In resource management games, I typically have a set of coefficients in my head for the current relative marginal values of different resources, and my primary heuristic is usually maximizing the weighted sum of my resources according to these coefficients.
In combat strategy games, I usually try to maximize (my rate of damage) x (maximum damage I can sustain before I lose) / (enemy rate of damage) x (damage I need to cause before I win).
These don’t seem especially profound to me. But I’ve noticed a surprising number of video games that make it distressingly hard to track these things; for instance, by making it so that the data you need to calculate them is split across three different UI screens, or by failing to disclose the key mathematical relationships between the public variables and the heuristics I’m trying to track. (“You can choose +5 armor or +10 accuracy. No, we’re not planning to tell you the mathematical relationship between armor or accuracy and observable game outcomes, why do you ask?”)
It’s always felt odd to me that there isn’t widespread griping about such games.
As a result of reading this post, I have started explicitly tracking two hypotheses that I wasn’t before: (1) that the value of tracking things-like-these is much less obvious than I think, and (2) that a lot of people lack the spare cognitive capacity to track the things I’m tracking.
Though I’m not sure yet whether they’re going to steal much probability from my previous leading hypothesis, “most players are not willing to do mental multiplication in order to play better.”
I’m very certain that you hypothesis are correct. Most people play to have fun, not to win. Winning is instrumental to fun, but for most people it is not worth the cost of doing some math, which is anti-fun. I like math in general, but I still would not make this explicit calculation, because it is the wrong type of math for me to enjoy. (Not saying it is wrong for you to enjoy it, just that it’s unusual.)
I think that making the game design such that it is hard or impossible to do the explicit math is a feature. Most people don’t want to do the math. The math is not supposed to be part of the game. Most people don’t want the math nerds to have that advantage, because then they’ll have to do the math too, or loose.
That seems like it could only potentially be a feature in competitive games; yet I see it all the time in single-player games with no obvious nods to competition (e.g. no leaderboards). In fact, I have the vague impression games that emphasize competition tend to be more legible—although it’s possible I only have this impression from player-created resources like wikis rather than actual differences in developer behavior. (I’ll have to think about this some.)
Also, many of these games show an awful lot of numbers that they don’t, strictly speaking, need to show at all. (I’ve also played some games that don’t show those numbers at all, and I generally conclude that those games aren’t for me.) Offering the player a choice between +5 armor and +10 accuracy implies that the numbers “5” and “10″ are somehow expected to be relevant to the player.
Also, in several cases the developers have been willing to explain more of the math on Internet forums when people ask them. Which makes it seem less like a conscious strategy to withhold those details and more that it just didn’t occur to them that players would want them.
There certainly could be some games where the developers are consciously pursuing an anti-legible-math policy, but it seems to me that the examples I have in mind do not fit this picture very well.
> Offering the player a choice between +5 armor and +10 accuracy implies that the numbers “5” and “10″ are somehow expected to be relevant to the player.
When I imagine a game which offers “+armor” or “+accuracy” vs a game which offers “+5 armor” or “+10 accuracy”, the latter feels far more comfortable even if I do not intend to do the maths. I suspect it gives something for my intuition to latch onto, to give me a sense of scale.
Do you mean that it’s more comfortable because you feel it provides some noticeable boost to your ability to predict game outcomes (even without consciously doing math), or is it more of an aesthetic preference where you like seeing numbers even if they don’t provide any actual information? (Or something else?)
If you’re applying a heuristic anything like “+10 accuracy is probably bigger than +5 armor, because 10 is bigger than 5”, then I suspect your heuristic is little better than chance. It’s quite common for marginal-utility-per-point to vary greatly between stats, or even within the same stat at different points along the curve.
If you’re strictly using the numbers to compare differently-sized boosts to the same stat (e.g. +10 accuracy vs +5 accuracy) then that’s reasonably safe.
The improvement to my intuitive predictive ability is definitely a factor to why I find it comforting, I don’t know what fraction of it is aesthetics, I’d say a poorly calibrated 30%. Like maybe it reminds me of games where I could easily calculate the answer, so my brain assumes I am in that situation as long as I don’t test that belief.
I’m definitely only comparing the sizes of changes to the same stat. My intuition also assumes diminishing returns for everything except defense which is accelerating returns—and knowing the size of each step helps inform this.
That seems opposed to what Linda Lisefors said above: You like the idea that you could calculate an answer if you chose to, while Linda thinks the inability to calculate an answer is a feature.
(Nothing wrong with the two of you wanting different things. I am just explicitly de-bucketing you in my head.)
My intuition also assumes diminishing returns for everything except defense which is accelerating returns
My model says that the trend in modern games is towards defense having diminishing returns (or at least non-escalating returns), as more developers become aware of that as a thing to track. I think of armor in WarCraft 3 as being an early trendsetter in this regard (though I haven’t gone looking for examples, so it could be that’s just the game I happened to play rather than an actual trendsetter).
I am now explicitly noticing this explanation implies that my model contains some sort of baseline competence level of strategic mathematics in the general population that is very low by my standards but slowly rising, and that this competence is enough of a bottleneck on game design that this rise is having noticeable effects. This seems to be in tension with the “players just don’t want to multiply” explanation.
No, we’re not planning to tell you the mathematical relationship between armor or accuracy and observable game outcomes
You wouldn’t have that in reality either, and in reality, the relationship would be even more complicated. I think a fair compromise would be to give you a simplified relationship like “+1 armor increases the damage it can absorb by 20%” when it is more complicated than that (min/max damage, non-linearity).
Many years ago, I used to think it would be great if a game gave you just the information that you would have had “in reality” and asked you to make decisions based on what “would realistically work”.
After trying to play a bunch of games this way, I no longer think this is a sensible approach. Game rules necessarily ignore vast swathes of reality, and there’s no a priori way to know what they’re going to model and what they’re going to cut. I end up making a bunch of decisions optimized around presumed mechanics that turn out not to exist, while ignoring the ones that actually do exist, because the designer didn’t happen to model exactly the same things that I guessed they’d model.
Fundamentally, losing a game because you made incorrect guesses about the rules is Not Fun. (For me.)
My current philosophy is that rules should usually be fully transparent, and I’ve found that any unrealism resulting from this really doesn’t bother me. My primary exception to this philosophy is if the game is specifically designed so that figuring out the rules is part of the game, which I think can be pretty neat if done well, but requires a lot of work to do well.
In most of the games I’ve played where the rules were not transparent, it didn’t look (to me) like they were trying to build gameplay around rules-discovery, or carefully calculating the optimum amount of opacity; it looked (to me) like they just ignored the issue, and the game (in my opinion) suffered for it.
Also, “in reality”, if there were important stakes, and you didn’t know the rules, you’d probably do a lot of experimentation to learn the rules. You can do this in games, too, but in most games this is boring and I’d rather just skip to the results.
In resource management games, I typically have a set of coefficients in my head for the current relative marginal values of different resources, and my primary heuristic is usually maximizing the weighted sum of my resources according to these coefficients.
In combat strategy games, I usually try to maximize (my rate of damage) x (maximum damage I can sustain before I lose) / (enemy rate of damage) x (damage I need to cause before I win).
These don’t seem especially profound to me. But I’ve noticed a surprising number of video games that make it distressingly hard to track these things; for instance, by making it so that the data you need to calculate them is split across three different UI screens, or by failing to disclose the key mathematical relationships between the public variables and the heuristics I’m trying to track. (“You can choose +5 armor or +10 accuracy. No, we’re not planning to tell you the mathematical relationship between armor or accuracy and observable game outcomes, why do you ask?”)
It’s always felt odd to me that there isn’t widespread griping about such games.
As a result of reading this post, I have started explicitly tracking two hypotheses that I wasn’t before: (1) that the value of tracking things-like-these is much less obvious than I think, and (2) that a lot of people lack the spare cognitive capacity to track the things I’m tracking.
Though I’m not sure yet whether they’re going to steal much probability from my previous leading hypothesis, “most players are not willing to do mental multiplication in order to play better.”
I’m very certain that you hypothesis are correct. Most people play to have fun, not to win. Winning is instrumental to fun, but for most people it is not worth the cost of doing some math, which is anti-fun. I like math in general, but I still would not make this explicit calculation, because it is the wrong type of math for me to enjoy. (Not saying it is wrong for you to enjoy it, just that it’s unusual.)
I think that making the game design such that it is hard or impossible to do the explicit math is a feature. Most people don’t want to do the math. The math is not supposed to be part of the game. Most people don’t want the math nerds to have that advantage, because then they’ll have to do the math too, or loose.
That seems like it could only potentially be a feature in competitive games; yet I see it all the time in single-player games with no obvious nods to competition (e.g. no leaderboards). In fact, I have the vague impression games that emphasize competition tend to be more legible—although it’s possible I only have this impression from player-created resources like wikis rather than actual differences in developer behavior. (I’ll have to think about this some.)
Also, many of these games show an awful lot of numbers that they don’t, strictly speaking, need to show at all. (I’ve also played some games that don’t show those numbers at all, and I generally conclude that those games aren’t for me.) Offering the player a choice between +5 armor and +10 accuracy implies that the numbers “5” and “10″ are somehow expected to be relevant to the player.
Also, in several cases the developers have been willing to explain more of the math on Internet forums when people ask them. Which makes it seem less like a conscious strategy to withhold those details and more that it just didn’t occur to them that players would want them.
There certainly could be some games where the developers are consciously pursuing an anti-legible-math policy, but it seems to me that the examples I have in mind do not fit this picture very well.
> Offering the player a choice between +5 armor and +10 accuracy implies that the numbers “5” and “10″ are somehow expected to be relevant to the player.
When I imagine a game which offers “+armor” or “+accuracy” vs a game which offers “+5 armor” or “+10 accuracy”, the latter feels far more comfortable even if I do not intend to do the maths. I suspect it gives something for my intuition to latch onto, to give me a sense of scale.
Do you mean that it’s more comfortable because you feel it provides some noticeable boost to your ability to predict game outcomes (even without consciously doing math), or is it more of an aesthetic preference where you like seeing numbers even if they don’t provide any actual information? (Or something else?)
If you’re applying a heuristic anything like “+10 accuracy is probably bigger than +5 armor, because 10 is bigger than 5”, then I suspect your heuristic is little better than chance. It’s quite common for marginal-utility-per-point to vary greatly between stats, or even within the same stat at different points along the curve.
If you’re strictly using the numbers to compare differently-sized boosts to the same stat (e.g. +10 accuracy vs +5 accuracy) then that’s reasonably safe.
The improvement to my intuitive predictive ability is definitely a factor to why I find it comforting, I don’t know what fraction of it is aesthetics, I’d say a poorly calibrated 30%. Like maybe it reminds me of games where I could easily calculate the answer, so my brain assumes I am in that situation as long as I don’t test that belief.
I’m definitely only comparing the sizes of changes to the same stat. My intuition also assumes diminishing returns for everything except defense which is accelerating returns—and knowing the size of each step helps inform this.
That seems opposed to what Linda Lisefors said above: You like the idea that you could calculate an answer if you chose to, while Linda thinks the inability to calculate an answer is a feature.
(Nothing wrong with the two of you wanting different things. I am just explicitly de-bucketing you in my head.)
My model says that the trend in modern games is towards defense having diminishing returns (or at least non-escalating returns), as more developers become aware of that as a thing to track. I think of armor in WarCraft 3 as being an early trendsetter in this regard (though I haven’t gone looking for examples, so it could be that’s just the game I happened to play rather than an actual trendsetter).
I am now explicitly noticing this explanation implies that my model contains some sort of baseline competence level of strategic mathematics in the general population that is very low by my standards but slowly rising, and that this competence is enough of a bottleneck on game design that this rise is having noticeable effects. This seems to be in tension with the “players just don’t want to multiply” explanation.
You wouldn’t have that in reality either, and in reality, the relationship would be even more complicated. I think a fair compromise would be to give you a simplified relationship like “+1 armor increases the damage it can absorb by 20%” when it is more complicated than that (min/max damage, non-linearity).
Many years ago, I used to think it would be great if a game gave you just the information that you would have had “in reality” and asked you to make decisions based on what “would realistically work”.
After trying to play a bunch of games this way, I no longer think this is a sensible approach. Game rules necessarily ignore vast swathes of reality, and there’s no a priori way to know what they’re going to model and what they’re going to cut. I end up making a bunch of decisions optimized around presumed mechanics that turn out not to exist, while ignoring the ones that actually do exist, because the designer didn’t happen to model exactly the same things that I guessed they’d model.
Fundamentally, losing a game because you made incorrect guesses about the rules is Not Fun. (For me.)
My current philosophy is that rules should usually be fully transparent, and I’ve found that any unrealism resulting from this really doesn’t bother me. My primary exception to this philosophy is if the game is specifically designed so that figuring out the rules is part of the game, which I think can be pretty neat if done well, but requires a lot of work to do well.
In most of the games I’ve played where the rules were not transparent, it didn’t look (to me) like they were trying to build gameplay around rules-discovery, or carefully calculating the optimum amount of opacity; it looked (to me) like they just ignored the issue, and the game (in my opinion) suffered for it.
Also, “in reality”, if there were important stakes, and you didn’t know the rules, you’d probably do a lot of experimentation to learn the rules. You can do this in games, too, but in most games this is boring and I’d rather just skip to the results.