A numerical analysis of MP builds

Summary / TLDR:
By distilling the composition of a build into basic categories (damage, mobility, control, utility) and totalling the value in each category, you can get a sense of the general potential of the build and its weaknesses. Furthermore, being aware of the values of various strong/proven MP builds can give you a good comparison point for your own deck building.

Outline:
Post 1) general description of numerical analysis system
Post 2) specific item comparisons, min/max examples
Post 3) numbers from actual posted MP builds

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1) The general numerical analysis system

Understanding why a certain build does or doesn't work in mulitplayer is a very complex process. If I look at the nice card list of my character's deck after it is complete, certain information is still not easily seen: do I have enough damage? Do I have a good ratio of mobility cards to control cards?

The usual way to answer questions like these is to either 1) follow your gut feeling or 2) try it out in the field, making adjustments as necessary. As the development of the scientific method has shown, gut feelings are extremely fallible and prone to inaccuracy [citation needed], and anecdotal evidence is an extremely poor basis to make considered decisions unless a statistically large sample has been taken.

I therefore propose an alternate method of judging a build's relative strengths and balance: numerical analysis.

The method I will outline breaks down a build into broad categories, and quantify the build's strength in each of these categories. This will allow you to make hard number comparisons from the small scope of individual cards/items, all the way up to comparisons of a character's build or even an entire team's collective build.

Before I continue, please understand that the act of breaking down cards into numbers strips away a lot of information, and therefore this model, like the others listed above, has some major flaws and absolutely should not be taken as gospel or be seen as the superior method. All numbers of a build are indicative of build strength instead of empirically showing strength, and that the specific circumstances of any given match can change things wildly.

Furthermore, the many unquantifiable effects have all been lumped together into the general "utility" category. These unquantifiables are the biggest weakness of a purely numerical analysis.

That being said, let's get into it, shall we?

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1a) The numerically quantifiable categories:

I have broken down the cards which can be put into your deck into the following categories (and sub-categories):

Damage:
A self-explanatory category. The total amount of damage from primary damaging cards in your deck is summed. Dividing your total by the number of non-trait cards in your deck gives you a general idea of how much damage you can expect to do per card drawn.

Cards which deal damage over time are assumed to do the full damage of the base ability plus one extra tick of damage.

Cards which are primarily used for some effect other than their damage (Force Bolt, Winds Of War, Unholy Frenzy, etc.) are not counted towards this total.

Mobility:
-personal mobility/movement (including step cards)
-team mobility/movement
-movement of enemy units

All mobility effects are lumped into this category. For simplicity's sake, the quantity of the move is discarded, and only the # of individuals moved will be counted. For example, Team Run has a mobility score of 3, Winds Of War has a score of 2, and Walk has a score of 1.

Control:
In the system described here, control is basically an encumbrance stat. Moving enemies is considered under the Mobility category, forcing discards is in the "Card advantage" sub-category in utility, and various other sundry effects such as walls, smoke, etc are also considered under utility. As everything else I can think of is eliminated, cards will be a scored by how much encumbrance they inflict multiplied by the duration of the encumber effect. So Frost Jolt has a rating of 4, Chilling Rime and Cold Snap have a rating of 2, etc.

Utility:
-gamechanger cards
-general utility cards
-heals
-buffs/debuffs
-defences (armor/blocks)
-terrain attachments
-card advantage effects (draws / discards)
-traits

Utility cards are the hardest to quantify and therefore each card with some associated utility simply increases a deck's utility score by 1, with the following exceptions:
-Extremely effective/strong utility cards ("Gamechanger cards") such as Impenetrable Nimbus are worth 2 points each.
-Cards which have more than one significant effect (Hard To Pin does a block + a move, Parry does a block + a card draw) have each effect counted (HtP is 1 utility 1 mobility, parry is 2 utility).
-Cards which force a discard of 2 or more cards, or cards which cause a draw of 2 or more cards count as 2 points of utility.
-Cards with very low effects (especially low-tier heals) are counted as 0 or 1/2 of a utility point. Yes, I know this makes the utility score become very subjective.
-Traits are counted as 0, and are instead tracked in a separate "trait score".

 

2) Specific item comparisons
Based on the system explained above, it becomes relatively easy to compare items which fulfill the same function and/or use the same item slot. This basically follows the same logic and common sense that we are already used to, as in many cases it is painfully obvious that some items are stronger than others.

On the other hand, we can also do some offbeat comparisons which might or might not have been generally obvious. Here are some examples:

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Vibrant Pain vs Bejeweled Shortsword
This is a classic comparison, but I want to use it to illustrate something: VP is not strictly better in every way, even though in practical usage it is indeed much better than the shortsword.

Vibrant Pain:
Damage: 36
Mobility: 6 (total of step: 24)

Bejeweled Shortsword:
Damage: 58
Mobility: 2 (total of step: 4)

Specifically, I can think of some decks/builds which need a higher consistent average damage, at which Bejeweled Shortsword is the most readily available item. If you build a warrior who is supported by a high mobility/control team, it is conceivable that Bejeweled Shortsword might be a better item.

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Militiaman's Pike vs Copper Zapping Wand x2
What madness is this? Comparing a 2 token warrior weapon to 2 copies of a no-token wizard arcane item???

Well, take a look:
Militiaman's Pike
Damage: 32 (6 range 2 attacks, 4 of them penetrating)

Copper Zapping Wand x2
Damage: 30 (6 range 2 attacks)

This illustrates 2 things: Militiaman's Pike, one of the better warrior weapons if you want a warrior with mostly range 2 attacks, isn't all that much better than the equivalent slot expenditure from a wizard (1 weapon has 6 cards, so it is equivalent to 2 arcane items). This leads us to the conclusion that warriors have relatively poor itemization for ranged attacks, and in general have to give up a lot (a yellow and blue power token!) for the privilege of being able to attack at longer than base melee range.

We can also conclude that wizards, if they had cards about as strong/useful as Copper Zapping Wand, could actually be pretty decent damage dealers. Unfortunately, this is not the case, and for some reason even the most powerful staffs only have a total of 27 damage (or 30 damage if you go legendary).

2a) Min/Max examples

Here are some min/max values for deck building, both for your information and amusement.

Warrior damage:
Highest damage possible (from 3 weapons only, as other damage sources are rather insignificant and are usually not a strong pick in MP builds):

For my available items, it is:
Bejeweled Shortsword: 58 damage
Bejeweled Shortsword: 58 damage
Infused Greatclub: 52 damage

Total Max: 168
Average damage per card draw: 4.941 (168 / 34, the typical size of a warrior deck after traits are taken into account)

Certain legendaries have slightly higher damage (Hackmasterwith 60), and you can improve your average damage per card by stuffing the rest of your deck with traits.

So keep in mind when you build your warrior, who is usually on a team primarily to deal damage, that it is theoretically possible to build him with around 5 damage per card drawn on average. Care should be taken not to fall too far away from the maximum or you will end up killing things too slowly. I've found hitting around 100 damage in total from weapons is about as low as it is comfortable to go, at least if you expect your warrior to be able to kill things quickly.

The lowest damage weapon I could find was the awe-inspiring Blocking Axe, clocking in at 9 total damage. 3 of those babies on a warrior would put you at 27 total damage, putting you at an impressive 0.7941 average damage per card draw.

Highest Mobility:
Warrior:
6 from Vibrant Pain,
4 from Lochaber Axe,
2 from Nifty Halberd (I'm not counting the many 0 token items with small step attacks as they are less useful)
4 from helmet (various 2x team move helms)
3 from Slippery Shield
4 from Salazar's Sandals (I think there's better boots that I don't have)
0 from Heavy Armor slot
4 from human item (various 2x team move items, could be 6x from elven mobility item, but no one plays elves...)
0 from Martial Skill slot
Total: 27 mobility from 34 cards (0.794 mobility per card drawn @ 34 cards)

Priest:
Way way WAY outclassed by the other 2 classes.

Wizard:
Variant 1 (less trait stacking):
4 from Whiterune Staff,
0 from random no-token staff (Trembling Staff used for trait stack)
16 from Locket Of The Gale x4,
3 from Green Hide Robe
4 from Salazar's Sandals (I think there's better boots that I don't have)
2 from Novice Command
0 from Arcane Skill slot
Total: 29 mobility from 29 cards (1 mobility per card drawn)

Variant 2 (max trait stacking):
0 from Trembling Staff 2x
8 from Runestone x4
3 from Green Hide Robe
2 from Greenguard Boots
5 from Perfect Command
2 from Superb Teleportation
Total: 20 mobility from 23 cards (13 traits!) (0.869 mobility per card drawn)

Variant 3 (max mobility/card ratio):
0 from Trembling Staff 2x
16 from Locket Of The Gale x4,
3 from Green Hide Robe
4 from Salazar's Sandals
5 from Perfect Command
2 from Superb Teleportation
Total: 30 mobility from 28 cards (8 traits) (1.071 mobility per card drawn)

Conclusion regarding mobility: warriors are great if you have VP, but even if you do wizards can beat them on mobility per card. Additionally, the bulk of warrior mobility is for themselves only, whereas the wizard's mobility is targeted (therefore ignoring encumber effects).

 

1st build: Scared Little Girl's 3pack of control wizards, post #1 from:
http://forums.cardhunter.com/threads/dwarven-control-wizards.4442/
Dwarven Wizard 1
Deck size: 24 (12 traits)
Damage: 37
Mobility: 8
Control: 20
Utility: 14

2 from walls of fire​

1 from path of knives​

6 from 3x short p. ray​

4 from 2x toughness​

1 from hard to pin (1 added to mobility as well)​

0 from cloth armor, rusty armor​

Dwarven Wizard 2
exact same as dwarf wizard 1

Dwarven Wizard 3
Deck size: 24 (12 traits)
Damage: 26
Mobility: 8
Control: 0
Utility: 12

2 from walls of fire​

1 from path of knives​

4 from 2x short p. ray​

4 from 2x toughness​

1 from hard to pin (1 added to mobility as well)​

0 from cloth armor, rusty armor​

In summary, this team is very strong because it stacks lots of control/encumberance, a decent amount of movement effects, and a good amount of utility. This is further enhanced by the huge number of traits on each character: deck sizes are cut by 33% (from 36 to 24), which results in an effective 50% increase of all numbers on a number per card drawn ratio. This makes the team incredibly consistant, which is one of the keys to achieving a high Elo rating.

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2nd build: Heretiick's Priest/Priest/Warrior card draw build (pre-nerf), post #15 from:
http://forums.cardhunter.com/threads/retail-mp-builds.3781/
Green (Dwarven Priest 1)
Deck size: 30 (4 traits 2 trait-like Spin Arounds)
Damage: 46
Mobility: 7
Control: 0
Utility: 27

3 from 3x Martyr's Blessing​

2 from Impenetrable Nimbus​

1 from Boosted Heal​

1 from Inspiration​

1 from Righteous Frenzy​

3 from Hard to Pin (+3 to mobility)​

1 from Horned Plates​

4 from 2x (old) Unholy Power​

4 from 2x (old) Demonic Feedback​

2 from Mass Frenzy​

1 from Savage Curse​

2 from Dwarven Battle Cry​

1 from War Cry​

1 from Purge​

Blue (Dwarven Priest 2)
Deck size: 32 (4 traits)
Damage: 34
Mobility: 5
Control: 0
Utility: 29

2 from 2 x Righteous Frenzy​

1 from 1 x Team Heal​

2 from 1 x Dwarven Battle Cry​

1 from 1 x Healing Blessing​

2 from 1 x Inspiring Presence​

2 from 1 x Parry​

0 from 1 x Light Heal​

0 from 1 x Unreliable Block​

2 from 1 x (old) Demonic Feedback​

4 from 2 x (old) Unholy Power​

1 from 1 x Unholy Frenzy​

8 from 4 x Impenetrable Nimbus​

2 from 2 x Unholy Wellspring​

1 from 1 x Block​

1 from 1 x Thick Hide Armor​

Backdoor Mudslide (Dwarven Warrior 1)
Deck size: 32 (4 traits)
Damage: 122
Mobility: 15
Control: 0
Utility: 13

0 from 1 x Unreliable Block​

3 from 3 x Hard To Pin Down​

2 from 2 x Chain Harness​

2 from 2 x Officer's Harness (normally I would give these 0, but stacked with the Chain harnesses they become semi-useful)​

1 from 1 x Reliable Mail​

2 from 1 x Dwarven Battle Cry​

2 from 2 x Mail​

1 from 1 x Frenzy Aura​

This is interesting. The build focuses on throwing tons of buffs on a step warrior (and also using a bit of the old broken card draw mechanics). I think it represents close to the maximum for utility on priests and damage/mobility on warriors who don't have Vibrant Pain.

 

Nice start to your analysis. I agree that breaking things down to the numbers often reveals very interesting things we'd been ignoring (such as how badly warriors suck at 2 range damage).

 

Definitely a nice start, however you really should not conclude that range 2 attacks are a weak option for warriors. While it's true that pure range 2 weapons are underwhelming there are plenty of good hybrids:

Blazing Shortsword, Polished Plancon, Powerful Sword, Double-Edged Sword

You also need to keep in mind that melee is much easier to buff compared to magic and the wizards lower hp/armor makes low range attacks less worthwile for them.

Edit: Also just for fun the highest damage value for a warrior if we don't allow all-out-attack is 209. 3* The Hackmaster +Gouging Helm + Advanced Chopping + Spiked Boots + Heavy Wooden Shield + Sharp Shell

 

I think the "for some reason" argument in regards to wizard high damage for epic/legendary items "the most powerful staffs" is very easily explained by the concept of class balance/role. Wizards occupy the control / ranged damage niche generally. As a generic rule, they exchange higher damage capacity for more control/utility. If this were not the case, then there would be less reasons to use warriors, and even less reasons to use priests (assuming no other changes were made with those respective classes to balance it out).

TLDR:
Wizards have 27-30 damage items because more damage would make wizards out of balance and have them occupy the same role of warriors as primary dds, making them control/dd; thus making them best class.

 

I really like this type of analysis. Please keep on going, Yth. One additional note may be the spread of the damage on cards - Vibrant Pain and Bejeweled Shortsword offer a much tighter spread compared to the Hackmaster. Infused Greatclub versus Rageblood Dagger is another great example.

Lumpiness in damage matters to some extent - it directly affects the variance of outcomes.

I know what you're thinking, punk. You're thinking "what's his last card?" Now to tell you the truth I forgot myself in all this excitement. But being this is a Hackmaster and you have only 10 HP left, you've gotta ask yourself a question: "Do I feel lucky?" Well, do ya, punk?

 

Right. In general, damage spread or damage spikes are absolutely relevant and useful in PVP situations, however this is nearly impossible to model on a purely numerical side. Damage spikes are circumstantially useful, which is where this kind of analysis falls short.

If I had 10 hp and my opponent had a Hackmaster, I would be happier than if I had 10 hp and my opponent had a Bejeweled Shortsword.

You are quite correct - trying to go for a pure range 2 build is pretty inefficient because the options available are not very good, but hybrid builds have some pretty good options. The thing is, I can imagine circumstances where you would want to build a pure range 2, for either thematic or composition reasons.

It is also dissatisfying that this is the case, because most other "pure" builds for warriors have good options.

Right again, I had forgotten that the Hackmaster has 1 yellow 1 blue orb required, so it is possible to stack 3 of them. Theoretical max damage is therefore 180 (I don't count damage coming from other slots, as it muddies the total without adding anything meaningful, although it is amusing to know the absolute total possible).


edit: added in the analysis of 2 builds in post #3 above.
Does anyone know a nicer way to format the text? I'd like to put the breakdown of utility cards into a spoiler or some other collapsable frame so it doesn't take up so much space on the post...

If anyone has another specific build they would like me to analyse, please let me know!

 

As I pointed out in this thread, https://forums.cardhunter.com/threads/improperly-graded-cards.4574/, the problem comes from the lack of consistency between attack cards :

as you can see, Impaling Stab "pays" for range 2 and penetrating for 5 damage, but penetrating Stab pays 8 for the same (both compared to Mighty Hack).
The lack of consistency makes items that use the cost inefficient step 2 penetrating cards non competitive.
Same goes for the non penetrating range 2 attacks :

There again, there is no consistency between the corresponding raw melee upgrade and the stabs, making Potent Stab, and Stab pretty good, and Strong Stab and Able Stab pretty bad for their cost.

Among the cards you mentionned, the Polished Plancon has only 2 weak cards, Powerful Sword 1, Blazing Shortsword 0, and Double Edged Sword 0. The argument that these cards that are weak for their cost allow the dev to balance the items don't hold water, as very few items are worth using with these cards.

 

Yth, as a relatively new player most of these example items are out of my reach, but your system is helpful for getting a grip on what can be a dizzying number of options for deck building. The amateur statistician in me has just one thought: perhaps you could incorporate the deviance or standard deviation of the damage values as a measure of spread per spacedust's comment. Unfortunately that would add decimals to the analysis and depending on how it was incorporated could over-emphasize the damage component of the deck, if it were simply added or multiplied with the total damage for example. Just a thought. Looking forward to seeing how this develops.

 

A quick thought about this: the amateur financial economist in me (sodding economists, they ruin everything don't they) suggests graphing a risk-return frontier, i.e. graphing means vs standard deviations to create a efficient frontier. Players can then choose which point they want to be on depending on their risk preferences. You would create multiple frontiers depending on token cost, so one for , , and etc.

 

I... I have no idea what you guys are talking about.

 

I'm sorry about derailing your discussion. I'll probably type out a more coherent response over the weekend and post it up here, or in a separate thread. Meanwhile, please continue, if you were intending to do so. I really like the idea of being able to compare class-specific items with each other, e.g. 2x Copper Wand vs Spear.

 

The current rarity / level system is a bit arcane. My feeling is that they had some initial guidelines, but then switched a few things around during beta and didn't really clean up afterwards.

Problem #2 is that card rarity / item rarity was not supposed to make a difference in power level (according to the developer blog) but looking at the actual game, it does. There are a number of rare cards that are strictly better than comparable common cards. In addition, on a cursory glance epic and legendary items seem to have better quality cards (example: Sharp Shell). I'm not sure whether this is intended or an oversight.

Problem #3 is that blue / yellow tokens cover a wide area. Level 1 items are crap, then items get good towards level 8. Blue token items are usually too expensive from levels 8-9 to around 12-13, then the good stuff starts. For yellow token, there is only level 18 currently, but a similar problem will occur when the level cap is raised...

This partially explains why Copper Zapping Wand has such a high comparable damage output - Big Zap has higher damage than any other reach 2 paper card. Militiaman's Pike on the other hand pays a penalty for having Penetrating attacks. Armor is not a big factor in MP as the game assumes, which is why the item appears to be weak / expensive.

In this case, it is somewhat balanced by the fact that wizards usually can't afford to go into melee. Reach 2 is valuable for a warrior, since he usually has to go base to base. For a Wizard, reach 2 is dangerously short. Usually, you want to keep your Wizard out of move range of melee enemies, which makes reach 6 so valuable.


There is only so much you can gather from looking at the finished deck perspective. In the end, this is a collectible card game and it needs to be balanced at card level.

Each PC has 12 items (counting weapons as two items), which creates a 36 (+ standard move) card deck. At level 18, 4 of these are yellow items, 4 are blue, 4 are tokenless. In an ideally balanced game, switching out items of the same token cost would shift power between damage, defense, mobility, control and support, but the power level would remain the same. Of course, a perfectly balanced game that is still fun to play only exists in theory, which is why game design is an art form, not a science.

 

The whole discussion of card rarity and how it interacts with item rarity is irrelevant to me. What I care about are the actual cards which are available on actual items in the game right now.

I do agree that the algorithm they seem to be using to create/balance items seems a bit off, with many many examples of specific cards being way overvalued or undervalued. Unfortunately this means that a very large percentage of in-game items are basically too weak or unusable to be seen in competetive teams. In my opinion the (multiplayer) game would be much more interesting if there were more viable/effective item options for all races and classes.

Instead, we make builds around the relatively small pool of items each class has which are actually worth their token costs (or have undervalued cards and are therefore worth more than their token costs).

 

Yth, I hope this helps to clear things up somewhat. It's slightly OT for this thread, so if it's too confusing, please reply and I will move it to a new thread.

Each item can be seen as a portfolio of damage. For warrior weapons, it's 6 cards of damage, if there are no traits. The mean of a weapon's damage is a useful way of assessing its damage potential; however, because card draws are random, the variance of draws plays a large role as well. If you expect the match to be over in 1 round (your warrior at 1 hp, enemy elf mage at 15 hp), you would want a high variance weapon (e.g. Infused Greatclub) and pray that you draw the heavy hitter to end the match. However, if you expect the match to go longer, or if you are packing buffs like Mass Frenzy, you may prefer a lower variance weapon (e.g. Rageblood Dagger) so as to ensure a consistent damage output over the course of the match.

Because I'm a stats nerd, and a badly trained financial economist too, I have here Excel/SPSS files that contain some sample weapons and their respective means and standard deviations of damage. There are three groups, with Group 1 being no token, Group 2 being double minor, and Group 3 being double major. A scatterplot of the data shows that there is a general trend - higher variance is positively correlated with higher means. In other words, in exchange for lumpy outcomes (high risk of whiffing with a low damage draw), you enjoy a higher average damage. This may sound familiar if you've been through business school (or what passes for business school nowadays) - it's the familiar risk-return metric.

Given this, the scatterplot contains some useful information. Firstly, you can see that the three groups are roughly tiered - spending more power tokens buys you an upward shift in mean damage. Running a linear regression for each group shows an interesting trend. The fit lines for Groups 2 and 3 are roughly parallel, but the slope for Group 1 is much more steep, indicating that the risk-return metric is more positively skewed for Group 1 as compared to Groups 2 and 3. I.e., you may want to blindly load up on powerful Group 1 weapons if your tokens can be better used elsewhere. However, note that the R-square (assessment of the fit of the line) for Group 1 is lower than that of Groups 2 and 3, indicating that the Group 1 trend line may not capture the characteristics of Group 1 very well.


Of course, there are major critiques to this approach - the most important being all the other variables that go into a game of Card Hunter. As Yth's eloquent essays outline, factors like mobility, control, and utility play a big part. There are other factors such as card advantage and tempo coming into play as well - Nimble Strike is a 3-in-1 Dash + cantrip + 6 damage powerhouse, for example, which explains its popularity to a large extent as it gives you +1 tempo and +1 card advantage.

Anyway, I hope this was helpful to some extent. And remember not to listen to any financial economists, especially if they start showing you fancy regressions and equations and telling you some story about how capital markets are expected to function. I know how the sausage is made in the factory, and I don't eat it myself.

Dataset in full:

 

@Spacedust: I think the chart would be more intuitive if X is the mean (less damage on the left, more on the right) and deviation was Y (less swingy at the bottom, more swingy at the top).

Although, if I remember correctly from business school, financial analysts like to switch charts against intuition to confuse the uninitiated...

It would be interesting (but a lot of work) to create a "card power metric" that takes all kinds of factors into account, not just straight damage.

For example, Steps could equal an X percent damage bonus based on the fact that you get to the opponent faster and avoid situations where you can't reach the target and have to discard.

Step 1: +33%
Step 2: +66%
Step 3: +100%
Step 4: +133%

(Like all good business metrics, I've pulled these out of thin air. I'm using percentages to make sure the bonuses scale.)

Reach is similarly effective to get an attack in, with some differences:
- Reach can only attack in straight lines, while Steps allow you to walk around corners (except Charge)
- Reach is immune to encumbrance
- Reach goes through pools and other non-entry terrain (except smoke, which is the opposite)
- Reach goes through squares blocked by allies and enemies
- If you corner your opponent, or he is out of movement, you can follow up steps with close range attacks. Of course, the enemy can then attack you in close range too, so that's not a good thing if you are squishy.

In total, I'd say a square of step is slightly better than a square of reach.

Reach 1: +0%
Reach 2: +20%
Reach 3: +40%
Reach 4: +60%
Reach 5: +80%
Reach 6: +100%
Reach 8: +120%
Reach 10: +140% (Long Spark)

For penetrating, the value depends on the opponents armor. A typical MP armor is Reliable Mail, which blocks 2 damage. Some armors block more, but they have a chance not to trigger. Enchanted Mail blocks 2.5 damage on average but you're unlikely to find it in MP.

Penetrating Zap (dam 2) and Penetrating Cut (dam 3) will be negated if the armor blocks the entire damage. More powerful penetrating attacks usually don't meet armor that could block it all.

I'd value penetrating at +1 damage up to 3 base damage, and +2 damage above.

Hard to Block is only worth it if the enemy is blocking in the first place. The assumption you need to plug in is how likely the opponent is to have a block or parry. 30%? 50%?
If you use a 3 parry shield and and no other items with blocks, you have 3 parries in a 36 card deck. So one in 12 cards or 8.3% of your deck is a parry.
If you assume first enemy contact in the second round, each PC has drawn 5 cards. With each draw, the remaining deck decreases by one. The calculation is a bit complex as the chance to draw a parry increases with each card you draw, but it ends up slightly under 50% to have one parry in the deck after 5 draws.

Each point of hard to block decreases the enemy's block chance by 1/6, so that's 16.6% chance to make a difference between damage or no damage (+ whatever effect the block has)

TL;DR, here are the bonuses for hard to block:
Hard to Block +1: +10%
Hard to Block +1: +20%
Hard to Block +1: +30%

This assumes your objective is to deal damage. It ignores tactical considerations like using cheap ranged attacks to draw block cards, which would make hard to block detrimental.

- - -

Some examples using the above:

Stab is worth 3 * 1.2 = 3.6 damage
Impaling Stab is worth (9+2) * 1.2 = 13.2 damage.

Dancing Cut is worth 3 * 2 = 6 damage
Nimble Strike is worth 6 * 2.33 = 14 damage

Shifting Stab is worth 2 * (1+0.33+0.2) = 3 damage
Big Zap is worth 5 * 1.2 = 6 damage

Long Spark is worth 2 * (1+1.4+0.1) = 5 damage

 

Martin, I like the modifications to measuring the damage of the card, but of course this still doesn't account for the multipurpose nature of some of these cards (like that nimble strike, beyond dealing damage in a wide area, is also a dash to a victory square or out of danger).

 

Sure. There is no way to factor everything into these numbers. It's not an exact science. In my formula, Nimble Strike is as valuable as Mighty Hack, which I think is a good rule of thumb but depending on your entire deck, your playstyle, the map and the enemy team the actual value in play could be quite different.

In any case Nimble Strike is not a silver card but I'm starting to sound like Cato the Elder.

 

Ok, now I kinda get what you are saying. I agree somewhat that it is interesting to track the standard deviaiton / mean damage of each item, which to my less trained mind is simply translated into the principle that burst damage is more valuable in PVP situations than average, predictable damage.

I think if there were thousands of weapons to analyze which were all nearly identical in power at each tier, such statistics would be absolutely key to picking out the best item for your intended build. But the current game has a fairly limited number of available weapons, some of which are clearly head and shoulders superior to others in the same tier.

It would be pretty cool to see your chart expanded to include a larger range of weapons, either with all weapons included, or with the clear weaklings culled out first. I have my own excel file (attached below), but I do not track the individual damge of each card on the weapon, only the general totals.

The problem I have with this idea is that the modeling/simplification might go too far. A card's usefulness is almost 100% contextual. Nimble Strike is in general much better than Powerful Hack, but there certainly are situations where you would prefer the 11 damage over the 6. And how do you value a weapon with 2 blocks versus a weapon with 6 attacks? My system described above can help identify strengths and weaknesses of a team, but does not (as of yet) assign any particular team a "power rating" of some kind.

The closest I can come to making general statements/judgements about builds is to compare them to other builds which are proven to work. If you want a powerhouse warrior who your team relies on to deal damage, and he has a total of 60 damage in his entire deck, then I can clearly say that it is too low. If you want a wizard with tons of control and utility, and he has a control score of 4 and a utility score of 6, again I would be able to say that is too low.