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ShadowJak

Reverse Engineered Squad Point Formula

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kmanweiss said:

R5Don4 said:

 

 Fascinating that the maneuver dials also do not factor into ship cost either.

  

 

This is my problem too.  I actually did the math on this weeks ago and came up with the same numbers, but it just didn't feel right.  The manuever dials add and detract so much value to the different craft.   The lack of value for abilities bugged me also.  I keep thinking something's missing.

I suppose they may have just decided to throw some of that stuff to the winds, but it feels so wrong mathmatically to ignore factos that make such a big difference to ships.

That's a bit of a facile view of the balance of the game. Just because the model doesn't take into account things like Action Bars, upgrade icons, the difference between Attack and Defense dice, etc. doesn't mean that the people at FFG ignored those factors as well.

That they didn't ignore those factors is obvious. For example, the Xs look like they are worse than the TIE/ADs on the surface but the Xs have more attack dice instead of defense dice. Each attack die is more than 15% better than a defense die. How should that be factored into action bar abilities and upgrade icons? My model doesn't go into any of that but the people at FFG obviously did or else Xs would have more icons on their bars than they currently do.

Take a look at the difference between the X's movement dial and the Y's. The X's is strictly better. How did FFG take that into account? I'm not sure myself but I think they took into account how powerful the Ion Cannon is (it really is an auto-include).

Part of doing modeling is knowing the model's limitations. The model I came up with is incomplete. It isn't an theory of everything in the game and doesn't claim to be. It models one part of the game, the effect of Ship stats on squad point values. Like I said before, it doesn't take into account action bars, icons, movement dials, abilities, or anything else. It doesn't make sense to say the game is balanced or imbalanced based on it.

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R5Don4 said:

 Yes it seems they went out of their way to force the point cost of the basic ships to correspond with Pilot Value to Point cost which is really quite detrimental.  TIE with Skill X will be 10+X, X-Wing with Skill X will be 20 +X.  And they were trying to fit it all in a 100 point squad because it is a nice sounding number.  If it was say 500, point costs could have been much more "accurate" as to actual effect in the game.

Not at all.

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 Not to demean the work you've done or the excellent work FFG has done with this game, but I really think you're all over-thinking this and missing some important insights into game design.

Typically we design systems with high and low ends, 1-9 seems to be the range on everything so far other than ship cost.  Who knows if anything will exceed that, but it hasn't so far.  Then it's often good to establish a baseline.  In my mind that would be the X-Wing.  So we guess the stats within out limits.  Keeping in mind we know we'll have larger ships, tougher ships, more heavily armed ones, faster ones, etc.  So we guess where we think the X-Wing stands in that range.  Then, we generally just say to ourselves, how much should it cost or how many should we be able to field in a standard point game.  So, we might say, 4 seems good (without upgrades of course), so let's make them 25 points each.  Oh, but with a great pilot like Wedge, it should cost more, or with a crappy Rookie Pilot it should cost less.  You then make more and more ships with that baseline established, making sure to test and balance with play as certain innocent-looking combinations that are balanced for their points can sometimes break things.  So, since some things might be too powerful, you boost their points up or lower their stats accordingly.  The key is that it's tested, repeatedly, until you and your testers all feel it's good.  It's generally far more trial and error and subjective feeling than science.  Not to say a good designer can't get you much closer to the mark initially, but rarely is any designer, no matter how good, going to get it exactly right the first time.

I love the work you're all putting into trying to find some formula for ship point costs, but I don't think I've ever seen a game where that effort pays off quite right.  Usually fans can get close and that's good enough for homebrew stuff, but like I said, the problem is likely that the ships aren't balanced by some magical point formula and more than likely balanced by intuition and repetition.  Initially there is probably a formula and your efforts have probably gotten you close to that starting point.  But there's a lot of variables to account for however, the maneuver dial as others have mentioned is definitely a big one.  I think there has to be some kind of point increase for ships that can take more upgrades as that makes the ship more versatile and that's a big advantage.

I guess that's the end of my rant, like I said, I appreciate the effort you've all put into trying to break this stuff down.  To be honest, I'm pretty good at math and I don't understand most what you're doing… regressions? I think I slept in that day. lol  In the end, though, with design, it's more of an art than a science in my experience and there's always a fudge factor that I think you're forgetting to account for.  Keep up the enthusiasm though, discussion like this is good and keeping the online community alive and excited with it will definitely help the game out in the long term.

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ShadowJak said:

DangerousFat said:

 

Typically we design systems with high and low ends

 

 

Who is "we"?

I'm curious about that as well.  Considering that most of the rant seemed fairly counter-intuitive to a successful game design formula.  There are always factors that aren't as easily accountable for, and variables, but I know from years of experience in discussion with designers, most designers nail down the math as hard as they can everywhere they can.  'Guessing' and 'Estimating' is called 'Playtesting' and where the designers try and balance out those factors and variables. 

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 I mean we as game designers, I do video games, so maybe the world of board games is completely different.  I didn't mean to insinuate that we don't try our best to nail down numbers at the start, of course we do.  Like I said, the better the designer, the closer those numbers will be.  But everything has to be playtested and things often change.  I'm not going to blow smoke at you guys saying how awesome I am or most designers are and I'm not going to tell you that we're awesome and can just get numbers exactly right the first time and anyone who says they can or do is either way better than any designer I've ever met, is luckier than anyone I've ever met, or is lying.  

I don't know how anything I said was counter-intuitive to good game design, however.  I'm sorry nothing I said jelled with the experiences you've had.  Maybe video games are different, maybe my methods are different, maybe the designers I've learned from are different.  

The ultimate point of my "rant" was simply that your math may never line up exactly with every ship as there is most certainly a core that all ships are balanced by initially, but if a ship is a tad too powerful, they may have just added a point or two to the total to bring it in line or knocked down the total is the ship is too weak.  Playtesting ultimately decides how good the initial design was and I've never seen some aspect of the initial design not get changed once the game hits playtesting.  I know Warhammer 40k works exactly like this, they work out the point total for a unit based on tons of factors and playtest it.  Sometimes it's just too powerful or too weak, based on how it plays and despite the numbers, and something has to change.  

 

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DangerousFat said:

 I mean we as game designers, I do video games, so maybe the world of board games is completely different.  I didn't mean to insinuate that we don't try our best to nail down numbers at the start, of course we do.  Like I said, the better the designer, the closer those numbers will be.  But everything has to be playtested and things often change.  I'm not going to blow smoke at you guys saying how awesome I am or most designers are and I'm not going to tell you that we're awesome and can just get numbers exactly right the first time and anyone who says they can or do is either way better than any designer I've ever met, is luckier than anyone I've ever met, or is lying.  

I don't know how anything I said was counter-intuitive to good game design, however.  I'm sorry nothing I said jelled with the experiences you've had.  Maybe video games are different, maybe my methods are different, maybe the designers I've learned from are different.  

The ultimate point of my "rant" was simply that your math may never line up exactly with every ship as there is most certainly a core that all ships are balanced by initially, but if a ship is a tad too powerful, they may have just added a point or two to the total to bring it in line or knocked down the total is the ship is too weak.  Playtesting ultimately decides how good the initial design was and I've never seen some aspect of the initial design not get changed once the game hits playtesting.  I know Warhammer 40k works exactly like this, they work out the point total for a unit based on tons of factors and playtest it.  Sometimes it's just too powerful or too weak, based on how it plays and despite the numbers, and something has to change.  

 

That's cool, you work on anything interesting or any multi-player strategy games?

I think you're not understanding the model I presented or the methods I used to come up with it. First of all, the model isn't complete and doesn't claim to be. The model only predicts ship squad building points based on stats. It doesn't say anything about movement dials, action bars, upgrades, pilot special abilities, or anything else.

It seems like you don't understand what a regression analysis is or how to read one. It isn't a creation tool. It can't be used to make a new game system. Ultimately, the formula the game designers used to come up with ship squad values was arbitrary and derived from intuition and testing. Regression analysis can only show what the underlying formula is, not why it was chosen. I don't know why each attack or defense die above 2 costs 8 squad points instead of any other number. I just know it does. The odds that it doesn't are infinitesimally small (1 in many trillion). That is shown in the regression analysis table in the 't stat' and 'p-value' columns. If you don't understand stats (and by 'stats' I don't mean something as banal as pop culture stat factoids), then you can't understand the significance of those numbers and will probably dismiss what I'm saying.

Also, if you read through the whole post (which I don't think you did, no offense), you will see that I agree with your last point. The formula doesn't fit perfectly and I speculate the deviations (Academy Pilots and most named pilots, specifically) were added for game balance reasons.

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Often times points are added or subtracted to influence game play. My experience so far is that maneuvering is still the most important factor.  Which, of course, I'm not sure how you could mathematically balance that in and of itself without serious playtesting.  I feel as if that may be what some of that mysterious initial cost may be attempting to influence. 

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 Wow.  Wierd to do all that for a game that involves pretending to shoot your plastic toy ships with my plastic toy ships.

 I would rather just play the game with some beer and friends than spend any time whatsoever dissecting it to death.

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Xnath said:

 Wow.  Wierd to do all that for a game that involves pretending to shoot your plastic toy ships with my plastic toy ships.

 I would rather just play the game with some beer and friends than spend any time whatsoever dissecting it to death.

You could say that about any game. That's hardly an enlightened, unique, or even interesting point of view. Classy use of a beer reference too; that really added to your comment.

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Xnath said:

 

 Wow.  Wierd to do all that for a game that involves pretending to shoot your plastic toy ships with my plastic toy ships.

 I would rather just play the game with some beer and friends than spend any time whatsoever dissecting it to death.

 

 

 

I'm sorry i'm asian, it's like an instinctual, innate kinda inclination you know? That, and high expectations asian father will kung fu you to death if you did not get A+ for your exams and a 100-win streak in star wars miniatures

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Hardrainfalling said:

as always interesting and as people have said no formula is perfect but interesting exercise all the same although i have to admit this level of maths scares me preocupado.gif

Excel did all the hard/tedious math. It really wasn't that bad. It is all in knowing how to set it up and then knowing how to read it.

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ShadowJak said:

Hardrainfalling said:

 

as always interesting and as people have said no formula is perfect but interesting exercise all the same although i have to admit this level of maths scares me preocupado.gif

 

 

Excel did all the hard/tedious math. It really wasn't that bad. It is all in knowing how to set it up and then knowing how to read it.

 

This is why I'm jealous of you Shadow….I don't remember my college math and am not very comfortable with Excel…so I just used the brute force method by trying tons of different numbers on scratch paper.  After like the 50th failure I was cursing myself for not having a more intelligent way to do it lol.

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You mentioned constants.  Way I see it, in addition to the above, each ship also starts off with universal/faction specific abilities (Focus for all and either Target Lock for Rebels or Evade/Barrel Roll for Imperials).

 Then, after a certain number of points, the Pilot selects a tactic/special ability that they can do.  This represents them learning how to use their fighter better instead of just an increase to Pilot Skill.

 

What do you think?

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Sarone said:

You mentioned constants.  Way I see it, in addition to the above, each ship also starts off with universal/faction specific abilities (Focus for all and either Target Lock for Rebels or Evade/Barrel Roll for Imperials).

 Then, after a certain number of points, the Pilot selects a tactic/special ability that they can do.  This represents them learning how to use their fighter better instead of just an increase to Pilot Skill.

 

What do you think?

No. Not at all.

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Well, I happen to know something about Linear Regression and its not the be-it-all mathematical tool. Yes, game designers use some sort of mathematical model to cost stuff, but quite often in games the "extremes" tend to be a lot better. Would a 0 defense and 1 hull ship with 5 attack and 4 shields be very good or very bad?

Linear Regression can give some awnsers, but linear regression as some serious problems if the extremes tend to deviate (either because they are a LOT better or a LOT worse). And ofcourse the second problem is the lack of data points and combinations (have we seen a ship with only 1 attack?). However, the "deviation from baseline" approach does tend to work; question would be if the baseline for the Imperial is the same one as for the Rebels. I have a hard time believing that, as point costs are usually relative to the type of army you can field. Rebels are slower. less defense but have shields and attack. Imperials are faster and have more defense, but have less attack and less shields.

I've played plenty of Warhammer 40k where costing units is quite hard. If you then compare one army with another army you tend to see discrepancies because the baseline of the armies are different baselines. Large deviation from that baseline tends to cost a LOT more than small deviation (attack 4 would cost less for the rebels than attack 4 would cost the Imperials, assuming the baseline is the ships provided in the base set). Moving a bit more when you are normally quite slow would cost more than moving a bit more when you are normally quite fast. Etc. In D&D for example getting a +4 bonus on a Stat would raise the cost by almost 50% compared to getting only a +3 bonus.

In these cases, Linear Regression would not yield anything UNLESS you modify the inputs to account for this, for example by subtracting the actual value from the baseline and then squaring the number if positive or taking it as the exponent to a power. Ofcourse, there are loads of options to play with using these mathematical tools but for games this might be overkill. For games, playtesting lots of games and testing out the values as well as the extremes will be at least more fun than the mathematical way, but you do need to know your statistical probabilities (what is the chance of a critical hit inflicting two damage? What is the chance of scoring at least 3 hits with 3 dice?).

 

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Very interesting thread indeed!

I decided to play around a bit and see what numbers I could come up with.  First I vetted my excel to match the original post's and my values seemed to match up.

I took Steven's specs for the CR-90 Corvette to see how many points it'd cost using your formula.  Here's what I came up with:

Pilot = 0

Weapons = 8

Agility = 1

Hull = 10

Shields = 10

Cost = 116.75!!!

I also decided to see what the Z-95-AF4 Headhunter would estimate to since it seems that people want it to be added as an expansion.  Here's what I came up with:

Pilot = 4

Weapons = 2

Agility = 2

Hull = 2

Shields = 1

Cost = 6.25 (Rebel swarm tactics anyone?)

I justfied my values from this quote from Wookiepedia: "When compared to the T-65, it was slower, less maneuverable, had lighter armor and shielding, and was not as heavily armed.

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marcelvdpol said:

Well, I happen to know something about Linear Regression and its not the be-it-all mathematical tool. Yes, game designers use some sort of mathematical model to cost stuff, but quite often in games the "extremes" tend to be a lot better. Would a 0 defense and 1 hull ship with 5 attack and 4 shields be very good or very bad?

Linear Regression can give some awnsers, but linear regression as some serious problems if the extremes tend to deviate (either because they are a LOT better or a LOT worse). And ofcourse the second problem is the lack of data points and combinations (have we seen a ship with only 1 attack?). However, the "deviation from baseline" approach does tend to work; question would be if the baseline for the Imperial is the same one as for the Rebels. I have a hard time believing that, as point costs are usually relative to the type of army you can field. Rebels are slower. less defense but have shields and attack. Imperials are faster and have more defense, but have less attack and less shields.

I've played plenty of Warhammer 40k where costing units is quite hard. If you then compare one army with another army you tend to see discrepancies because the baseline of the armies are different baselines. Large deviation from that baseline tends to cost a LOT more than small deviation (attack 4 would cost less for the rebels than attack 4 would cost the Imperials, assuming the baseline is the ships provided in the base set). Moving a bit more when you are normally quite slow would cost more than moving a bit more when you are normally quite fast. Etc. In D&D for example getting a +4 bonus on a Stat would raise the cost by almost 50% compared to getting only a +3 bonus.

In these cases, Linear Regression would not yield anything UNLESS you modify the inputs to account for this, for example by subtracting the actual value from the baseline and then squaring the number if positive or taking it as the exponent to a power. Ofcourse, there are loads of options to play with using these mathematical tools but for games this might be overkill. For games, playtesting lots of games and testing out the values as well as the extremes will be at least more fun than the mathematical way, but you do need to know your statistical probabilities (what is the chance of a critical hit inflicting two damage? What is the chance of scoring at least 3 hits with 3 dice?).

 

 

What you have pointed out is that linear regressions don't work well for functions that are not linear.

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marcelvdpol said:

Obviously, I didn't read the post.

"Well, I happen to know something about Linear Regression and its not the be-it-all mathematical tool. Yes, game designers use some sort of mathematical model to cost stuff, but quite often in games the "extremes" tend to be a lot better. Would a 0 defense and 1 hull ship with 5 attack and 4 shields be very good or very bad?"

I never claimed it was. It appears you didn't read my post. The point of the model isn't to determine if certain stats are "good or bad." The point of the model is to show how the ships' squad building points are determined.


"Linear Regression can give some awnsers, but linear regression as some serious problems if the extremes tend to deviate (either because they are a LOT better or a LOT worse). And ofcourse the second problem is the lack of data points and combinations (have we seen a ship with only 1 attack?). However, the "deviation from baseline" approach does tend to work; question would be if the baseline for the Imperial is the same one as for the Rebels."

You would have seen that the baseline appears to be same, if you had read my post.


"I have a hard time believing that, as point costs are usually relative to the type of army you can field. Rebels are slower. less defense but have shields and attack. Imperials are faster and have more defense, but have less attack and less shields."

Incredibly facile. It seems like you didn't read all of my post or if you did, then you didn't understand it.


"I've played plenty of Warhammer 40k where costing units is quite hard. If you then compare one army with another army you tend to see discrepancies because the baseline of the armies are different baselines. Large deviation from that baseline tends to cost a LOT more than small deviation (attack 4 would cost less for the rebels than attack 4 would cost the Imperials, assuming the baseline is the ships provided in the base set). Moving a bit more when you are normally quite slow would cost more than moving a bit more when you are normally quite fast. Etc. In D&D for example getting a +4 bonus on a Stat would raise the cost by almost 50% compared to getting only a +3 bonus."

X-Wing has simple stats compared to most other miniature games. Also, there are only 4 ship types so far. If you had read my post you would have seen there is a base line. Just because other games have different baselines between factions doesn't mean that X-Wing does.


"In these cases, Linear Regression would not yield anything UNLESS you modify the inputs to account for this, for example by subtracting the actual value from the baseline and then squaring the number if positive or taking it as the exponent to a power. Ofcourse, there are loads of options to play with using these mathematical tools but for games this might be overkill. For games, playtesting lots of games and testing out the values as well as the extremes will be at least more fun than the mathematical way, but you do need to know your statistical probabilities (what is the chance of a critical hit inflicting two damage? What is the chance of scoring at least 3 hits with 3 dice?)."

If you had read my post, you would have seen that I did modify the inputs.

If you had read my post, you would have seen where I mentioned the fact that attack dice are better than defense dice.

The probabilities of attack vs. defense are outside the scope of this post and don't matter because they aren't accounted for in squad building points. if you had any understanding of what I posted, you'd already know that.

I know the attack and defense probabilities. I know the probabilities when taking into account Focus, Target Lock, and/or Evade. I even know how well missiles and torpedoes stack up against normal attacks. I could make a post about it but won't because it isn't interesting; most of it is entirely intuitive (more dice is more damage, hurr durr).


I'm not trying to be overly harsh but taking a stats 101 class isn't experience with linear regression. Knowing how to click the buttons to do a regression in excel isn't the same as understanding it. Nothing you said was insightful in the least. Everything you brought up has already been addressed. You obviously don't even know what the t stat or p-value mean. If you did, you wouldn't have said half the things you said. If you had read the post and the rest of the comments in the thread, you wouldn't have said the other half of the things you said.

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magadizer said:

marcelvdpol said:

 

Well, I happen to know something about Linear Regression and its not the be-it-all mathematical tool. Yes, game designers use some sort of mathematical model to cost stuff, but quite often in games the "extremes" tend to be a lot better. Would a 0 defense and 1 hull ship with 5 attack and 4 shields be very good or very bad?

Linear Regression can give some awnsers, but linear regression as some serious problems if the extremes tend to deviate (either because they are a LOT better or a LOT worse). And ofcourse the second problem is the lack of data points and combinations (have we seen a ship with only 1 attack?). However, the "deviation from baseline" approach does tend to work; question would be if the baseline for the Imperial is the same one as for the Rebels. I have a hard time believing that, as point costs are usually relative to the type of army you can field. Rebels are slower. less defense but have shields and attack. Imperials are faster and have more defense, but have less attack and less shields.

I've played plenty of Warhammer 40k where costing units is quite hard. If you then compare one army with another army you tend to see discrepancies because the baseline of the armies are different baselines. Large deviation from that baseline tends to cost a LOT more than small deviation (attack 4 would cost less for the rebels than attack 4 would cost the Imperials, assuming the baseline is the ships provided in the base set). Moving a bit more when you are normally quite slow would cost more than moving a bit more when you are normally quite fast. Etc. In D&D for example getting a +4 bonus on a Stat would raise the cost by almost 50% compared to getting only a +3 bonus.

In these cases, Linear Regression would not yield anything UNLESS you modify the inputs to account for this, for example by subtracting the actual value from the baseline and then squaring the number if positive or taking it as the exponent to a power. Ofcourse, there are loads of options to play with using these mathematical tools but for games this might be overkill. For games, playtesting lots of games and testing out the values as well as the extremes will be at least more fun than the mathematical way, but you do need to know your statistical probabilities (what is the chance of a critical hit inflicting two damage? What is the chance of scoring at least 3 hits with 3 dice?).

 

 

 

 

What you have pointed out is that linear regressions don't work well for functions that are not linear.

I like how you summed up in one sentence what I took a whole page to explain.

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marcelvdpol said:

Ok, so my post was not quite taken the way it was meant. My appologies. In any case, while the analysis is interesting, I would not design games with such a rigorous application of mathematics.

I did not come up with the formulas behind X-Wing; FFG did.

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