In this post I will use some basic probability theory to show that, in essence, the Warhammer 2nd edition combat system is not deadly, as I think is often claimed, but is actually really slow and boring, and inherently survivable.

This assumption of deadliness arises, I think, from the fact that PCs at low levels are poor at doing anything, and the assumption is that if you’re bad at stuff then you’ll die quickly doing that stuff if it’s also dangerous stuff. I think this assumption also lies beneath claims that early D&D was deadly, an assumption which I don’t test here (due to lack of familiarity with early D&D rules) but which is probably somewhat better placed than any assumptions about Warhammer’s relative riskiness.

I came to this comparison because on Friday and Sunday last week I role-played respectively in Pathfinder and Warhammer 2nd edition, and I was struck in both instances by the length and inevitable dreariness of the combat, and by the fact that both combats had to be ended by a non-combat act of the GM’s. This post, about the probability of survival in each of three systems, will serve to show how this comes about and also I think reveals some obvious conclusions about tactical combat rules in role-playing. I aim to expand on this post in future with a proper simulation and statistical analysis, complete with survival curves, but that will take a bit of time.

**Introduction**

The probability of surviving a single round, and the cumulative probability of surviving multiple rounds, are calculated here based on the underlying combat mechanic of three systems – Warhammer 2nd edition, D&D 3.5, and my own Compromise and Conceit modifications of the d20 system. All three are compared with a putative “control” system in which the mechanics are not specified, but are assumed to result in a 50% probability of a hit in any given round, and death after 3 successful hits. The chief conclusion for each system is the number of rounds required to fight before reaching a 50% chance of death, referred to hereafter as the “median survival time,” though strictly speaking this is not a median survival time. In practice of course time to death varies according to the good or bad luck of the player, and how much they lie about their rolls to the GM, so survival time should here be assumed to be roughly representative of a long-run probability. The methods presented here also use various simplifications and approximations, specifically ignoring the role of criticals, fate points, and the death spiral in the Compromise and Conceit system, which makes the order of hits important for survivability.

In all cases, the survival probability is calculated for a fighter-type PC attacking an NPC with exactly the same skills as themselves.

The fundamental mechanics assumed are set out below. The fundamental problem with Warhammer can be seen to derive from the number of defensive manoeuvres available to a fighter in a standard combat round. Once a successful hit has been scored, the defender can then roll a defensive roll using their own combat skill, and then (if a fighter-type character) can roll a damage reduction check against their constitution. For a typical fighter we will see that this reduces a fighter’s successful hit chance to just 15%, and in a series of binomial trials requiring 3 successes, this can significantly extend the run of rolls required.

**Method**

For each system, a typical build of first level fighter was generated, using average statistics that might be expected for such a system, and pitted against exactly the same fighter character. No special feats were assumed in D&D or Compromise and Conceit (C&C), and the special feat of “Damage Reduction” was assumed for the Warhammer fighter (though as we shall see, it is not an enormously important feat). Other assumptions are outlined in detail below.

The combat method for each of the systems was summarised as a single probability of successfully scoring damage against an opponent. Damage was assumed to be the average for the type of character, and the number of hits required to kill the PC for the given average damage was used as the number of hits required before the PC or their opponent was killed. In each round, the cumulative probability of death was calculated as the probability that the given number of hits occur by that round, which is practically given as 1-P(less than that number of hits occurred). Formally, given a requirement of *x* hits to achieve death, the probability that a character survived to round *k* is the probability that they have received at most *x-1* hits in *k* trials. The *adjusted probability* is the probability that they have survived to round *k, *or that they killed their opponent in round *k-1*. This probability in turn is given as the probability that they survived to round *k-1* *and* they delivered 3 or more hits by round *k-1*.

This problem reduces to a simple binomial distribution for a given probability of a hit. Note that inclusion of critical hits, special moves, fate points, or death spiral effects renders this calculation completely different, and will be handled subsequently in a simulation.

Assumptions for each system are set out below.

*Warhammer*

A fighter-type character (for example, mercenary or watchman) is assumed to have rolled an average *attack* and *constitution* value on 2d10, giving values of 30 in each. The character is further assumed to have added 5 to the attack score, giving a value of 35. The chance of a successful attack is thus 35%, the chance of a successful defence is also 35%, and the chance of a successful damage reduction is 30%. The character is assumed to absorb 3 points of damage (30/10), and does 1d10+3 damage, and so final average damage is the average damage on a d10, or 5.5. The character is assumed to have 13 hit points, and be wearing leather armour (AP 1), so overall average damage is 4.5. Probability of doing any damage in one round is given as the Probability of a successful attack AND a failed defense AND a failed damage reduction. Since the opponent is exactly the same, this gives us the following results vis a vis the PC:

- Chance of being damaged by the opponent in one round=0.16
- Number of hits required to die: 3

*D&D3.5*

The D&D fighter is assumed to have a +2 strength bonus, BAB of 1, and weapon focus, for a total attack bonus of 4. Armour is chain with a shield, +2 dexterity bonus, and +1 dodge bonus, for a total AC of 19. The fighter is assumed to have maximum hit points, the Toughness feat and a +1 constitution bonus, giving 14 HP. Damage is from a longsword with +2 strength bonus, giving average damage of 6.5, so 3 hits are assumed to be required to kill the fighter. No other feats are assumed. This means that the chance of a successful hit is 25%, because the PC needs to roll over 15 on a d20, giving a 25% chance of success. This gives the following results:

- Chance of being damaged by the opponent in one round=0.25
- Number of hits required to die: 3

*Compromise and Conceit*

The Compromise and Conceit (C&C) fighter is assumed to have 4 ranks in attack, with a +3 strength bonus, and 4 ranks in defense, with a +3 agility bonus. The fighter is assumed to be wearing armour with Damage Reduction 3, and to have a maximum damage of 5 wounds. The fighter is also assumed to have 4 ranks in fortitude, with a total of 7 wounds. When fighting against himself, this means the fighter would need to roll a 10 to hit, but a 14 to do damage. Calculating average damage is tricky because the probability distribution is truncated between 1 and 5 with uneven probabilities, so for now we assume it is weighted towards the lower boundary of the damage distribution (due to the nature of the 2d10 roll), so assign an average damage of 2. Recall that this system uses a 2d10 attack roll, so we have a final result of:

- Probability of successfully doing damage = 0.34
- 4 hits required to kill the PC

*Control system*

This system assumes a 50% chance of doing damage, and 3 hits required to kill.

With these results we construct the probability distributions.

**Results**

The median unadjusted survival time for each system is:

- Warhammer: 17 rounds
- D&D: 11 rounds
- C&C: 11 rounds
- Control: 5 rounds

Figure 1 shows the unadjusted survival times (D&D has been misnamed AD&D).

The adjusted times were:

- Warhammer: 23 rounds
- D&D: 15 rounds
- C&C: 14 rounds
- Control: 7 rounds

and the probability curves are plotted in figure 2.

Recall that these are not true survival curves, but simply cumulative probability distributions.

**Conclusion**

It actually takes a long time to die in Warhammer, with a concomitant number of die rolls. At the unadjusted median survival time, if the player wins, he or she will have rolled 17 attack rolls and 3 damage rolls (on average); he or she will also have suffered an average of 6 attacks that required defensive rolls, giving a total number of defensive rolls of between 6 and 12, for a total of 26 – 32 rolls. The D&D player will have rolled 11 attacks and 3 damage rolls, for a total of 14 rolls. The C&C player will have rolled just the 11 attack rolls, and the control player will have rolled 5 attacks and 3 damage rolls for a total of 8 rolls.

It’s worth noting that, fiddling with the underlying parameters of the game assumptions for warhammer shows that damage reduction is a significant factor in the slowness – losing this feat increases the base hit chance to 23%, similar to D&D. However, the relative ability scores of the enemy are not that important. If the enemy has only a defense score of 15, half that of the PC, hit probability increases to 20% and the survival time drops (for the person with the higher skills) to 13 rounds, only shaving off 4 rounds. Also, if both fighters have an attack ability of 55%, the overall chance to hit remains roughly similar, at 17%, so gaining levels doesn’t significantly speed up combat.

Even if we assume that the warhammer system represents reality in its long drawn-out slugfests, we have to ask if this is a system that we want to actually play – fights this long are very boring. Also we note that a player has fate points to spend, and that in the “low power” world of warhammer these are one of the player’s main advantages over NPCs. But the average player will have 3 fate points, which can be used to reroll a single roll. Given they have to roll 26 – 32 times to win, it seems that these fate points aren’t going to make a significant difference to the battle’s progress. Also, unlike in D&D and C&C, the absence of other powers and magic means that the player has little else to do in combat but roll to hit, making these 26 rolls considerably less interesting than in other systems.

We also can note that there is no particular reason for a given number of rolls to be made for one attack. Combat systems abstract combat, so we could in essence reduce combat for the Warhammer case to a single roll against a 15% hit chance, and have the same result as described here, at the cost of 6-12 rolls less. Players want a certain amount of argy-bargy in combat, but I think most people would argue (and I think certainly the people I’ve played Warhammer with have agreed) that a little less argy bargy and a bit more fun could be had from a different system.

In a subsequent post, I will consider a full simulation for a set of sample fights, include criticals and death spirals, and give a statistical analysis.

May 7, 2010 at 12:48 am

[…] was because the only battle just kept going on and on and on. Pathfinder battles take a long time! I’ve done some comparisons and been thinking about this, and I’ll be getting back to this in more detail later, but I […]

May 10, 2010 at 9:19 pm

I’m intending to poke at this later, but I wanted to start with some research from the WFRPG e2 core book. In it we find:

1. That the average starting human wounds is 11, not 13

2. That the odds of rolling a “fighter-type character” is about 34% by my count of the careers (though you do get two rolls which you can then pick from, which pushes it up to about 56% likely). This does mean you’ve got about a 50% chance of being a graverobber, camp follower or rat catcher instead. [1]

3. You can parry one blow per turn (at weapon skill so 35% chance) and dodge one (at agility, so 30% chance). This assumes you’ve got the right talents. If you’re a rat catcher you aren’t given options of those skills and you can parry one attack per round. If you’re attacked a third time that round you better hope that your opponent sucks as much as you do. Also, these are no good against ranged weapons, so good luck against Skaven with bows.

[1] Sure, there are optional rules to let you choose a career, but where is the fun in that? You may as well play D&D 3.5e if you don’t want to be a rat catcher or valet.

May 11, 2010 at 8:58 am

[…] problem is at least partly the rule system, which at low levels is about consistently failing, and long-drawn-out battles to nowhere. I don’t see how anyone can think this is […]

May 12, 2010 at 10:24 am

Paul, sorry for not responding to your comment earlier, I’ve had an infestation of Germans…

In response

1. our wounds were calculated at 13 by being 10 plus your constitution statty-thing (I only know the Japanese name!) which was 3 for a human. Thus 13.

2. Yes, this is true, but if I stick a rat-catcher against a rat-catcher it’ll take even longer to resolve. As an example, I played a graverobber and I fought a higher-level racketeer in a duel, and it took him a long time to beat me up, even though I had no special combat talents and only a slightly above-average constitution and attack. This would be like sticking a first level thief against a higher-level (maybe 3rd) fighter in D&D and expecting him to last more than a few rounds.

3. You’re right, but I don’t think it’s a statement on any specific deadliness of warhammer to say “if you’re a thief up against 3 fighters you’ll die quickly.” The test we’re giving it here is a straight duel, between two roughly evenly-matched characters.

I did, however, consider a person with attack value of 55% against someone with an attack value of 35%, and survival was still pretty long. Low hit probabilities need to be accompanied by limited defenses and/or low wound values to make a game deadly, rather than boring.

May 12, 2010 at 8:25 pm

[…] | Tags: Probability, RPG Systems, Warhammer | Leave a Comment In this post I further explore the probability structure of Warhammer 2nd edition combat rules, to show that there is never a situation where it is worth a character’s while to use the […]

May 13, 2010 at 9:48 am

[…] fights between characters with very low or very high weapon skill will last for a very long time. Previous analysis showed that a total attack success probability of 16% is associated with a 50% survival of 17 […]

July 24, 2010 at 11:53 am

[…] This game is cool! The dice give a lot of role-playing opportunities and the rules have liberated Warhammer from the two grinding problems that made Warhammer 2 so hard to enjoy: the inability of beginning PCs to actually do anything, and the intense, grinding tedium of the battles. […]

November 3, 2010 at 8:32 pm

I agree actually. Though it must be said Warhammer 2nd edition combat is quite tactical (lots of opportunity for parrying, dodging, etc.).

The only properly deadly combat system I can think of is the one I’m using in my zombies game – i.e. cyberpunk 2020 without armour. Most fights last about three or four rounds at the very most. Though MERP/Rolemaster and Pendragon come pretty close.

As I get older I get less and less patient with protracted combat, so these systems consequently have got more and more appealing to me. The next time I run a fantasy game I think I’ll give Rolemaster a whirl.

November 4, 2010 at 8:23 am

I agree about how getting older makes you lose interest in long combat. I spent the weekend before I wrote this post bogged down in huge pathfinder battles and then this long-winded warhammer dual, which made me think of actually investigating them. However, I also investigated a tactical aspect of warhammer and found that the tactical rules aren’t necessarily very helpful – they just further slow down the game. Warhammer 3rd Edition is quite fast, with most fights over in 3 rounds.

I played cyberpunk 2020 once and I remember it being lethal until you started using armour, then it was terrible. Rolemaster is actually not as quick as one expects, because although death can be instant, it’s largely a process of grinding through a slowly unwinding death spiral of increasing penalties. The penalties mean that the tail end of the fight can drag on for a while, as no-one can hit each other. Also the table-referencing is a pain in the arse. I really like character creation in RM, and the versatility of the skill system, but the saving throw process is clunky and combat can be a terrible bore (though usually it is quite a bit of fun).

November 18, 2011 at 1:54 am

You have forgotten about modifiers to hit which drastically change the speed of yours/the npcs demise. Also what is the obsession with speed???? its not a race to see who finishes the fight first. Also combat is not supposed to be a bare bones dice rolling contest – abstracted combat is supposed to be theatrical and dramatic with PC and GM descriptions of the fight keeping things interesting and alive. Also positive modifiers are applied to actions that are particularly dramatic or enjoyable thus (guess what) speeding up combat ðŸ™‚

Stop seeing the system as a problem and use it as a tool for fun which is what the whole thing is about anyway!

January 11, 2017 at 2:56 am

Hi, while there certainly are things I’d view as seriously wrong with the 2nd edition of WFRP’s combat system (and the increase in Wounds did turn out to be an error that protracted combat unnecessarily) I think you’re looking at this in the wrong way. More dice rolls does not necessarily mean more boring.

WFRP is medium crunch whilst D&D has a highly abstracted combat system.

The dice rolls in WFRP actually tell you what happened. In WFRP you know whether the character parried, dodged, if the armour absorbed the force of the blow or whether injury accrued. By contrast in D&D you just get a hit or miss result. As such there is far more narrative in the WFRP combat system -which should be more interesting and satisfying.

Another thing to note is that your results may actually contradict your claim that WFRP is not so deadly. The point you make that increases in skill do not give you as much of an advantage points towards characters remaining more vulnerable -thus in that sense the combat remains deadly. The length of time or the number of dice rolls required in a combat between two evenly matched characters does not actually tell you anything about the ‘deadliness’ of a system.

January 11, 2017 at 3:03 am

P.S. Incidentally, Paul is correct that the average human starting Wounds is 11 not 13. Why did you add the Toughness bonus to the Wounds total?