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Preface - I enjoy campaign games and friendly lists that are still "competitive" but not overly so. I feel you see more of the game that way. That being said, when I was a tourney gamer I was huge into the math hammer and it served me quite well.

I took a spreadsheet design I used in the early 2000s and turned it into a database that I hooked my website into. Currently all it does is show me all the units and gives me letter grades based on the raw data. Its not tremendously useful except to show me where everything ranks up.

Offense is simply the average offensive output based on the hard math based on no save, and all the various saves averaged out.
Defense is how many wounds a scroll actually has based on saves and the various rends (averaged out)
Efficiency scores are how many points per point of damage or how many points per actual wound you pay. The less points you pay, the more efficient.
Overall is a sum of offense and defense multiplied by average efficiency score in percent.

The letter grades are simply taking all of the unit entries and ranking them against each other. The website does not currently display these raw values, but I am working on a chart system that will.

To come: chart system that graphically displays rankings.
To come: the ability to add units and see how a list stands up against another list by the math, as well as display the "actual points" of the game. For example, in a 1000 point game, if one list is 25% more effective then that list has effectively 1250 points to the others 1000.
To come: the ability to adjust on the fly to see how an ability affects te overall score. For example: a bloodsecrator gives a unit of reavers and blood warriors +1 attack in a game. How much of an influence was that? You'll be able to add the +1 attack to both units, see how they now stand with that extra attack, and the extra score added to the bloodsecrator's score as a "utility" score. Or the ability to take a monster's abilities down as it takes damage to watch how damage affects its rankings.

Applications: to see how mathematically powerful one list is to another; to gauge the power level of a list to tone it down or bring it up against another to make for a closer game; to view underperforming units and overperforming units. I'm using this for our competitive league to gauge A lists vs B lists vs C lists and give B & C lists a couple more ranking points for playing with a list that is a little harder to use.

Flaws: this just shows you the hard math. Abstract spells and abilities are not reflected, those will be more useful when the site is updated to allow dynamic adjustment of stats and numbers.
Flaws: I don't have every legacy unit in the system due to time constraints. I will add those as my league needs them, if they need them but the tomb kings and bretonnians for example are not present. I did my best to get most of the current units in though.

Lot of ideas in the works. This is just the beginning. I thought i'd share the raw letter grades. I plan on having the charts up today or tomorrow and start working on the list comparison functionality.

http://www.louisvillewargaming.com/AOSStats.aspx

It is rough, but I suppose you do have to start somewhere.

Thanks for sharing this! Just generally curious why there is such a delta between various shooting units? An example is judicators with bows which are poorly rated and we know are amazing.

I would imagine thats because compared to all other units they aren't as amazing by the numbers.

The rankings are simply the percentile they fall in when you order by a certain column.

A unit could be amazing but get a "C" because there are units above it more amazing.

Also a "C" ranking is not poor, its in the middle of the pack. A D+ is just under average.

As amazing as we may feel they are, the numbers given are the average output of said unit and the letter grade the ranking of that average output compared to everything else in the game.

You know... complaining the game has too optimal/too powerful units, and putting all that work into empowering bad gamers to finding them that much more easily, seems like a strange choice. :-p

That said, I absolutely respect the thought and work that went into this, even if I adamantly disagree that it is a viable way of getting snap-shots of how units perform. Until, of course, you do the insane task of adding the metrics for every possible buff/support synergy, at which time, yes... it will at least cover the pure efficiency of a given model/list.

Good work man. As a fan of a little math-hammer myself, I definitely enjoy seeing the process.

You know... complaining the game has too optimal/too powerful units, and putting all that work into empowering bad gamers to finding them that much more easily, seems like a strange choice.

Most powergamers already do this math. I know a lot of guys that have their own spreadsheets.

There are many applications of this data. Finding the most powergamey element is one of those but not the primary use that I am using it for.

The website addition where you can add the actual modifier effects will give you a turn by turn actuality. The data presented right now is how everything performs before any abilities have been applied.

It does show you very well what units need buffed vs units that can stomp around on their own in isolation (for example stormfiends need no help, they put out and take a lot of damage in isolation, whereas khorne reavers are poor in isolation and really need buffs to make them worthwhile) without needing help.

Thank you for the comments I appreciate the feedback.

I am primarily using this to gauge league lists and give bonus points to B and C lists as well as to see how badly skewed a game really was and how out of whack official points are and where.

An example though, of how "real world" impact differs from raw math...

Chamleon Skinks in an objective game are incredibly disruptive and powerful, but at a glance people will see this and all they'll see if the "F" rating. That's my sole concern.

Thats up to the people to read my disclaimer that this is pure numbers rankings.

It is up to them to decide if an ability is worth it.

A chameleon skink raw without abilities or who never uses those abilities is in fact an "F". During a game where they are sitting in cover on objectives, you'll be able to adjust that on the website to see how they perform (I believe they go up to a C). I can also add that entry in myself but there is a ton of inane data entry that needs done and my free time doesn't allow for that, which is why I'm adding in the ability to edit on the website.

My reavers can be amazing. They just require me to put two bloodsecrators near them for that to happen, which is not always easy. On their own they deserve their "D" rating because they are horrible without both being buffed and going before the enemy.

Mighty Lords of Khorne are another. By the pure stats they are ok at best. If they go in and wound Nagash and roll a 5, Nagash dies, putting that model into the A+ category for that game. If they are up against a player that only takes 5 wound heroes, then that mighty lord of khorne is still pretty ok overall but his potential is far less, but you can't make that a hard math value. Thats one of those situational values that the website edit feature will model better.

So there is an actual value and a potential value. It is the potential value that is nebulous and will be worked on in the future since that is dependent solely on abstract abilities that you cannot determine.

Another general question, why are mages ranked so low across the board?

Because mages by the numbers are pretty low. Their spells cannot be mathed because they could be doing arcane bolt, mystic shield, or their own spells. You'd have to add entries for each of the spells that they can cast that have hard math (mystic shield you cannot put hard math to, because it could be cast on anything in the game and each unit you cast on would have a different value depending on their wounds, ability to reroll saves, and their save value itself)

Which again would go toward the edit feature of the website to ascertain their true value from turn to turn (because in each turn their value would fluctuate... a mage that is shut down all game and gets no spells off would only have its hard math to fall back on which is generally very poor)

A mage that gets off mystic shield on large high wound high save units every turn would be much more valuable.

A mage that gets off mystic shield on something with few wounds and a weak save would be much less valuable.

A mage that puts out 10 mortal wounds with a lucky roll on a spell would be worth much more that turn than if he rolled 1 mortal wound.

All of that is highly circumstantial and would need modeled on a turn by turn basis. Their *potential* would be high, their actual average is quite low until they get those spells off and the player picks the right units to cast them on though.

I *can* put an arbitrary bonus on those spells, but I'm trying to keep personal conjecture out of the equation because then its "this mage is a B because Auticus feels that this spell he can cast is powerful" and then someone else goes "no that spell is not that powerful" and there is no longer math behind it but personal opinion.

Some things like Slaan I sat down and math'd out an average based on their constellations and spells but that took quite a bit to write so I only did that for a few models that had a more concrete "hard math" set of abilities and am leaving the rest to the edit feature that I am putting in.

 auticus wrote:
Because mages by the numbers are pretty low. Their spells cannot be mathed because they could be doing arcane bolt, mystic shield, or their own spells. You'd have to add entries for each of the spells that they can cast that have hard math (mystic shield you cannot put hard math to, because it could be cast on anything in the game and each unit you cast on would have a different value depending on their wounds, ability to reroll saves, and their save value itself)

Which again would go toward the edit feature of the website to ascertain their true value from turn to turn (because in each turn their value would fluctuate... a mage that is shut down all game and gets no spells off would only have its hard math to fall back on which is generally very poor)

A mage that gets off mystic shield on large high wound high save units every turn would be much more valuable.

A mage that gets off mystic shield on something with few wounds and a weak save would be much less valuable.

A mage that puts out 10 mortal wounds with a lucky roll on a spell would be worth much more that turn than if he rolled 1 mortal wound.

All of that is highly circumstantial and would need modeled on a turn by turn basis. Their *potential* would be high, their actual average is quite low until they get those spells off and the player picks the right units to cast them on though.

I *can* put an arbitrary bonus on those spells, but I'm trying to keep personal conjecture out of the equation because then its "this mage is a B because Auticus feels that this spell he can cast is powerful" and then someone else goes "no that spell is not that powerful" and there is no longer math behind it but personal opinion.

Some things like Slaan I sat down and math'd out an average based on their constellations and spells but that took quite a bit to write so I only did that for a few models that had a more concrete "hard math" set of abilities and am leaving the rest to the edit feature that I am putting in.

Awesome explanation and thank you again for sharing.

Anytime. As more functionality gets added I'm hoping this becomes more useful.

Yeah, looking at a lot of these stats, I'm not sure how certain some rankings came to be, even with your formula.

Some examples:
a 10-man squad of handgunners is only a D+. the ONLY way I can see this making sense is if you factor out any general/battalion buffs, and even the inter unit buffs.
Same applies to the Freeguild general, and ESPECIALLY to the pistoliers/outriders. Pistoliers are, without a doubt, MUCH worse than Outriders in the freeguild list, yet they are ranked as overall better than outriders.
From what I've seen, crossbows a 4+/4+ ranged unit isn't an F, but simply average. ESPECIALLY when you factor in the chance for rend.
You gave Iron Breakers (the dudes with a 4+ rerolling save that's immune to most all rend, and has a 5+ save against spells) a B in defense, when they are debate-ably one of the best anvils in the game
Don't see how Longbeards (or warriors) with greatweapons are a D-. 4+/3+ with rend -1 is on par with Greatswords and other generic "greatweapon infantry"
The Warden king, who's on par with a vampire lord in terms of shredding (4 attacks, 3+/3+/-1/d3) is hardly below average.

My point is, while I think this is a neat endeavor, the data just does not match what I've seen in my games. Another fine example of this is the Ale-guzzler gargant. His base stats are amazing, but with a 5+ save, he tends to loose wounds so quickly that he almost never gets to use his best stat-line. Methinks that for this to be more accurate you need to either figure out a way to factor in what a unit can do (i.e. shield, banner, and musician bonuses alongside base warscroll bonuses)


As I mentioned with the handgunners, methinks these stats are misleading either due to 1) Not factoring in what the armies can do, 2) not comparing units within the faction, or 3) not taking into account buffs on the warscrolls. Sorry if I came off as overly critical, I don't mean it to come off that way.

Thats fine. Average outputs are average outputs. Numbers are numbers.

If it is given a "B" in defense that means it sits at about the top 70-80th percentile, which is pretty good actually. It also means that if it has a "B" in defense that there are other units above it that have more wounds per save. Particularly units that regenerate and can reroll and have good saves as well.

Abstract buffs cannot be taken into effect because they are impossible to model as mentioned above.

Hard buffs that always exist were all taken into account.

As also mentioned above, this is just the armies in a vacuum before abstract buffs can be taken into account.

The edit feature of the site will allow you to plug in actual values turn by turn to see where they stack in. There is no way to hard code abstract circumstantial events.

If you're after something like "a mage will always rank as a "B"" then you'll never get that because it will depend on player choice of spells, if the spells go off, and how they roll or what they affect (as explained above with mystic shield). The only way you'd get a solid rating on something like that is to apply an opinion-based rank, which leaves the realm of math and toward the realm of arbitrary personal opinion.

In any typical game I play I will see a flux.

Turn 1 - my bloodsecrator moves and my reavers move. They are both an "F" and a "D"
Turn 2 - my bloodsecrator plants standard and my reavers charge. My bloodsecrator is now a "D" and my reavers are a "C".
Turn 3 - my blood warriors get into range of the standard. They are now boosted to a B and my bloodsecrator is a D+.
Turn 4 - my reavers are wiped out and my blood warriors are out of range. They fall to a "C" and my bloodsecrator is again an "F".

Throughout the course of the game I can find an average score for all of that, but at the beginning of the game in the vacuum they begin how they begin.

Really the big thing I'm seeing is that Destruction is on the top of the heap as far as raw stats go. Which is interesting because these numbers don't really take any synergy into account - of which some destruction units have a decent amount. Not to mention this doesn't quantify mobility at all, which will probably add quite a bit of swing to a unit's value in different scenarios and the like.

I think the area where synergy is really undersold is in the Stormcast tag, which seems to rely heavily on the buffs their leaders can give out. An interesting project, but as you point out, raw numbers don't tell the entire story. If you're looking to maximize results though, the chart is an interesting place to look.

I get what you mean, however I think certain non-number things DO need to be taken into account: The fact that handgunners and crossbowmen can shoot again if they are charged, things like rend and rend immunity (Don't know if you factored those in), and a units ability to buff (or synergy in general), BUT I see your point on why those can't really be quantified. However, that does leave a pretty big gap in the info provided, especially when it comes to setting that final ranking.

Those cannot be accurately data modeled without it being opinion.

Those can only be accurately data modeled by going through a game and saying that is what they did on a turn by turn basis. Which again is what the final destination will be.

There would be another entry in your example:

handgunners (having been charged) which would have them shoot again. Then you would have two data points.

You will be able to do that. The data presented right now is handgunners... at the beginning of the game having not been charged. Granted I did do this for some units (you will see... Unit X and then Unit X when charging or Unit X and then Unit X near some hero that buffs them) but again I got to a point where if I wanted to see this done I decided to let users model that how they needed with edit functions.

I understand everything you're saying Auticus... and your work here is so commendable, at the very least for your dedication to it...

... but man... what the numbers can't convey is damning to the value of the endeavor.

Pull up Ironweld Arsenal and behold a whole list of "F" ranked units, that under real-world testing have proven to be some of the most fear units in the entire game of Age of Sigmar... so strong in fact that many, myself included, believe they were a part of why war-machines have Force-Org limitations.

Again, I definitely respect your work, but readers really need to do their due dilligence and understand exactly how these results are calculated and what they're trying to convey.

I've honestly never feared artillery because its usually so awful that it doesn't warrant taking. In 100% of every game I have ever played going back to sept of last year, the only time artillery has ever played a role in hurting my army is when i faced elven Repeating Bolt throwers, and those were focusing on my blob of reavers which have no save. Thats a lot of games where anyone that ever takes artillery never has a good return against me with it.

I don't see where anyone would ever fear most of the artillery in this game. Their average damage output is almost across the board universally poor.

The only saving grace for artillery are the ones that don't require line of sight that can pick out characters and kill them easier. They are worth that.

You'd have to demonstrate to me why artillery is so feared. Its never been something that has swayed any of my games and in my area over the past few months it has mostly gone away because players have started putting points into things that they know are going to have a stronger output.

By the numbers on average, especially for how much they cost, artillery is generally quite horrible.

Note the offense is how many ON AVERAGE overall DAMAGE you will do (after saves, averaged between no save all the way down to 2+ save to take rend into account)
Efficiency is for its cost how many points you pay for each output point (where 1 point for 1 point of damage would be an efficiency of 100)

Automatically Appended Next Post:
Order - Ironweld Arsenel - Cannon: Offense: 3.32 (F) Efficiency: 46.78313 (F) Defense: 5.2 (F)
Efficiency: 66.38461 (F) Overall: 4.82094557268481 (F)

Order - Ironweld Arsenel - Cannon with Engineer: Offense: 4.98 (C) Efficiency: 64.85542 (F) Defense:
5.2 (F) Efficiency: 66.38461 (F) Overall: 6.68011772030255 (F)

Gonig over the numbers we can see a cannon with an engineeer gets boosted to 4.98 (5) damage it can inflict. Thats not bad. And a "C" rating is not bad either. A "C" rating is where it should be...

Why does it get an "F"? When you combine its poor defensive capability... dealing with warmachines is elementary if you are prepared for them.

Order - Ironweld Arsenel - Hellblaster (one deck): Offense: 1.7956 (F) Efficiency: 34.16998 (F) Defense:
5.2 (F) Efficiency: 77.92308 (F) Overall: 3.92079082800158 (F)

Order - Ironweld Arsenel - Hellblaster (three decks): Offense: 4.0401 (D) Efficiency: 71.29777 (D)
Defense: 5.2 (F) Efficiency: 77.92308 (F) Overall: 6.89407807491705 (F)

Order - Ironweld Arsenel - Hellblaster (two decks): Offense: 2.6934 (F) Efficiency: 56.44665 (F) Defense:
5.2 (F) Efficiency: 77.92308 (F) Overall: 5.30317032856228 (F)


There we have hellblasters. Firing all three decks its going to average 4 damage (this is after saves). Thats not horrible... but its not that great either considering its cost. And again its super easy to take out.

Having the range is useful but for the cost you are paying in points you are better off with something else because most artillery pieces require serious buffing to bring them up to par with an average unit.

And again average is not bad. Average is middle of the road and fully functional. We can get functional output from artillery, but compared with the other scrolls that have much higher output for less cost I just don't see why I'd ever really take many of them if I'm playing competitively.

Obviously this does not stop someone from having hot dice totally blow through a unit with a great roll, but this takes the average into account.

I also think the hang up on what the grades mean may be a sticking point.

This is a rank where all scores are laid out and where a unit sits in the line is their percentile score, and thats what they are graded on.

That means a unit could be very functional but only come out a "C" which some people may think of as "bad".

The Screaming Skull and Trebuchet are the two I fear as they don't need LoS. Just arcing away and rainging down death.

But since they removed pie plates from AoS, I don't fear artillery like I used to.

Edit: all good now.

So, big question, based on the data what is statistically the best and worst unit in the game?

Quick guess is scrap launcher for the worst, because it is.

 Uriels_Flame wrote:
The Screaming Skull and Trebuchet are the two I fear as they don't need LoS. Just arcing away and rainging down death.

But since they removed pie plates from AoS, I don't fear artillery like I used to.

Yeah thats their one use that I still use them for - being able to hit heroes hiding in a corner since most heroes are 5 or so wounds and can be killed easily. Then those warmachines are worth it because they are dropping heroes equal to or greater than their cost, plus removing army buffs.

But that is very very situational as well.


Automatically Appended Next Post:

 buddha wrote:
App seems to be broken for me at the moment.

I added my first chart, you may need to refresh. I can get on it ok.


Automatically Appended Next Post:
Got all four graph types working.

So what are statistically the best and worst units in the game? Perhaps top 5 bottom 5?

Off hand the changeling is very bad.

Best units in the game seem to be something along the lines of The ogor stornhones, stormfiends, the stormcast cavalry.

(thats not counting the heroes on monsters, just units)

Can you not factor range into account? Seems your math is made on how powerful one round of attacks from a unit is, but of course some units get to make more attacks than others.

If you could assume units starting between 24-36 inches apart, take the average movement to close that gap over 5 turns and calculate roughly how many shooting attacks and melee attacks could be made I think you'd get a better representation.

I'm pretty sure its supposed to be just the potency of a unit attacking or receiving attacks so that subjective qualities are specifically left to the players. Note the discussion on artillery - many have low grades despite being extremely useful within the context of a battlefield. Like the Matched Play points themselves, its an efficient guideline and not trying to be more.

[edit] A particularly good example would be Grot Fanatics - they score an F based off raw stats (as they should), but I think we all know how much better they actually are.

Yes, another prime example is the Judicators with Crossbows coming out above the Judicators with Bows.

I admire the work you've put in Auticus - but when you have to take it with that much of a pinch of salt, what worth does it have? Even your suggestion of using it to give players with "weaker" armies doesn't seem useful because the armies might not be weaker at all.

As it can't take into account synergy, range, bravery and various other aspects of the game, is this not just another SDK?

 Bottle wrote:
Yes, another prime example is the Judicators with Crossbows coming out above the Judicators with Bows.

I admire the work you've put in Auticus - but when you have to take it with that much of a pinch of salt, what worth does it have? Even your suggestion of using it to give players with "weaker" armies doesn't seem useful because the armies might not be weaker at all.

As it can't take into account synergy, range, bravery and various other aspects of the game, is this not just another SDK?

That's somewhat similar to the argument "if AoS points have to be negotiated anyway, whats the point of having them at all?" I think something is better than nothing and while it does indeed need salt this guide is still useful. Even for units that are very context-powered newbies could look at that units score, see it does not reflect how it performs in game, and thus be steered towards examining its abilities. Were I new to AoS I know that would be useful to me.

This is the average potential of raw stats. Nothing more. This shows me what units need supported more than others. This shows me what to expect from a given unit without any buffs etc.

Arbitrarily assigning more value to ranged attacks simply because they are at range leaves the realm of math and turns into the realm of personal opinion, which I am not going to do with this project. However the army comparison tool that is in the middle of being written does take into account ranged output vs melee output and will rate an army with a higher ranged output over an army with a lower ranged output for that category. That doesn't make the units that have range worth more than the melee just because they have ranged though.

What this has proven to show me is taking something like khorne bloodbound and then matching up against stormcast cav and star drake, the lists are grotesquely skewed toward the stormcast.

Thats a great indicator that if I'm looking for a closer game, that khorne vs stardrake cavalry is not the game I'm looking for.

Its also good to gauge if I'm going too over the top in a friendly game.

This also lets new players see what armies they will likely struggle with running vs which ones they will have earlier success with. I have been playing the game for 25 years or so, so taking a "C" list and winning with it can and does happen because I've simply played for a long time. Giving that same "C" list to a new player will often result in them getting frustrating and quit or going off and picking up a stronger army (something we have all seen I'm sure with no math at all lol)

If you're looking for a magic number that says "this unit will always be "X"" yo uwill never get that because everything in AOS is context sensitive.

What you will get are trends and average scores and the ability to see what units can operate more by themselves vs which ones need baby sat.

There's also a discrepency between the letter grades. People see something that has a "C" and go "well that means it sucks and thats not true it doesn't suck!"

In Auticus-speak, a "C" is a fully functioning and useful unit.

An "F" rated unit after buffs could very well pull up to a "C" like grots can. But that requires the variable "player skill" which will always be nebulous.

Now I will be adding formations to the mix and a utility score coming up which will take spells and abilities and apply them to every unit in the game and then come up with a mean value using data modeling service code. That will then solve for the nebulous "but the wizard can cast mystic shield so shouldn't be an "F", but right now thats not what the data being modeled is for.

You can never model synergy or bravery because it is a useless number without its context, and its context will always be changing and thus cannot be properly modeled.

A unit with a bravery of 4 that never has to take a battleshock test is a much different context than a unit with a bravery of 6 that takes battleshock tests for most of the game with varying degrees of modifiers.

Last - the edit ffeature which I have mentioned a few times will allow you to put in the real value of a unit by keying in exactly what it did in a turn.

 auticus wrote:

the ability to see what units can operate more by themselves vs which ones need baby sat.

This alone was worth the price of admission for me. Thank you for the hard work you put into this. I've been trying to figure out where to go next with my Slaves/Khorne army. By seeing which units can hold their own without buffs, and which units need buffs to be more effective and survivable, has helped me figure out the next few units and/or heroes I'll be adding. I feel I need to add, however, that I'm a vteran 40K player, and only got into AOS back in February. For me, this was a very valuable tool. For those, like you, who've been playing for years, maybe not as much? Again, kudos, and thanks for helping me.