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Reverse Engineered Squad Point Formula


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#1 ShadowJak

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Posted 17 October 2012 - 01:07 PM

 

In another thread, I mentioned that I had reverse engineered the formula the game uses to determine squad point values on ship cards. In this post I will be sharing my findings.

Unfortunately for most of you, understanding how I came up with the formula will be difficult, requires some knowledge of performing a regression analysis, and will take some time.

Fortunately for all of you, the formula they seem to use is fairly simple and easy to understand even for people without a degree in some sort of Math related field. I personally have a degree in finance which is why I know how to do analyses like this but I don’t have much statistical background beyond that. Please keep in mind that FFG does tend to modify the formula in a few cases (Academy Pilots and most Named Pilots) presumably for game balance reasons. I'll go more into that later in the post.

When first trying to compile the data to perform the analysis, I just took all the generic ships stats and tried to run a regression.

Picture of Orig. Stats

 

 

That didn’t work out. I ended up getting weird results that didn't make much sense. I even tried changing the order of the ships because that can make a difference in the results. Eventually, I realized that there is no way each point in each stat is contributing to the cost because there weren't enough squad points to go around. I hypothesized that only stat points which rose above a certain threshold were contributing points, stat points at the threshold were 0, and stat points below that threshold were removing points (e.g. Y-Wing agility which is why it can have such high hull and shields yet still be cheap).

By looking at the stats on the ships, I came to the conclusion that the base stats must be 2 Weapon, 2 Agility, 3 Hull, and 0 Shields. I was not sure how upgrades or actions would play into the equation so I left them in to see what would happen.

Picture of Modified Stats

 

 

After changing the order of the ships and running several regressions I was able to come up with a regression without any weird negative numbers or other counterintuitive coefficients.

Picture of Regression Table

I know this looks like a scary number of numbers to most people so I’ve highlighted the most important part in green. The numbers with “E” in them are written in scientific notation. 3E-15 means there are a decimal point and then fourteen zeros before the 3 (i.e. extremely close to 0). Conversely, 5E+14 means there are 14 zeros after the 5 (i.e. 500 trillion). Basically, those numbers indicate that there is a high probability the coefficients are accurate and not anomalies.

Now we get to an explanation of the important numbers and how they can be used to predict squad costs or to make custom cards. Please remember when we are talking about ships’ stats, we consider them relative to their threshold value as I mentioned above (Weapon 2, Agility 2, Hull 3, Shields 0)

“Intercept” is the y intercept of the formula when graphed. It is 2; every ship starts out costing 2 squad points before ever taking into account the rest of the stats.

“Skill” is Pilot Skill. It is 1; each point of pilot skill is worth 1 squad point.

“Attack” is Weapon. It is 8; each point of weapon above 2 is worth 8. A Weapon stat of 2 is worth 0. Eight points are subtracted for each point less than 2 although no ships have an attack that low yet. EDIT: Attack dice are actually under priced compared with defense dice. They have an additional damage dealing side.

“Defense” is Agility. It is 8; it works the same as the weapon stat. The only ship with negative squad points in this stat is the Y-Wing so far.

“Hull” is Hull. It is 4.25; each point above 3 is worth 4.25. There are no ships with less than 3 hull yet but we know the A-Wing will have 2 Hull.

“Shields” is Shields; each point of shields is worth 4.5.

Interestingly, action bar and upgrade icons seem to have no effect on squad points. This is most obvious when comparing a TIE Advanced with an X-Wing or an Obsidian TIE with a Black Squadron TIE.

When writing the formula algebraically it looks like this:

‘Squad Points’ = 2 + ‘Pilot Skill’ + (‘Weapon’ – 2) x 8 + (‘Agility’ – 2) x 8 + (‘Hull’ – 3) x 4.25 + ‘Shields’ x 4.5

Order of operations is immensely important.

 

Let’s plug in some numbers to demonstrate how it works. Starting with a Rookie X-Wing we get the equation:

‘Squad Points’ = 2 + 2 + (3 – 2) x 8 + (2 – 2) x 8 + (3 – 3) x 4.25 + 2 x 4.5
‘Squad Points’ = 21

Now for a Black Squadron TIE:

‘Squad Points’ = 2 + 4 + (2 – 2) x 8 + (3 – 2) x 8 + (3 – 3) x 4.25 + 0 x 4.5
‘Squad Points’ = 14

A Gold Y-Wing because Y-Wings are the only ones with a negative score in their stats:

‘Squad Points’ = 2 + 2 + (2 – 2) x 8 + (1 – 2) x 8 + (5 – 3) x 4.25 + 3 x 4.5
‘Squad Points’ = 18

Now for the Interceptor; the preview picture looks like it could be an 18 or a 19 but we can find the true answer with the formula:

‘Squad Points’ = 2 + 1 + (3 – 2) x 8 + (3 – 2) x 8 + (3 – 3) x 4.25 + 0 x 4.5
‘Squad Points’ = 19

 

 

Here is a chart with most of the generic ships, their stats less the threshold values, their squad points according to my formula, and their squad points as printed:

Blue and Red Chart

As you can see, everything is consistent for these ships. The blue section is the modified ship stats and the red part shows how much each of those stats is worth.

Some of the quicker among you might have noticed that Academy Pilots and non-TIE unique pilots are overpriced by 1 squad point. Presumably that has to do with game balance and the special nature of the Pilot Skill stat.

EDIT: For most Named Pilots and Academy Pilots the formula is:

‘Squad Points’ = 2 + ‘Pilot Skill’ + (‘Weapon’ – 2) x 8 + (‘Agility’ – 2) x 8 + (‘Hull’ – 3) x 4.25 + ‘Shields’ x 4.5 + 1

The Academy Pilot “should” cost only 11 points, but that would allow a 9 ship swarm which may have been determined to be too much. In addition, the named TIEs are not over priced but every named rebel ship is; having the academy pilot cost an extra point may help maintain the power balance. Also worth noting is that X-Wings cost the same as TIE Advanced ships but have less action bar abilities. Attack dice are better than defense dice and the X-Wings have a droid slot which may make up for it.

 

You may be thinking that playing an extra squad building point to get a powerful ability on your X-Wing, Y-Wing, or TIE/ad might be cheap but I think it evens out because of the nature of the Pilot Skill stat. Those of you with a less nuanced opinion on the stat might think that having a higher pilot skill is better (it obviously is) and having an 9 skill is significantly better than 4 skill (it isn't always). Pilot Skill isn't immensely important, attacking first is. Take a look at the rebels going against an 8 Academy Pilot swarm (skill 1). As you all know, they only need Rookie Pilots (skill 2) to always attack first; using Red Squadron (skill 4) pilots would be a total waste of squad points. Similarly, the Red Squadron pilots facing all 6 named TIEs (their lowest skill is 5) would always go last so they might as well be Rookies. Having the special abilities on the named pilots makes up for their always high cost. Wedge’s 9 skill might be major overkill (and really expensive) against an Academy Pilot, but at least he still has his special ability.

 

 

Anyway, that’s enough talking about game balance. Back to more predictions using the formula:

Falcon et al.

As you can see, these new ships don’t work out to having round numbers so I rounded them up. For the unique ships, I added an additional squad point to be consistent with most of the ships already released. It is hard to tell from the picture elsewhere on this site, but the 8 skill A-Wing could have a cost of 24. The rest are too blurry for me to make out.

TL;DR  This isn't Reddit. There is no TL;DR.

EDIT: I removed some of my editorial comments from this post because they gave the wrong impression.


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#2 -Istaril

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Posted 17 October 2012 - 01:54 PM

I'll have a look at the numbers tomorrow in more detail, but I find the analysis quite intriguing.

What surprises me most of all are those abilities that do not affect the point cost according to your regression analysis (Upgradability, Maneuvrability, available actions). I would definitely have expected those skills that offer a significant alternative to "Focus" (eg, Barrel roll) to come at some cost, and given that the benefit is highly dependent on pilot skill, for that cost to increase with pilot skill. Shields being more valuable than hull makes perfect sense, but attack and defense being equally costed doesn't. I'd also have expected attack to be costed as a function of pilot skill, and defense as a function of hull and shield available. 

Your correlation looks quite strong, but I really hope there are more factors involved in the calculation. How robust is your point association if you limit your regression analysis to subgroups (Eg, comparing within Imps or within Rebels, or other subgroups (even randomly picked ones)).

 

 



#3 ShadowJak

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Posted 17 October 2012 - 02:02 PM

-Istaril said:

I'll have a look at the numbers tomorrow in more detail, but I find the analysis quite intriguing.

What surprises me most of all are those abilities that do not affect the point cost according to your regression analysis (Upgradability, Maneuvrability, available actions). I would definitely have expected those skills that offer a significant alternative to "Focus" (eg, Barrel roll) to come at some cost, and given that the benefit is highly dependent on pilot skill, for that cost to increase with pilot skill. Shields being more valuable than hull makes perfect sense, but attack and defense being equally costed doesn't. I'd also have expected attack to be costed as a function of pilot skill, and defense as a function of hull and shield available. 

Your correlation looks quite strong, but I really hope there are more factors involved in the calculation. How robust is your point association if you limit your regression analysis to subgroups (Eg, comparing within Imps or within Rebels, or within Ties - even though I realize the sample sizes are smaller).

 

 

Yes, I was also surprised that the action bars had no effect on squad points. I wasn't surprised the upgrade icons have no effect because that extra cost can be shifted to the upgrade cards themselves.

The samples sizes get way too small and excel isn't a perfect program.

When you have time to read through my post you will see I have written out the formula and it works for all the ships. Most of the named ships use the same formula but end up costing an additional squad point.



#4 CaptainRook

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Posted 17 October 2012 - 02:12 PM

I feel really ignorant right now, but it seems solid.  It's difficult to account for special abilities and I have to wonder how they did calculate them in or what their interpretation of not needing to do so is. 


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#5 R5Don4

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Posted 17 October 2012 - 02:44 PM

 Yep, that's pretty convincing.  It says a lot about the imbalance issues with the Rebs.


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#6 ShadowJak

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Posted 17 October 2012 - 03:02 PM

R5Don4 said:

 

 Yep, that's pretty convincing.  It says a lot about the imbalance issues with the Rebs.

 

 

The data I presented isn't the whole game. It isn't possible to say that the game is imbalanced based on what I posted. It is important to look at team building as a whole instead of focusing on only one ship. Sure, X-Wings might get shafted a little compared to TIE/ADs, but Academy Pilots get shafted a little compared to everyone else (and that is important because they are used on many Imp teams). In a way, having more ships is a disadvantage in squad building points because every ship costs 2 points before the stats are even taken into account and that almost always hurts the Imps more.

Also, I didn't look at how good the Droids are at all. The X-Wings might seem to be lacking in abilities because they have the option of taking droids that are under priced. R2-D2 is extremely cost effective for what it does. Every green maneuver that regenerates a shield is like an extra 4.5 squad points for the rebels and the upgrade itself only costs 4 squad points; R2-D2 more than pays for itself after using it just once. The Imperials don't have anything like that.



#7 R5Don4

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Posted 17 October 2012 - 03:26 PM

 What the Rebs lack is attacks.  With numbers on their side their is no reason the Imps should ever not be pouring on attacks every round once engaged.


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#8 R5Don4

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Posted 17 October 2012 - 03:31 PM

 Attack dice and Shields are way overcosted to the effect they will have on a match.  While the Skills on the upgrade bar and the pilots Special talents which should cost something and do have a big effect on a match are not factored in.


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#9 ShadowJak

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Posted 17 October 2012 - 04:19 PM

R5Don4 said:

 

 Attack dice and Shields are way overcosted to the effect they will have on a match.  While the Skills on the upgrade bar and the pilots Special talents which should cost something and do have a big effect on a match are not factored in.

 

 

Do you have any data or evidence to back up your assertions? I do:

Attack dice are actually under priced relative to defense dice. They have one more surface that can deal damage than the defense dice have that can evade it. 

Each shield is 4.5 as opposed to a hull that is 4.25. Yes, it costs a little more but they absorb crits and the rebs can regenerate them. With 7/33 of the cards doing straight up double damage, crits do more than 20% more damage on average than normal hits and that isn't even counting the other damage cards that do damage or have bad effects. Crits happen quite often because they are the last to be removed with evades.

Pilot special abilities are factored in to the cost but that cost is somewhat hidden. I explained how in my post.

Referring to one of your previous posts, the rebels don't have a problem with attacks and they certainly won't once the new expansions are released. Right now the most attacks (and attack dice) the imps can perform in a round is 8 (16 dice) with all Pilot Skill 1 Academy Pilots. When the expansions arrive, the rebs will be able to have 4 X-Wings and 1 A-wing for a total of 5 attacks and 14 dice. That looks like a crappy match up for the rebs on the surface, but the rebs 4 X-Wings will all be attacking first and will be taking out TIEs before they can attack. It is also worth noting that 8 TIEs have a combined 24 hull and the Xs and A have a combined Hull+shields of 24 that is actually better because the shields will absorb some crits. In the first round of attacking, if the rebs focus fire with their X-Wings and kill a TIE before it even gets to attack, they will have brought the Imp player to 14 attack dice and only 21 hull remaining before the imp player could have done much about it. On average, it takes 6 Focused TIE fighter attacks to kill one X-Wing (really 5.882 but I'm rounding) not counting crits. Good luck having 6 out of 7 TIEs all able to fire on the same X-Wing. It only takes 3 (actually 2.465) Focused X-Wing attacks to take out a TIE not counting crits; that is much more doable at the beginning of the game when everyone can be in some sort of formation.

Even now when the rebs don't have the A-Wing, 4 Rookies have 12 attack dice and 20 Hull+shields. They have 16 points to spend on buying under priced upgrades like R2-D2 or the named pilots. The TIEs have 4 points left over. With that they can upgrade one guy to Backstabber. Wow, Backstabber.

Don't blame losing on imagined imbalances.

Typing all this out makes me want to try the Rebels.



#10 radiskull

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Posted 17 October 2012 - 04:48 PM

 Well done.

Fo real. (hopefully this is long enough to publish now?)



#11 KarmikazeKidd

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Posted 17 October 2012 - 04:59 PM

ShadowJak said:

R5Don4 said:

 

 Attack dice and Shields are way overcosted to the effect they will have on a match.  While the Skills on the upgrade bar and the pilots Special talents which should cost something and do have a big effect on a match are not factored in.

 

 

Do you have any data or evidence to back up your assertions? I do:

Attack dice are actually under priced relative to defense dice. They have one more surface that can deal damage than the defense dice have that can evade it. 

Each shield is 4.5 as opposed to a hull that is 4.25. Yes, it costs a little more but they absorb crits and the rebs can regenerate them. With 7/33 of the cards doing straight up double damage, crits do more than 20% more damage on average than normal hits and that isn't even counting the other damage cards that do damage or have bad effects. Crits happen quite often because they are the last to be removed with evades.

Pilot special abilities are factored in to the cost but that cost is somewhat hidden. I explained how in my post.

Referring to one of your previous posts, the rebels don't have a problem with attacks and they certainly won't once the new expansions are released. Right now the most attacks (and attack dice) the imps can perform in a round is 8 (16 dice) with all Pilot Skill 1 Academy Pilots. When the expansions arrive, the rebs will be able to have 4 X-Wings and 1 A-wing for a total of 5 attacks and 14 dice. That looks like a crappy match up for the rebs on the surface, but the rebs 4 X-Wings will all be attacking first and will be taking out TIEs before they can attack. It is also worth noting that 8 TIEs have a combined 24 hull and the Xs and A have a combined Hull+shields of 24 that is actually better because the shields will absorb some crits. In the first round of attacking, if the rebs focus fire with their X-Wings and kill a TIE before it even gets to attack, they will have brought the Imp player to 14 attack dice and only 21 hull remaining before the imp player could have done much about it. On average, it takes 6 Focused TIE fighter attacks to kill one X-Wing (really 5.882 but I'm rounding) not counting crits. Good luck having 6 out of 7 TIEs all able to fire on the same X-Wing. It only takes 3 (actually 2.465) Focused X-Wing attacks to take out a TIE not counting crits; that is much more doable at the beginning of the game when everyone can be in some sort of formation.

Even now when the rebs don't have the A-Wing, 4 Rookies have 12 attack dice and 20 Hull+shields. They have 16 points to spend on buying under priced upgrades like R2-D2 or the named pilots. The TIEs have 4 points left over. With that they can upgrade one guy to Backstabber. Wow, Backstabber.

Don't blame losing on imagined imbalances.

Typing all this out makes me want to try the Rebels.

ShadowJak, I don't think he was disputing your post. I think he was just commenting on how it ought to be, compared to what it is. Pointing to why he personally thinks the Rebels suffer a little bit from the formula they chose to use. But I could be wrong.



#12 ShadowJak

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Posted 17 October 2012 - 05:12 PM

That is true. I get a little carried away sometimes because assertions made without evidence irk me. But everything I said still stands even if I would type it a little less aggressively next time.



#13 LethalDose

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Posted 17 October 2012 - 05:56 PM

 Are you willing to share your data set?  I'd like to see what what I can do with it.  Thanks!

-WJL



#14 ShadowJak

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Posted 17 October 2012 - 05:59 PM

LethalDose said:

 Are you willing to share your data set?  I'd like to see what what I can do with it.  Thanks!

-WJL

It is all there in the post. Or do you mean the data for the attack and defense dice?



#15 Ellyrik

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Posted 17 October 2012 - 08:09 PM

 Very nice work! I applied the formula to Han Solo and I obtained 54.75pts (!) I believed it costed 45… And 48.75 for Bobba Fett where I thought it was 39.

I hope there's a cost reduction for bigger ships. But I obtained 22.75 for Tycho Celchu on a-wing where I read 26.

I may be wrong but we'll have to check the formula again when the new wave is out.



#16 Fabster

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Posted 17 October 2012 - 11:59 PM

Very well done!!

 

Maby with bigger ships the size itself will be cost reducing factor? Easier to hit and morre difficult avoid asteroids.



#17 Ellyrik

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Posted 18 October 2012 - 01:17 AM

 Right! If I replace (hull-3) by (hull-6) in the formula (assuming they count double) I obtain 42pts for the Falcon and 36 for Slave-1. This could be it.

But I don't understand for the a-wing



#18 Cid_MCDP

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Posted 18 October 2012 - 02:52 AM

 Fascinating under-the-hood look at things ShadowJak. Good stuff! Thanks for taking the time to write it up!



#19 ShadowJak

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Posted 18 October 2012 - 03:05 AM

Ellyrik said:

 

 Very nice work! I applied the formula to Han Solo and I obtained 54.75pts (!) I believed it costed 45… And 48.75 for Bobba Fett where I thought it was 39.

I hope there's a cost reduction for bigger ships. But I obtained 22.75 for Tycho Celchu on a-wing where I read 26.

I may be wrong but we'll have to check the formula again when the new wave is out.

 

 

Yeah, the model I came up with seems to work great for the current ships but that might just be some sort of coincidence. The different base sizes might affect it some how.

The picture of the A-Wing skill is way too pixelated for me to see the ones digit. The tens is obviously a 2 but the ones looks like a blob to me. It is possible they didn't add a +1 to the 8 Skill A-Wing for being unique (or rounded down) and it only costs 23.

For the larger ships, maybe they didn't or didn't add the +1 for being unique, subtracted 10 for being large, and rounded down instead of up. That would make the skill 9 Falcon cost between 44 and 46. The skill 8 Slave I would then be between 38 and 40.

Their images kind of look like a 44 and 39 to me, but after staring at the pixels long enough they can start to look like anything.

EDIT: We are referring to these pictures for anyone that hasn't seen them:

New Starfighters

 



#20 R5Don4

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Posted 18 October 2012 - 03:19 AM

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

 

From wave 4, The super borken ship:

Techno Union Starfighter

Pilot Skill 1

Cost 3

At 2

Ag 2

Hl 3

Sh 0

Actions: Evade, Focus, Barrel Roll

 

 


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