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Systems can be boiled down to input, process, and output.
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ā Monster: AC 17 ā āā> ā ā <āā ā Player: Attack +3 ā
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ā Player: Long sword ā āā> ā ā <āā ā Player: Strength 14 ā
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ā Monster: Lose 3 HPā
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I don't want to cover the vivid descriptions that GMs might sprinkle onto a game - that's their business. The final result may well have a 'basilisk's leg-tendons sliced open, as it belches a cloud through its screams', but I only want to look at the system support here. So when PCs roll to persuade a guard to let them speak with prisoners, the results are just 'yes/ no' here.
From the point of view of the system, the world has very little life or colour (and this is fine - the system should not strive to define everything possible).
In game terms one might think of a result as a blacksmith successfully making a sword, or being able to hit someone, or pick a pocket. But while those are story results, the real results of the system are often much smaller than that. Within D&D the results for most actions are <yes, no>; either you'll kick in that door or you won't, either you'll climb the wall or fall. Some extend that to {1, yes, no, 20} where '1' and '20' are the die results which grant a special condition each. In combat, the results of a hit extend to {no, 1, 2, 3, 4, 5, 6, critical} where 'critical hits' entail still more results being possible. After this, everything is interpretation - just painting on the statue. Exactly what someone is crafting is left to players' choices and not the system, what someone who has a pocket to be picked owns is a matter for the GM to decide, not the system. And where that short sword has hit, and what it does, are purely GM window-dressing. This isn't to disparage them, but we are here only interested in the meat of the system. With this in mind, D&D can be said to have in its entirety, only the following possible results: {1, 20, no, yes, n damage}.
Games should determine their inputs and outputs by their genre, and those inputs and outputs will determine the genre, even if the designers thinks otherwise.
If sword have stats, that means swords are important. If they don't have stats, it means they're not important.
If the PCs get a 'reputation' stat, then the game is partly about gaining (or losing) reputation.
The last part of a system is marrying up the variables to the results, which is made by a combination of choices and rules, generally including dice.
This is where people are warned away from rolling dice too much, and the reason behind the mistake is clear; if we are to marry variable to result and the only tool the system gives us is to roll dice, then any result will call for a dice roll, else it becomes an arbitrary ruling without the validation of a real result from a rule.
The best kind of mapping is, ceteris paribus, the one which allows us to get results from variables in the shortest amount of time.
Two systems can have the same variables and results while they have a different mapping, and if both have an acceptable probability distribution but one is faster, then that one is better.
As an example, take the soak system of the Storyteller system. The Stamina variable is used to create a result which stipulates how much incoming damage is reduced by. How is the variable mapped to the possible results? The Stamina is rolled as a dice pool and each success is retracted from the damage total, once it is produced. Now to the alternative: when Damage is calculated, the Stamina score is subtracted from the dice pool. We've gotten rid of a dice roll and all the initial results are still possible. The probabilities have changed and the exact range of possible results have changed but the new probability distribution isn't intrinsically bad, it's just different. The result is a cleaner, more efficient system.
Choices generally occur before the system - players chose what to do then the rules take over. I recognise three types of choices.
A good example of complete choices is chess - nobody knows the best move for all occasions but the better players routinely do better.
As an example of a pseudo choice, a D&D fighter in combat might be asked 'What do you do?', but the possible variables are either 'fight' or 'run'. The 'run' mechanic is uninteresting and leads to certain defeat, the 'fight' button is the only choice which allows victory, and even if it doesn't; nobody knows how tough an enemy is so there's little use thinking of stats - one just hits things. Such systems pantomime choices in front of people, occasionally putting in more, small choices such as which of two types of enemies to hit first but largely sticking to the old routine of doing the work for the player and occasionally pretending to care about their input. The biggest aid in this illusion are the dice. It can give players a sense of agency and control - it seems important to players that they roll their own dice instead of the GM rolling for them. The result, of course, won't vary either way. And if dice were absent from the game, with the options of 'continue combat y/n?' blinking from the GM, it would become apparent that this combat is as empty of any participation from them as the overhead light bulb in the room. Pseudo-choices may continue to entertain, but for obvious reasons I consider them to be a poor move for any system.
As to basic choices, there are 'tactical' moves in plenty of games. The Storyteller system, for instance, allows players to make a targeted head-shot, with the penalty of a +2 difficulty (the target number on a dice pool of D10's) and the bonus of an additional die. There is a simple answer to whether or not one should take this tactical move - if you're rolling 4 or more dice then you take it, otherwise you don't. Again, this is a fake choice with a slightly thicker disguise. It suggests a little skill to the game, and suggests players are making a 'brave move' when they go for that head-shot. In reality, no deep tactical decisions are being made, a more skilled player simply knows not to take that option.
Lastly, there are complete choices - the ones which will allow a player to make decisions without being told by the system what the best decision is. Here, players can gain real advantages in terms of results. What should be worrying is that few games can lay claim to a Complete Choice being present anywhere in the game. A Complete Choice would allow a more skilled player to get ahead - perhaps being able to beat a less skilled player with a more experienced character. The only place we commonly find such Complete Choices is within character creation. Within D&D's 3rd Edition, a multitude of Feats, Classes and Spells could be selected. Good players could get ahead, so the system allows true agency. Unfortunately after character creation the choices leave the game; it's an initial rush of ability for the players, followed by an eternal lag into becoming a part of the dice-rolling engine in a system which doesn't require further player input.
Of course, this isn't to say that games do not present real choices, but those choices are system-independent. If the players could attack a group of thugs or just hand over the money - and if both are presented as real options - then that's a real choice. However, the system isn't giving you the choice, it's a choice which you could have had in any system. The systems present in most games do not support any real decision-making.
Different games often require different variables and results - this is a matter of genre, and there can only be a good or bad set of results in relation to what a game is attempting to represent. However, the mapping of variable to results is far more objective - it should require as little time as possible, and therefore as little computing-power as possible. If a game adds more possible results at the cost of more system-faff then that might, for some, be a preferred option. However, for any given range of fixed results, the system should provide those results with the least amount of faff. People asking for 'more crunchy' systems are, I suspect, imagining that a wider range of results necessitates more faff when in fact it does not.
In addition, while so many systems lack in-game Complete Choices, we can still see that they are good, and that they are well worth paying for in terms of a little system-faff.
These two goods a game can provide - efficient rules and complete choices - are paid for with system faff. And while two people may be able to stomach more or less system faff, or enjoy better mapping or more variables to different degrees, there are objectively better and worse ways of making a system, given any fixed variables and desire for complete choices. There are plenty of pairs of games which share nearly identical inputs and outputs, but one is simply slower than the other. There are also games which add small details which are unwanted at the cost of too much faff. Take for example D&D 3.5's distinction between spotting something, hearing something and searching for things - that's a lot of fine distinctions between one's ability to perceive things, and may as well have just been a perception stat (as it was later).
The value of a complete choice must be high, or else we only value the illusion the game gives of choices. However, it will inevitably vary in value from person to person. If the value of a choice could be given an absolute number, in comparison to a roll or recording of an action's results then systems could be given a more complete rating of how good they are. For example, in an earlier post I suggested that a die roll be given 2 'faff points'. If a complete choice is valued at 4 faff-points then we are saying we are ambivalent between one system, and an identical system which adds in two additional dice rolls and a single complete choice.