions. I just ask ze questions!

  4. You should check out the latest Heavy Gear Blitz - Beta rules. The difference between the attacker's and defender's rolls are worked out as traditional, for a Margin of Success. That Margin of Success is how much damage is done. However, if a weapon's PENetration power is great than the target's ARmour rating, you add the difference to the amount of damage done. Alternately, if a weapon's PEN is less than a target's AR, then you subtract the difference from the damage done. Where the MOS + PEN = Ar, then the target gets a point of damage on 4+ on 1D6.

    Of course, what's also neat is that models have a Damage Capacity divided into Hull points and Structure points, with Hull points representing superficial damage, and Structure points representing essential, model-removing damage.

  5. I've been chewing on some rules that might be described as 'Buckets of Dice'. I'd like to hear your thoughts on it.

    1. Sure. I don't entangle myself in serious playtesting (too much like hard work) but happy to tinker with mechanisms. maj_lovejoy at hotmail dot com is the email I check most often.

  6. Personally I like to get my Hit and Damage done on the same dice roll. I really don't like saving throws.

    1. Like any simplification, it's harder from a game design standpoint. When playing with my homebrew space rules, I had a single d10 roll work as "to hit" "to damage" and "hit location(!)" but I've moved away from that. The idea was cool, though.

    2. Legions of Steel Planetstorm does it this way. D6 vs Target Number. Equal the TN and the target is Pinned. Exceed the TN and the target takes a Kill.

      I'm toying with a D10 version of that and adjusting the TN based upon tech level of weapon vs. tech level of armor and troop quality vs. troop quality... ideas borrowed from TW.

  7. I object to successfully hitting but not damaging. If I didn't damage anything the hit wasn't successful so the initial 'success' was a lie. To Hit rolls followed by Damage rolls are an exercise in time wasting as far as I'm concerned.

    In a story driven game I don't object to heroes having saving throws, that's different. But basic grunts should not get them, no gods are looking out for them.

    As someone who teaches maths I am willing to bet that the more calculations a player has to do during a game the less players the game will have. Reading dice is not a calculation of course so the GW method appeals to people for this reason.

    As an aside, 'Hit, Damage, Save' is designed to appeal to children. It gives each player the illusion of doing well but ensures that usually nothing of any import actually happens so neither player feels that they're 'losing' and consequently doesn't just give up.

    The more blind chance as opposed to player skill a game relies on is directly proportionate to the game's popularity. Unfortunately.

    Football is a good example of this. Supporters of the losing team can always hope for a turn around right up until the final whistle and thus remain involved in the match. If the better team always won, if football was purely skill based like chess, there would never be any 'giant killer' games so popular in the FA cup.

    1. I'd agree that more work on the part of the players means fewer players, and some uncertainty can take the edge off of entry-level experiences. That's why Heavy Gear Blitz moved from multiplying the Margin of Success by the Weapon's Damage Multiplier, to adding it to the Weapon's Penetration. It combines less than perfect certainty with less 'difficult' arithmetic.

    2. Heavy Gear rules didn't need radical changes, so much as all the flipping rules to be put into one coherent rulebook!

  8. "As someone who teaches maths I am willing to bet that the more calculations a player has to do during a game the less players the game will have. Reading dice is not a calculation of course so the GW method appeals to people for this reason."

    I was thinking about this the other day. Why is buckets of dice regarded as "fun?" It sort of is, as long as it doesn't get to silly i.e. a dozen or more dice. I was fiddling with a VSF aeronef game (kinda pulpy sci fi) and am considering the GW approach for the lighthearted factor, even though it pains me from a design standpoint.

    "The more blind chance as opposed to player skill a game relies on is directly proportionate to the game's popularity. Unfortunately."

    Oh, I think there has to be a balance. You need skill, so you can attribute your wins to your own skill. You need luck, so you can blame the dice if you lose.

    (I say this semi sarcastically, but statistically, how many old White Dwarf AARs moan about the dice rolls? I'd say all of them!)

    1. Buckets of dice has a benefit up to a point, in that you get "average" results similar to a bell curve.
      Whether its practical depends greatly on the size of the bucket though.

      In 40K, its mostly a legacy issue. Rolling for every attack wasn't a problem when you had 20 guys each.

  9. I try to do this in most of my games although it's achieved in very different ways across titles.

    For example, Battlefield does this in a very straightforward manner. The attacker rolls a number of dice determined by weapon range, unit type, tactical advantages, and gear. The defender does the same [both players only adding dice and never subtracting]. Both roll dice and compare with successes canceling one another out. A success is always on a 4+. Any remaining successes for the attacker are rolled for damage or suppression as the situation and attack dictates.

    This does everything in two rolls and judges not only the quality of the attack but the quality of the defense as well. The math and probabilities involved are very transparent.

    Now, let's look at Rogue Planet... :)

    With a single 2d6 roll and no charts, Rogue Planet tells you:
    - if an attack was a success or failure
    - the degree of a success and any critical effects
    - if any enemy reactions are generated as a result of a partial success or failure
    - damage [if any] based on comparative skill levels, degree of success, and armor rating

    It's worth noting that the greater the gap on a particular skill level in the system, the greater the damage potential on a particularly good shot is. This seems obvious at first, but it's often forgotten. Everyone expects elite units to regularly decimate low level grunts. I think it can be just as important that a grunt unit with a poor stat line making a amazing hit in an against-all-odds attack versus an elite unit be rewarded by causing damage that's commensurate with the 'surprise success'. This should be built into a system if possible to avoid the hit that's not really a hit that Paul alluded to while creating drama and story. It also makes for some interesting decisions when creating a force and building units. That's my two cents anyway. :)

  10. MacavityandMycroft22 April 2015 at 10:21

    An Interesting take on this is in the Board/Miniatures game Star Wars: Imperial Assault. It is a finicky system, but functions well. They have specialized dice, different for different weapons/characters.

    The dice can come up with 3 things: Accuracy, Damage, and Surges

    Accuracy is flat numbers, the total must reach the distance your target is away. As you have 2 actions per 'turn' with a character, deciding whether or not to move closer for a better chance of hitting or stay 'safe' and squeeze off a second shot is a real choice.

    The Surge effect is another help in dealing with this issue, as most units have at least one damage increase (or armour penetration) Surge, and one for accuracy. So if you are close up, and accuracy is no problem, you can make your point blank shot count.

    It does a good job of giving you a lot of decision points, even if the abilities of each unit get hard to keep track of.

  11. Hi! Interesting article. I'm working on a miniatures game and this was something I was thinking about, since I see hits and damage tied together so much lately (x-wing miniatures in particular), and my game doesn't have it tied together.

    I'm definitely no fan of "buckets of dice". Do you think this problem of disconnected hit/damage is at least mostly negated by no die rolls for damage (just do damage printed on the unit's card?).

    I'm trying to figure out if maybe I need to rework things and tie hit with damage.

  12. "Do you think this problem of disconnected hit/damage is at least mostly negated by no die rolls for damage (just do damage printed on the unit's card?). "

    Not quite sure what you're asking... but I'll try to answer what i think the question is...

    If a hit does a set (different) amount of damage (i.e. 2 damage for laser, 3 for blaster, 5 for a photon torpedo) like on a unit card...

    ... they still are disconnected to the quality of the hit roll, as it doesn't take into consideration that the photon torpedo might only be a glancing hit, or the laser might hit a vital reactor.

    Here's a sample of how you might connect the roll to hit, to the damage inflicted.
    "If a weapon scores DOUBLE the target number needed, it does DOUBLE damage."
    "If a weapon scores ABOVE the target number needed, it does NORMAL damage"
    "If a weapon scores EQUAL to the target number needed, it does HALF damage (rounded up."

    Let's say the X wing fires at a dodging TIE fighter. It needs a "4" to hit on a d10 with its laser, which normally does 2pts of damage.

    A roll of 8+ will double the target number, and do double - 4pts - damage.
    A roll of 5-7 does normal - 2pts - damage
    A roll of exactly 4 does half - 1pt - damage

    That's an example of connected "to hit" and a fixed damage score.

    Did I help, or did I miss the question... :-/

  13. You got what I meant.

    Actually the game does kind of have a system like that, so maybe it does work alright. Though it is a bit more limited.

    Players play cards and if the attacker's total is => that the opponent's card, but the base card value is not 5 or more greater, thjey hit.
    If the attack's card is 5 or more greater than the opponent's card, that's a counter (the opponent does damage instead). If the defender's card is 5 or more greater than the attacker's card the attacker does +2 damage (but I might make it double instead).

    So, there's not quite the same granularity as your example with .5x 1x and 2x damage, it's just 1x or 2x.. Does this system sound like it could make sense?

    1. From what I understand, the degree you win by influences the effect of your attack (i.e. a better attack does +2 damage, a normal attack does normal damage, and a poor attack means the defender does damage)

      So yes, your level of success IS impacting the damage done.

    2. OK, perhaps I'm over-worrying about this aspect. Thanks.