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A little bit of a riddle and challenge for all you mathematicians out there! Could you use maths to create an equation to give each unit a point value set around stats? Basically, have 40k work like a spreadsheet. You add the units toughness, number of shots, weapon type, bs, ect... into some boxes and the maths converts them into points. Then you do the same to every unit and boom! Balance game.

Obviously extra rules and bonuses on top would throw everything off but for argument sake let's pretend they don't exist.

One issue would be how some stats synergies with each other. A wound on a toughness 1 model is not worth the same as a wound on a T8 one, same with saves

Attacks are worth more on models with better move/strength/WS.

While it might be possible to make a complex formula, it would not be easy, or even possible to set up so it could not be gamed/broken.

And that’s not even going into things like access to gear, or role. Marines pay for a statline they only use part of for each type of squad. But they do get some utility for being well rounded.

Yes, you could. It would take some work, but you could.

The problem would be extraneous effects, spells, stratagems, etc. Those would complicate everything. But a basic stat-line and basic weapon components could be costed out. The initial values would be somewhat arbitrary of course.

I have a character creation method for one of the games I sell. It's not nearly as complex, but each of the six stats has a simple cost associated with it - costs increased for more "important" stats (shooting, fighting, etc.). I use the same method when I create actual characters for the game.

As the depth increases the arbitrary decisions would increase - but as a basic premise, yes it's possible.

This is not remotely feasible. You can do a pretty good job just identifying some known well-priced units and then comparing what you've got to them and making small adjustments, but figuring out an all-inclusive formula for whatever oddball combination of stats you can come up with is just not worth attempting, especially if you're trying to include things like units where models can be equipped differently, etc.

There's also no one right way to do it. Relative costs for very different units are to some extent arbitrary. Tanks and light infantry are vulnerable to very different kinds of weapons, and so the durability of tanks relative to light infantry depends on the costs of anti-tank and anti-infantry weapons, as well as on the meta you're trying to cultivate.

Probably not across all units and factions, no. That's simply too much data for one formula.

GW has somewhat tried this with the "one wargear per codex" concept. However there's non-points based balance here, like the Rhino not being able to use twin lascannons.

 lolman1c wrote:
A little bit of a riddle and challenge for all you mathematicians out there! Could you use maths to create an equation to give each unit a point value set around stats? Basically, have 40k work like a spreadsheet. You add the units toughness, number of shots, weapon type, bs, ect... into some boxes and the maths converts them into points. Then you do the same to every unit and boom! Balance game.

Obviously extra rules and bonuses on top would throw everything off but for argument sake let's pretend they don't exist.

Almost certainly not. There's far too much contextual variability in 40k, which is why balance always seems so weird.

How do you balance taking a powersword vs a powermaul on a squad sergeant in a game involving titans? How do you value long range weapons that dont need LoS when tables can be barren and empty or densely packed with terrain? What about playing on a 4x4 table versus a 6x4? Etc ad nauseum.

There's a reason GW doesn't stick doggedly to some formula or set of equations. Most of it is kinda subjective feel and comparison to equivalents.

You can in theory do it. In practice the amount of work required will be vastly more than what it would take to do the conventional iterative playtesting process, where you start with a rough guess of a unit's point cost, and alternate playing test games and making point changes until you get it right.

What you’re describing is effectively a pricing model. How does your insurance company determine the price of insurance? Pricing model. Same concept here; anyone who says that a bound system like 40k is more complex than the real world is wrong. In the real world, financial analysts, actuaries, and other people typically associated with the finance sector will undertake the activity described.

If we take a few samples of units that are considered balanced as the baseline, we can check the effectiveness of our model against other units (by comparing the rule book price to our model’s guess). When we’re happy with the quality (read: accuracy of guesses), we can use the model to determine what the pricing should be on new and arbitrary stat blocks.

Sorcererbob wrote:
What you’re describing is effectively a pricing model. How does your insurance company determine the price of insurance? Pricing model. Same concept here; anyone who says that a bound system like 40k is more complex than the real world is wrong. In the real world, financial analysts, actuaries, and other people typically associated with the finance sector will undertake the activity described.

If we take a few samples of units that are considered balanced as the baseline, we can check the effectiveness of our model against other units (by comparing the rule book price to our model’s guess). When we’re happy with the quality (read: accuracy of guesses), we can use the model to determine what the pricing should be on new and arbitrary stat blocks.

The difference is that in the real world, averages are good enough.

How do you price a 1-shot, 2+ to hit rerolling 1s, strength 60 100 damage weapon with Macro that ignores Void Shields? It's got about a 50% chance of killing a 3pt Brimstone Horror and about a 100% chance of killing a 6000 point Warlord Titan.

The average is going to be horrible (well, the average between 2pts and 6000 points is like 3001 points, right? Clearly this weapon should cost 3000 points), with a points efficiency of like 0.0013 against conscripts.

Sorcererbob wrote:
What you’re describing is effectively a pricing model. How does your insurance company determine the price of insurance? Pricing model. Same concept here; anyone who says that a bound system like 40k is more complex than the real world is wrong. In the real world, financial analysts, actuaries, and other people typically associated with the finance sector will undertake the activity described.

If we take a few samples of units that are considered balanced as the baseline, we can check the effectiveness of our model against other units (by comparing the rule book price to our model’s guess). When we’re happy with the quality (read: accuracy of guesses), we can use the model to determine what the pricing should be on new and arbitrary stat blocks.

The big problem (beyond the degree to which you need different prices for weapons on units depending on a number of variables) is weighting range and movement properly, but I've got some ideas on that front.

I figure if you wanted to pick a few baseline units to use as a pivot you could theoretically figure out which units, when chosen as the pivot, require the fewest changes to the rest of the game, and then make your baseline assumption based on that.


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 Unit1126PLL wrote:
...How do you price a 1-shot, 2+ to hit rerolling 1s, strength 60 100 damage weapon with Macro that ignores Void Shields? It's got about a 50% chance of killing a 3pt Brimstone Horror and about a 100% chance of killing a 6000 point Warlord Titan...

My theory on that is to figure out an average distribution of targets (based on some kind of archive of army lists) and then value the weapon based on how effective it is against a "normal" distribution. Not perfect (not only because the act of repricing things based on that model might change the distribution of army lists), but it's a place to start asking the question.

What is a "normal distribution" of units? Armies change all the time; heck, you'd have 6 months of data in this presumed "archive" from 8th edition in it right now and the top tournament lists have been 3 Lords of War fighting against 400 conscripts and Guilliman, and shifted considerably from the 5 Stormravens of yore.

I'm not sure you could make a "normal distribution" that would give that weapon a fair price ever.

If the question is "can it be done with the current 40K to achieve ultimate ballance" then the answer is no, because you have abilities that depend not on your stat or trait, but on the TARGETED ENEMY stats or traits. In such environment all you can do is to cost abilities on statistical utility in a "meta", i.e. how likely you are to face an enemy against whom such ability is usefull. But not only meta changes constantly, it is also localized, so a single world-wide point costs won't get rid of all FLGSs rage. This was more pronounced during 7th than now (how much is Haywire USR worth agains Tyranids?), but is still a thing. You would need something like constatnly updated "stock market" for point costs.

But if the question is "can such system be utlised to develop a game from scratch" then this is largely an open question. You can do such formulas for simple games but with added complexity such formulas get complicated quite quickly. Depending on how exactly you count "unique factions", 40K has more than 400 faction vs faction matchups alone. Then you must take into account, that 40K is based on a premise, that every faction should feel different enough from all others. Then add sandbox nature of listbuilding, and "environment conditions" such as table size, terrain setup style, winning conditions etc... Seeking mathematical ballance is pretty much the same goal as solving increasingly larger GO boards. Even in modern days of cheap computing power availability, 5x5 board was only solved in 2002, largest solved GO board now is 6x6 while standard game takes place on a 19x19. And this is a game with very, very simple rules and only one type of "unit" and very basic "unit interactions".

Edit: largest solved GO board is now 7x7...

No you can not because there are too many variables involved. How do you value a weapon that ignores LOS? That depends on terrain which is not standardized. How do you value a unit with the conscript stat line? The value is different in an army like AM with good shooting, than it is for orks. It is also different depending on buffs available. Balance can only really be approximated with math, then would need adjusting through testing.

Assuming you factored in enough variables, you could probably get the basic cost of a given unit to be pretty well balanced using such a "unit builder." However, this would really only apply to unit's statline and weapons (assuming you didn't just rely on the codex prices for existing weapons).

The thing is, you have to start making a lot of assumptions in order to have any kind of pricing framework at all. X points might be a great cost for a given buffing aura on a given unit assuming you have Y of those units in range of the aura for most of the game. But does that aura become significantly better if you build a list around it?

Actually, here's a more specific example: A captain has an aura that lets marines reroll to-hit rolls while they're around him. Obviously this is much more potent when the captain is standing near missile launcher devs or centurions than when he's standing around regular bolter marines. So do you price the ability based on the assumption that the captain is going to be surrounded by devastators all game, or do you assume the player won't be optimizing quite as hard? If you assume the former, then you're basically overcharging any player that wants a captain to hang out with their tacs and assault marines or whatever.

Now you can set assumptions about a lot of these considerations. You can assume that a captain will frequently be within range of X units that will do about A, B, and C more wounds to GEQs, MEQs, and vehicles as a result of the aura. But that's still not really ideal and will fall apart to context.

A lascannon devastator might be perfectly balanced for its cost using mathematical formula, but it's woefully overpriced when fielded against wave after wave of gaunts.

tldr; You can use such a formula to balance out stats if you make certain assumptions, but it's very easy for any balance you might achieve to quickly become skewed if your assumptions don't happen to hold up for a given match.

You guys are making this more complex than it needs to be. Your pricing model is as strong as the inputs. You want it to consider buffs, line of sight, the impact of movement? Great! You can!

You simply need a way to record and quantify the actions of individual units / kitouts over thousands/millions/billions of games. The best way to do this is probably to create a game simulator with all of the modern rules, and allow the computer to play itself several billion times ala AlphaZero (Google’s chess bot).

Feed the data from that back into your pricing model, adjust pricing, rinse and repeat until everything is within a balance tolerance.

For those of you saying this is impossible, how does this approach fail? It’s infeasible, not impossible.

Exactly, too many moving parts.

And that's not even looking into things that are simply incomparable
How do you price a +6" shooting range compared to +1 weapon strength?
+2" movement range, or +1 to WS.

Then the more unique abilities that bend the rules.
Shooting without line of sight.
The whole fly mechanic
Advance and charge
Free vertical movement
Etc

None of these can be mathed out to point efficiency like simple shooting comparisons are.

And to make matters worse, the game devs CAN'T know what kind of battlefield you are on.
Free vertical movement is worth a whole lot more in tables with a lot of multi level ruins, or outright cityscape than it is in a woodland table or a desert table.
Likewise ignoring line of sight is rather useless when there is hardly anything that blocks lines of sight.


All these situational abilities range from useless to amazing, depending on factors you can't possibly know during development/balancing as they are not constants nor predictable.
You either have them cost right when the ability is weak, and then it's situationaly OP, or cost right under the proper conditions and then they are usually useless.

The advantage video game RTS games has is that the realm of possibility is far more narrow, and devs can tell about how likely these conditions are to happen, or even enforce every match to have a given amount of these conditions that is enough to matter, but not enough to dominate.
Add the fact "army building" is far more reactive there, so you can afford to have your games have units who are only useful in odd conditions, as players (at least good ones) can tell by map and opponent when said conditions apply and THEN build these units.

You want all the oddities to be even remotely balancable, you need to change the way the game is played.
If lists are made only after you see the table and know what faction you are facing, they could balance all the "silver bullet" choices to be good only in given scenarios, and it will be fine, as the will only ever show up under said scenario.

Sorcererbob wrote:
You guys are making this more complex than it needs to be. Your pricing model is as strong as the inputs. You want it to consider buffs, line of sight, the impact of movement? Great! You can!

You simply need a way to record and quantify the actions of individual units / kitouts over thousands/millions/billions of games. The best way to do this is probably to create a game simulator with all of the modern rules, and allow the computer to play itself several billion times ala AlphaZero (Google’s chess bot).

Feed the data from that back into your pricing model, adjust pricing, rinse and repeat until everything is within a balance tolerance.

For those of you saying this is impossible, how does this approach fail? It’s infeasible, not impossible.

with google and microsoft farming out AI tools to different companies now, it might not be as infeasable as you think for GW to work with one of them to apply that kind of AI approach to game analysis, the thing is they'd need at least two people reviewing the data that play the game to ensure the resulting stuff is actually "fun"

Given a particular formula for pricing everything in the game, how would you even know if the formula had a mistake?

Proving that the formula is correct is nearly impossible - I don't even think we could get past the step of defining what balance is. How many games need to be simulated (there's no way you're playing enough games by hand)? How do you know you covered enough army lists? How do you validate your game-playing AI?

What if I spotted a flaw, and I just wanted to prove the formula is wrong? What counts as a counter-example? Is showing that one list nearly always beats another enough? How many games do I have to play? Do joke lists count? How do you test if a list is a joke?

Let's say my formula is that every model costs zero points. How do you even prove that's unbalanced?

 Elbows wrote:
Yes, you could. It would take some work, but you could.

The problem would be extraneous effects, spells, stratagems, etc. Those would complicate everything. But a basic stat-line and basic weapon components could be costed out. The initial values would be somewhat arbitrary of course.

I have a character creation method for one of the games I sell. It's not nearly as complex, but each of the six stats has a simple cost associated with it - costs increased for more "important" stats (shooting, fighting, etc.). I use the same method when I create actual characters for the game.

As the depth increases the arbitrary decisions would increase - but as a basic premise, yes it's possible.

It honestly doesn't matter if they get 'perfect mathematical balance'.

Players would still SAY it was imbalance.

ERJAK wrote:

 Elbows wrote:
Yes, you could. It would take some work, but you could.

The problem would be extraneous effects, spells, stratagems, etc. Those would complicate everything. But a basic stat-line and basic weapon components could be costed out. The initial values would be somewhat arbitrary of course.

I have a character creation method for one of the games I sell. It's not nearly as complex, but each of the six stats has a simple cost associated with it - costs increased for more "important" stats (shooting, fighting, etc.). I use the same method when I create actual characters for the game.

As the depth increases the arbitrary decisions would increase - but as a basic premise, yes it's possible.

It honestly doesn't matter if they get 'perfect mathematical balance'.

Players would still SAY it was imbalance.

The basic problem with the question (and with the responses I'm seeing) is that you can produce decent mathematical balance for a general case of a "40k game", but everything is still going to be matchup-dependent to enough of a degree that something that's "balanced" in a general sense may be unbalanced in the context of a specific game.

A mathematical approach isn't going to produce a perfect answer, but I do think it could produce something better than what we've got in a number of cases.

You can’t expect a perfect answer; many of the responders in this thread are seeking a beautiful unison of mathematically perfect moving parts. It won’t happen.

To those comments saying “you can’t compare X to Y”, yes you can. Is a bishop or a rook more valuable going into the chess end game? How do you compare moving diagonally to moving up and down? The answer is in the impact the piece has over a large number of games.

The original poster wanted to specifically omit complexities such as buffs. Within the confines of the original question, it’s entirely possible to create a model that will tell you which units are strong for their points and which units are weak for their points based on stat line online.

You cannot balance 40k mathematically due to so many subjective factors that go into the efficiency of things.

There are too many issues where stuff can be good or bad depending on the scenario. Yes Grapnel Launchers are great... when there is adequate terrain and LOS blocking buildings to take advantage of it. Open field? Completely worthless. Then you have the efficiency of things like weapons being costed differently for different units based on a mathematical vacuum. You can't price something correctly in a vacuum. In a vacuum, psykers with full smite were priced correctly. When used in an army and spammed multiple times, it became a problem. So now what? Do you price them where they should be assuming people won't abuse them or do you price them out of viability to prevent it? A balanced game is completely subjective and there is no objective answer. Chess is arguably one of the most balanced games in the history of gaming but is still arguably unbalanced in the favor of the first turn player.


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Sorcererbob wrote:
You can’t expect a perfect answer; many of the responders in this thread are seeking a beautiful unison of mathematically perfect moving parts. It won’t happen.

To those comments saying “you can’t compare X to Y”, yes you can. Is a bishop or a rook more valuable going into the chess end game? How do you compare moving diagonally to moving up and down? The answer is in the impact the piece has over a large number of games.

The original poster wanted to specifically omit complexities such as buffs. Within the confines of the original question, it’s entirely possible to create a model that will tell you which units are strong for their points and which units are weak for their points based on stat line online.

Actually a rook is worth more since you can checkmate someone with two rooks alone and not two bishops alone. From what you're saying, there is an objective end game in chess that is static. 40k isn't. That's what people need to understand.

Hoodwink wrote:
...A balanced game is completely subjective and there is no objective answer. Chess is arguably one of the most balanced games in the history of gaming but is still arguably unbalanced in the favor of the first turn player...

There is an objective answer. The problem with balancing 40k is that it isn't a "game" in the sense that there's a defined set of conditions that exist and a clear game tree, it's a set of conditions used to construct a "game". The "game" starts with army selection, which (assuming both players have brought a list not knowing what the game is going to be) is a matter of guesswork. Comparisons to chess are sort of wonky for that reason.

(The first-play advantage in chess is quantifiable and objective by looking at the winrate over a large number of games, by the way. https://en.wikipedia.org/wiki/First-move_advantage_in_chess for more details.)

Chess has a single objective condition in a static environment. 40k is not remotely close. How do you quantify the cost of a lascannon's range when you might deploy on the long side or short side. Its usefulness is absolutely less when deployed long side of the board. Its range outranges the table. You could just split the difference down the middle, but then you force people to play a static game. What if my area enjoys deploying on the long side of the board? Am I supposed to just say the extra cost associated with the extra negligible range is still balanced?

You can't perfectly balance a game like 40k that includes so many subjective environmental factors. You can achieve a very good balance. But it will never be a perfect balance. You can only balance the game for those who play within a set and defined list of parameters. For everyone else, it will be unbalanced.

Sorcererbob wrote:
You guys are making this more complex than it needs to be. Your pricing model is as strong as the inputs. You want it to consider buffs, line of sight, the impact of movement? Great! You can!

You simply need a way to record and quantify the actions of individual units / kitouts over thousands/millions/billions of games. The best way to do this is probably to create a game simulator with all of the modern rules, and allow the computer to play itself several billion times ala AlphaZero (Google’s chess bot).

Feed the data from that back into your pricing model, adjust pricing, rinse and repeat until everything is within a balance tolerance.

For those of you saying this is impossible, how does this approach fail? It’s infeasible, not impossible.

The issue is chess has a limited set of possible moves in any given scenario, 40k does not. Further terrain will be different, there are millions of possible army combinations, different points values etc. so maybe given unlimited time it is possible, but with all the options you could probably have the thing play a billion games and not even fully test every possible unit in the space marine book, in every combination at multiple points values. There are something like 170 load outs for a 5 man tactical squad alone

Also let's not forget that units vary in efficiency based on the matchups. A T8+ model is absolutely better against an army like Grey Knights than melta Sisters of Battle. So if I have an army almost solely T8, I will absolutely do better on matchup alone against Grey Knights. Balance would dictate a 50/50 scenario. On the flip side, Grey Knights will do much better than melta Sisters against a Daemon army.

The thing about balancing games is that the only way to get as close to balance as possible is to create imbalances.

Also, great video on perfect imbalance.

https://www.youtube.com/watch?v=e31OSVZF77w

Just because it's not possible doesn't mean GW will be forgiven for not achieving it.

Sorcererbob wrote:
What you’re describing is effectively a pricing model. How does your insurance company determine the price of insurance? Pricing model. Same concept here; anyone who says that a bound system like 40k is more complex than the real world is wrong. In the real world, financial analysts, actuaries, and other people typically associated with the finance sector will undertake the activity described.

If we take a few samples of units that are considered balanced as the baseline, we can check the effectiveness of our model against other units (by comparing the rule book price to our model’s guess). When we’re happy with the quality (read: accuracy of guesses), we can use the model to determine what the pricing should be on new and arbitrary stat blocks.

Sooooort of. The problem is that with 40k, you're essentially smashing multiple markets and segments into the same thing and treating it as one whole. At my work, I'm not trying to price aftermarket motors alongside brazing torches or refrigerant, I'm not trying to compare furnace filters and FLIR instruments, my pricing on heat pumps is completely unrelated to my pricing on tool bags, I'm not going to even bother trying to price out some things individually but rather by the ton, while other items may only be feasible as individual items, they're their own unique markets and segments and scales. With 40k, the game fundamentally mashes everything together, mixing scales of combat freely, and has widely variable contexts in which stuff may be employed.

 Elbows wrote:
Yes, you could. It would take some work, but you could.

The problem would be extraneous effects, spells, stratagems, etc. Those would complicate everything. But a basic stat-line and basic weapon components could be costed out. The initial values would be somewhat arbitrary of course.

I have a character creation method for one of the games I sell. It's not nearly as complex, but each of the six stats has a simple cost associated with it - costs increased for more "important" stats (shooting, fighting, etc.). I use the same method when I create actual characters for the game.

As the depth increases the arbitrary decisions would increase - but as a basic premise, yes it's possible.

No you can't. Any formula attempt to balance things out don't work out. Never been, never will. Or else it would have to be super complex as everything would have to depend on everything. Value of attack would have to depend on WS, S, weapons it can carry and survivability etc.

Hoodwink wrote:
Balance would dictate a 50/50 scenario.

This is not true. Balance dictates a roughly 50/50 win rate over a large number of games against a diverse range of opposing lists, not that every single matchup be 50/50. For example, having a 60/40 matchup against one list is fine if it's balanced out by a 40/60 matchup against another list.


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Wyldhunt wrote:
Actually, here's a more specific example: A captain has an aura that lets marines reroll to-hit rolls while they're around him. Obviously this is much more potent when the captain is standing near missile launcher devs or centurions than when he's standing around regular bolter marines. So do you price the ability based on the assumption that the captain is going to be surrounded by devastators all game, or do you assume the player won't be optimizing quite as hard? If you assume the former, then you're basically overcharging any player that wants a captain to hang out with their tacs and assault marines or whatever.

Easy answer: you price based on buffing the devastators. Balance can not and should not account for stupid plays, if a player wishes to use a poor strategy and put their captain in a less-effective location then that's their fault. Pricing units based on anything but their ideal usage means that there will be an overpowered use available for those players who wish to abuse it.


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Breng77 wrote:
No you can not because there are too many variables involved. How do you value a weapon that ignores LOS? That depends on terrain which is not standardized. How do you value a unit with the conscript stat line? The value is different in an army like AM with good shooting, than it is for orks. It is also different depending on buffs available. Balance can only really be approximated with math, then would need adjusting through testing.

These variables are not an obstacle to math. You handle it the same way you handle it with playtesting, by evaluating a unit/list/whatever against a diverse metagame. As a very rough approximation you'd have something like point cost = (best-case value)x(probability of seeing best-case scenario) + (worst-case value)x(probability of seeing worst-case scenario), where each situation contributes a share of the point cost approximately equal to how frequently it occurs. And if you can figure out the relative frequency of each situation well enough to have meaningful playtesting then you can incorporate this into your mathematical model.