Models, simulations and games all seem to use modifiers, but there doesn’t seem to be any explanation for what they are and why they have the set values they are assigned. So I have to ask, what are modifiers? No, seriously, what are they? I’m sure the question comes across as being rhetorical, but it’s not. I’ve been designing games for over thirty years and I don’t have an answer. Sadly, anyone who thinks that I would have a solid idea of what they are because I use them would be mistaken. I know how to use them enough to fake it, and I suspect that I’m not alone. I understand how to use the math well enough, but that isn’t the same thing as understanding the concept. I might stumble through this essay the way I often find myself doing when developing a game, but my attempt here is to explore the ways in which modifiers are used and try to discern what they are.
The first thing is to recognize that the math behind any game is arbitrary. It’s clear that anything designed to simulate reality is an artifice at best and cumbersome at worst. The goal is to have a semblance of balance. So, a game utilizing discrete probability like Chutes & Ladders is predicated upon. The fairness in such a game is that the results are random for everyone and the bonuses and penalties are contingent on what space you land on for your next move. The situation is theoretically outside of player control with the exception of a person’s dice rolling or spinner manipulation skills. Monopoly uses doubles to modify the game with bonuses and penalties. Mathematically, you have the same chance of rolling a 7 as you do doubles. The board has 40 spaces. If the average value is used, it should take six rolls to go around the board (5.7 if you divide the number of spaces by the average). With a one-in-six chance of a double or 7, this comes out to about five turns to complete a circuit around the board. The modifier means everyone gets paid around the same time. Equilibrium a game does not make, however. Unlike linear board games with instructions printed on them like “go back 3 spaces,” Monopoly uses three options to break up equilibrium: Chance, Community Chest, and going to jail. All modify board position or resource management, which effectively amount to the same thing. The dice rolls, a board space, and a Chance card can even halt progression on the board by sending a player to jail. Pay the fines, wait three turns, or throw doubles before then to get out and resume progression. Three rolls later, you should find yourself on the other side of the “Go to Jail” space. There is a recurring value with the dice or turn sequencing and is thus used as a modifier that gets tied to the dice rolls.
Some games just have skewed math, like Risk. The more armies you use to invade a territory, the more likely you are to win even if the opponent has the same number. Part of this lies in the limitations of the defender. In the early stages, it is easier to defend as the number of free armies available to attack is low. This is why consolidation by continent control is vital. Once players begin drawing enough cards to turn in sets for additional reinforcements on top of those gained at the start of a turn, the game begins its runs towards a tipping point. Several modifiers are at play: bonus armies for owning all the territories of a continent, progressively larger numbers of armies gained from turning in a set of cards, and the skewed math that gives an attacker three dice to roll compared to the defender’s two. The game becomes less risky if you make your position as defensible as possible in the early stages. That strategy will have repercussions that might mitigate the effects of probability.
Wargames also use modifiers, but they don’t operate with quite the same abstract nature as board games, though Risk does point to the same type risk/reward scenarios found in wargames. Since the creation of Kreigsspiel, wargames have been built around the notion of relative strength, which Risk represents abstractly. This is the reason many games are limited to specific eras. The value of the units is defined in such a way that the arbitrary math that makes game play possible appears to be less so. Now, the same rules may work quite well for different eras, but this hinges upon the units never appear in battles not of their historical timeframe. One of the reasons is that the modifiers will skew results outside of the artifice of the game mechanics and expose said mechanics for what they truly are: arbitrary. The other is verisimilitude, straining the math too much reveals how it’s just a grainy approximation. Imagine a unit of English longbowmen squaring off with machine gunners from WWI, WWII, or the American Civil War which introduced trench warfare and hand-cranked machine guns.
Tactics introduced tabletop board wargaming. It based combat resolution around abstracted odds that reduced each side’s relative strength to a value from one to six for or against and then a die roll on the appropriate table to determine outcome. As a result, it was a game that took the step towards situationally-based modifiers in board games. The amount of strength you brought against your opponent, in this case. Optional rules in Tactics II carried the premise further by doubling defense values based on the terrain in which the unit occupied. These same rules applied to Kriegsspiel, but Tactics set the stage for many of the conventions, including those from Kriegsspiel, for tabletop play without the need for a third-party referee watching over the game. The modifiers didn’t really emphasize what they defined other than an advantage of some sort over the opponent. Modifiers spoke of some element that affected the overall usefulness of a unit in varying terrain or weather conditions. Even a game like Squad Leader doesn’t mention how the numbers translate. Its big brother, Advanced Squad Leader, with its intricate rules does not mention what the modifiers represent, only when they apply. The best guess from reading and playing such games is that they represent relative strengths of position, meaning the modifiers are inherent in the situation as much as they are in the unit’s composition. This is no different from Chutes & Ladders and what space you land on if you remove the strategic element.
A lot of this sort of math made its way into roleplaying games because they are the progeny of wargaming. This is why levels of experience have built-in modifiers to combat abilities. The more seasoned one becomes, the more efficient he is in combat. Likewise, the more proficient one becomes in a profession increases the speed and ease at which tasks can be preformed. But what measures the strength of position for noncombat related events? Performing research or conducting and investigation are not the same as holding the high ground in a firefight. While having the right tools is paramount, they don’t fully explain how or why some modifiers apply to their use.
Performance under stress shows how artificial modifiers are. Why are characters performing a task during combat or under a time crunch considered to be stressed but a combatant facing an obvious superior foe isn’t? Some games, like Dungeons & Dragons, use a morale check to see if creatures and nonplayer characters will flee or fight, but not player characters. Unless a player decides otherwise or the character is compelled supernaturally to turn and run, the character stands his ground. Both provide sources of undue stress, but in the case of combat, it’s somehow subsumed into the system. Physical actions, or those not related to Wisdom and Intelligence, also seem to catch a break so that only mental actions that require concentration of any amount bear the brunt of situational modifiers in combat, unless they are related to environmental conditions.
The question remains, however, of what the modifiers represent. The strength of position argument seems invalid since there can never be an advantage to performing a task under pressure during combat that isn’t related to fighting opponents. What strength in position is there in having access to a vast library if you do not know where to start? Consider that even if you find the right sources, do they have enough pointers (index, table of contents, etc.) that would speed up the process? Say the character has to diffuse a bomb. Outside of the device’s complexity and his knowledge of explosives or electronics, there is not strengths of position to measure. The threat of death should be enough that a firefight should not be an additional stressor if the character is protected by allies. That said, ducking bullets is another issue altogether meriting its own modifier. The circumstances aren’t the same however. The math might be, but that doesn’t seem to be a logical or reasonable fix.
Complexity might come close to replicating the challenges faced in the midst of combat, but the methods by which the actions are resolved are still suspect. In an attempt to discern what is going on, let’s look at a few systems and try to untangle the issue’s nuances. Dungeons & Dragons 3.5 uses a rather simple system modeled on the bell curve used to generate ability scores which it has inherited from the original rules. The average value of the three six-sided dice is the same as a twenty-sided die. The average result for a d6 is 3.5 and 10.5 for a d20. As such, 3.5 x 3 = 10.5. While the new method of character generation uses 4d6, drop the lowest value, the average is still 10.5 as scores will still fall between 3 and 18. So the modifiers from ability scores (which roughly coincide with standard deviations) shift the average as much as the number of ranks in a skill. The difficulty is set as a target number or higher to be rolled with the bonuses from skill proficiency and ability scores. It is the same mechanic as combat, but again there is no penalties for facing a superior opponent that aren’t already factored into the target’s Armor Class, the character’s level, and environmental conditions. When you attack a noncombat challenge, its “Armor Class” is the Difficulty Check. Granted, combat can be – and often is – construed as an environmental condition, but if you are trained for combat conditions or can perform certain tasks without thought you’d pay attention to other stimuli, like tying your shoes; you don’t think about the steps involved, you mastered it and look at your surroundings. So, why is it that the characters can’t do the same for something like First Aid if they are reasonably free from attack, ranged or melee? D20 Modern should follow the same line of thought as it has options for characters in military service. A demolitions expert shielded by allies and obstacles should get the same break, but doesn’t. Being trained under fire or pressure doesn’t grant a reprieve, to include not drawing an attack of opportunity because you aren’t on your guard. One can argue that feats like Skill Focus or class abilities count, but a +3 bonus or taking a flat 10 on a roll plus skill ranks and other bonuses is not the same if the penalties for combat still apply to the character. If anything, it papers over the issue by reducing everything to just the numbers.
The problem of the approach is in the mechanics as much as it is the math used to hide any concerns. Ability scores are generated using a bell curve and then resolutions are done using a linear system. Yes, the aggrate of the dice rolls average out to 10.5, but the rolls can’t be taken across the lifetime of the character when increases in skills are also linear. The Difficulty Check is also linear. It’s weighted towards the average, but it is still a flat line. The die itself will always roll from one to twenty. As a character progresses through levels, the accumulated skill points and feats require that the DC continues to increase like the AC of opponents to keep apace to provide a challenge. In effect, you have a system that ranks the differences between success and failure in 5% increments. A DC of 15 means there is a 70% chance of failure; a DC of 20, 100%, and a DC of 25, 125%. Now, when you factor in skill ranks, bonuses, feats, etc., that failure rate starts to drop, but it’s always uniform. The higher DC scores are meant to put some tasks out of reach for the nonprofessional, but the effects of the bell curve average over time always remains. The characters are essentially just getting better in their specialties, but the bell curve is just shifting. The character is like a surfer riding a wave with the adjustments acting like a tidal force to keep them moving.
How does this modifier fall short? The assumption is that the bell curve still applies to everyone of the same level of skill. Everyone is essentially the same and it becomes the province of the die’s results. The modifier doesn’t account for the situation, it accounts for likely factors that move the percentage of failure up or down while masking that the unquantifiable aspects of the situation are referenced in the die roll. It’s a mask because the modifiers affect the fixed value of the character’s proficiency in the skill. That said, if you change the DC, you are saying the task is not as hard as one believed it to be. Thus, either anyone can (almost) do it, or few can. The game is still fun, it just doesn’t do a good job explaining why, how or what adjustments are or represent and it’s too easy to manipulate a fixed incremental percentage value. The artifice requires players to interpret outcomes in a way that also deflects from the shortcomings of the game’s mechanics.
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Anatomy of Game Design: Driven Towards Extinction
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Anatomy of Game Design: Modifiers, Part 2