Variance Supplemental 2: SotC (Wonkish)


This is the second supplement to the Variance and Game Design article. While there are some new observations, it covers much the same ground as the first supplement but for a different system, Spirit of the Century. So if you haven’t read the first supplement you should do that. If you have and are a glutton for punishment then this article is for you.

The System

For my first test I chose a system I was familiar with and had some old questions about. For the second test I chose Spirit of the Century (SotC) because it is a game I haven’t played but really want to, due to some cool sounding mechanics. My biggest reservation about the game, however, was that combat would be heavily influenced by skill level compared to non-combat rolls. So, I looked at SotC mostly to satisfy my own curiosity.

Spirit of the Century Mechanics

SotC has a much more complex combat system than Feng Shui. Skills are rated by descriptions but really translate into a number from 0 to 5. To make a skill check, you roll 4 Fudge dice. These are special dice that can roll –1, 0 or +1. Thus for four dice the roll will run from –4 to +4 with an average value of 0. This roll is added to the skill. For simple tasks, if the roll equals or exceeds the target value the character succeeds. In combat, the attacker rolls whatever skill they are using for the attack while the defender rolls whatever skill they are using for defense. If the attacker’s roll plus skill exceeds the defender’s, then the defender takes damage. Damage occurs in terms of stress and complications. Everyone has a stress track, basically a series of numbered boxes. For a basic character they run from box 1 to box 5. The amount by which the attack beats the defender is the damage and the box corresponding to that number is checked off. For example, if the attacker wins by 3 then the number 3 box is checked off. If the attacker later wins by 2 then the number 2 box is checked off. Notice that checking off box number 3 had no effect on box 2, so when the 2 damage hit occurred box 2 got checked off. If the corresponding box is already full then the next highest empty box is checked off. So if the attacker gets a third hit for 2 damage, this would normally check off box 2. However, box 2 is full so we look to box 3, but box 3 is full so we look to box 4. Because box 4 is empty, box 4 is then checked off. If the damage goes past the end of the stress boxes then it results in a complication. Under most circumstances, a character can suffer 3 complications. The first time the stress track is exceeded they take a minor complication, the second time a moderate complication, and the third time a major complication. If they take damage that would result in a fourth complication the character is taken out. It should be noted that the same mechanics apply to mental or social contests as well, though being a pulp game, most combats will likely be physical. SotC also has Fate points, a limited supply of points that can be spent to reroll a die roll or add two to a result, and this can be done after the dice are rolled. Exactly when and how many Fate points can be spent for any die roll is entirely dependent on the character and the circumstances of the roll.

Assumptions and Simplifications

Initiative is much easier to handle in SotC, but I left it out to make things more comparable to the Feng Shui results. I left out “spin”, a rule where if someone’s defense roll is much higher than an attacker’s attack roll, the defender gains a temporary advantage. It would have been somewhat annoying to code and would just serve to make higher skills even more advantageous. The big thing I left out was Fate points. There use should matter greatly, but because they are highly character- and situation–dependent, there is simply no way to reasonably model them. However, I do discuss Fate points later. I assumed that both Pain and Suffering had 5 boxes on their stress tracks. Some skills can make this number go up, but that should just serve to make the combat longer and increase the differences between skills. So I decided to use the base 5 boxes. I also assumed that neither combatant had any applicable combat stunts. Some stunts can affect combat, but not all characters have such stunts and certainly not for all types of combat, so I ignored them. Finally, I assumed that each combatant’s offensive and defensive skills where identical. This is not always the case in SotC. The guns skill normally only gives offense, not defense, while athletics gives defense but no offense. However, skills like melee can provide both and, even if using different skills, they can easily be the same level. So for simplicity’s sake I assumed that they were the same.

Spirit of the Century Results

Again, I tested the model by setting Pain and Suffering to equal skill levels and running 50,000 simulated combats until one combatant, the other, or both were taken out. As before, the results showed Pain and Suffering with an equal number of wins and a small number of ties (Figure 1). sotcpaine At first blush it might seem odd that the combats lasted much longer than the Feng Shui fights, tending to be around 16 to 19 rounds long rather than 8 to 10 (see supplement 1). After all, it takes only 9 minimum damage hits to take someone out in the SotC example while it takes 12 minimum damage hits in the Feng Shui model. Two things are causing this. First, in Feng Shui an attack causes damage if it equals or exceeds the defender’s defense. In SotC, only attacks that beat the defense total cause damage, so damage-causing attacks are less likely. Second, the stress and complication mechanics generally suppress the variation in damage results. For example, imagine a defender hit by the following amounts over their defense, in order, 4, 5, 1, 1, 1, 5, and 4. In SotC this would result in box 4 being checked, then box 5. The third hit would check off box 1. The fourth hit would normally check off box 1, but it is full, so it checks off box 2 instead. The fifth hit would check off the 1, but it is full, as is the 2, so it ends up checking off box 3. The sixth hit, for 5 damage, would check off box 5, but it’s full, so it goes over the stress limit and causes a minor complication. Finally the 4 damage hit can’t fill boxes 4 or 5 as they are both full, and causes a moderate complication. Compare this to the result if all the hits did minimum damage, i.e., were 1 above the defender’s total. The first hit checks box 1, the second box 2, since box 1 is full. This continues until the fifth hit fills the final stress box. The two subsequent hits cause a minor and moderate complication, respectively. The end difference between a series of mostly powerful hits and a series of minimum damage hits is nothing. If the same series are compared in Feng Shui, assuming our base damage of 3, the first series does a total of 42 damage, more than enough to defeat an opponent. The second series would do 28 damage, leaving the opponent standing. A couple of solid hits in Feng Shui can really shorten the fight. But what about unequal skill levels? I had assumed that the results would look a great deal like those for Feng Shui (see supplement 1). My jaw dropped when I saw the results presented in figure 2. sotcpain1 When Pain was set to one lower skill than Suffering, out of 50,000 simulated combats Pain won once and tied once. Again, that is out of 50,000. In the absence of Fate points, a difference of a single level in combat skill is insurmountable! For what it’s worth a comparison to non-combat rolls is presented in Table 1. Again, I use the sum of Pain’s wins and ties, not that it matters much.

Table 1: SotC Combat Versus Non-Combat Results

Pain’s Skill relative to difficulty Non-Combat Combat
% chance of success % chance of win or tie
2 94 100
1 81 100
0 62 53
-1 38 0.004
-2 19 0

These results have a couple of implications. First, Fate points aren’t an important mechanic. They are an absolutely critical mechanic. In the case of unequal skill levels, the only variation in combat results comes from the use of Fate points. Second, GMs really need to keep an eye on characters’ combat skills. An opponent with a skill of 4 would be zero threat to a character with a 5 combat skill but, barring Fate points, an unstoppable foe to a character with a 3 combat skill.

Why the difference?

Why are the results so different between Feng Shui and Spirit of the Century? Variance seems a likely explanation. A lower variance dice mechanic should exacerbate the problem of multiple rolls. However, comparing Feng Shui and SotC takes a little maneuvering. In Feng Shui, only the attacker rolls. In SotC, both the attacker and defender roll. Fortunately, with Fudge dice, unless there are rerolls, having the attacker roll 4 dice and the defender roll 4 dice is mathematically equivalent of having the attacker roll 8 dice and the defender not roll. So I compared the Feng Shui roll with a roll of 8 Fudge dice as shown in Figure 3. fengsotc Feng Shui does have more variance in its results, but not huge amounts more. It seems difficult for that to completely explain the difference. But remember that the stress and complication mechanics tend to reduce variance. In SotC a large hit like a 4 or 5 is at the end likely to be pretty much the equivalent of a minimum value hit. A couple of lucky blows by the underdog are not going to have much effect on the combat’s outcome.


The results here reinforce the finding that combat results are more consistent. But what really comes through is that the choice of mechanics has a very large effect on how much consistency is present in combat. The analysis has also given my some insights into how SotC would work if I ever manage to actually run it.


6 Responses

  1. Great stuff Erik!

    In a con, I played in a SOTC game. The character was a Face character, Social Skills out the wazoo. In one scene, we were at a party, and two of the other players, bricks, tried to engage a NPC in a contest of wills and were having their clocks cleaned by the NPC. I just walked up an prevented them from getting 5 ticks and in a matter of a couple of rounds I totally devastated the NPC with my social skills.

    In combat he wasn’t as good, but he did do a couple of interesting moves and pulled a finishing move that ended the combat.

    What does this have to do with your analysis? Well, it sort of confirms it. My character’s social skills were so massive, he could render anyone to putty in his hands with ease. His combat skills were only comparable to the NPCs and subsequently they were much harder to deal with. That’s why I had him hold back and let the bricks do their work. And they did a very good job. They were substantially better at shooting and fisticuffs than their opponents.

    What’s amazing is the fact that one point difference in levels yielded such overwhelming results… It’s amazing!

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