The Hyper Cynic

December 22nd, 2007 by gdoghomes

One of the most talked about cards in magic, but also one of the most difficult to evaluate. How should we value brainstorm? I’ve decided to breakdown the value of mechanics that form the card brainstorm. This should give us insight into why and when we use brainstorm.

I separate brainstorm’s effect into 3 components:

1.) [Cantrip]
2.) [Library Manipulation]
3.) [Hand+Library Manipulation].

1.) [Cantrip]–Guaranteed +1 Card in your hand, but more importantly, a guarenteed -1 card in your library. Brainstorm, like many cantrips, is 1 blue mana for 1 card, which is already a fair effect. This thins your deck like a street wraith or fetch land. A cantrip replaces lower quality cards in a deck, allowing you to see the highest quality cards of a specific function.

If you run 4 brainstorm in a 60 card deck, and you go through a quarter of your deck on average before the end of a game, then you are paying, on average, a single blue mana over the course of the game to have a 56 card deck. The scaling of the cost to cycle through more of your deck per average game is linear too.

Why would you want to turn 60 cards into 56? Some cards have a higher utility, value, or relevance to your deck or specific circumstance than others, and in reality, we only want to play those instead of lower quality cards if possible. Cantrips, like brainstorm, remove lower utility cards from the equation, allowing the remaining 56 cards to have a higher average utility value than the average 60 card deck. The question then becomes: was the average cost of using cantrips worth the card-quality gains?

I’ll use as straightfoward a case as I can think of to show you what a cantrip means to card quality. This case by no means showcases the brokenness that is Brainstorm that we might find in decks that abuse it best, but the case shows the principle behind cantripping.

Let’s say you were playing a deck that had 16 Volcanic Island, 40 Lightning Bolts (120 damage value), and 4 Shocks (8 damage value). Notice that shocks, on average, are 1/3rd less valuable than a bolt. We’ll say you see 11 cards per an average game, putting you at (11/60)*4 (total mana cost of cantrips in deck), or 0.733 of a U, on average, to go from a 60 card deck to a 56 card deck. What happens when we replace the lower quality cards of a deck, shock in this case, with a cantrip?

[Total value of win conditions]/[Total mana cost of win conditions]=[Average Win condition to mana ratio per card].
Shocks–   128/44=2.909
Cantrips– 120/(40+0.733)=2.946

The gain, in part, is one of mana efficiency. The otherside of the cantrip is how it affects your average “win-condition” value met per card.

[Total value of win conditions]/[Total cards in deck]=[Average Threat value per card] (Think of DPS for you MMORPGers)
Shocks– 128/60=2.133
Cantrips– 120/56=2.143

What if we made a deck with with 40 shocks and 4 ‘Flashback-less’ lava darts, how good is a cantrip then? Presume we see 13 cards per average game, or (13/60)*4=.866. Notice that Flashback-less lava darts are only 1/2 as effect as a shock, and contribute proportionately less to the total win condition value of the deck. The Shocks are more relevant to the bolt-deck than lava-darts are to the shock deck. This difference in proportion will illustrate the rising advantages on cantrips in decks and formats that have larger card quality disparities.

[Average Win condition to mana ratio per card]
Lava Darts– 84/44=1.909
Cantrips– 80/40.866=1.958

[Average Win condition value per card]
Lava Darts– 84/60=1.4
Cantrips– 80/56=1.429

The worse your cantrip-replaced cards proportionately compare to the average mana-efficiency and win condition values of the rest of your deck the better a cantrip becomes. Here are your comparisons:

Bolts’n'Cantrips/Bolts’n'Shocks Mana efficiency ratios– 2.946/2.909=1.013
Shocks’n'Cantrips/Shocks’n'Darts Mana efficiency ratios– 1.958/1.909=1.026

Bolts’n'Cantrips/Bolts’n'Shocks Win Condition density ratios–2.133/2.143=1.005
Shocks’n'Cantrips/Shocks’n'Darts Win Condition density ratios–1.429/1.4-1.021

As the win-condition value of the least valuable cards of a deck (those to be replaced with cantrips) proportionately decreases as compared to the more valuable cards in a deck, the proportionately better a cantrip becomes.

If all your spells have fairly equal win-condition value, then the effectiveness of a cantrip decreases. So, while the greater variation in the value or relevance of your cards, the better a cantrip becomes, the other side of this equation is that perfectly balanced decks with card quality equivalence would not want to use cantirps. For example, if you ran 16 Volcanic Island and 44 Bolts, would replacing 4 bolts with 4 cantrips be worth it? Let’s say you see 11 cards per game.

[Average Win condition to mana ratio per card]
Bolts–132/44=3
Bolts/Cantrips–120/40.733=2.946

[Average Win condition value per card]
Bolts–132/60=2.2
Bolts/Cantrips–120/56=2.14

Running straight bolts is simply better than having a cantrip. Why? There is too little variation in the mana-efficiency and win-condition values of the cards in a deck with nothing but bolts and land. In cases where all things in your deck are equal in value, then cantrips are not worth it. A perfectly balanced deck would not need cantrips. Building this “perfectly balanced” deck is more complicated than many would realize though. Remember the arguments against running more than 60 cards in a deck? Usually, because there is such extreme differences in the quality of cards in older formats, we seek the smallest decks possible to abuse the few cards that are just too darn good for their mana costs. Cantrips act as the glue between the broken cards of eternal formats in these cases. However, technically, there are cases where 65-card decks could be perfectly balanced, even better than 60 card decks. Perhaps you could make a 65-card deck that had a several functions, all maximal and equal quality cards for their slot and function, and any removal of a card would imbalance the deck’s card quality. Here, you would take a 65-card deck over a 60-card deck. But, how many decks do you know are this well made? The sort of perfection in balancing card value to make it such that a 65-card deck would be preferred to a 60 card deck is the same sort of calculation and balance that a deck would need in order not to consider cantrips. If there is any imbalance in the value of the cards in your deck, then cantrips are worth considering.

Since that perfection rarely exists, often due to format card pool constrainsts, we opt for cantrips. The proportionately less valuable a card is compared to the average card quality of a deck the more likely we should replace it with a cantrip.

Take a more extreme case, say 16 Volc-Islands, 40 4-damage for 1 mana burn cards (henceforth: Uber-Bolt), and 4 Flashback-less Lava darts. Say you’ll see 10 cards in an average game. (10/60)*4=.667 mana cost to goto 56 cards.

[Average Win condition to mana ratio per card]
Lava Darts– 164/44=3.727
Cantrips– 160/40.667=3.934

[Average Win condition value per card]
Lava Darts– 164/60=2.733
Cantrips– 160/56=2.857

Cantrips give proportionately larger gains when they replace cards of proportionately lower relevance. In this case, cantrips let us not run flashback-less lava darts and stick to straight uber-bolts, giving much higher mana efficiency and average card quality.

Cantrips aren’t the end-all-be-all solution though. Take a case where we ran 16 Volcanic Islands, 24 cantrips, and 20 Uber bolts vs. 16 land and 44 Uber Bolts. Say we’ll see 20 cards per game; (20/60)*24=8. Ouch, that is 8 mana, per game, spent on just lowering the count to 36. It will take too many turns to see the cards we need to see to be mana-efficient at all.

[Average Win condition to mana ratio per card]
Cantrips– 80/32=2.5
Uber Bolts– 176/44=4

[Average Win condition value per card]
Cantrips– 80/36=2.222
Uber Bolts– 160/2.667

This is an extreme example, but it shows that there is a specific number of cantrips we wish to run in any given deck. You can easily run too many or too few cantrips in a deck.

Burn, of course, can be a more straightfoward calculation than other decks. And, you’ll notice several burn decklists use bauble-cantrips to maximize and balance average card quality..for good reason. Other decks are certainly more complicated, but the principle still remains the same though:

The higher degree of disparity found between the relevance and value of the different cards in your deck, the more useful a cantrip becomes. Eventually, if you follow this path, you’ll see the extreme in silver-bullets and tool-box decks that rely upon card-quality, cantrips and tutors to consistently find the singleton card that may be the only relevant thing in your deck against an opponent.

This is why running Yawgmoth’s Will with cards that aren’t nearly as powerful would drive us to use cantrips: by running cantrips we will receive a higher average use and benefit of Yawgmoth’s Will over the course of many games. The benefit, often enough, is worth the cost of replacing weaker cards with cantrips.

Decks that have similar components are less likely to desire cantrips. An aggro deck, for example, may have few deviations from the mean value of cards in the deck. On the other hand, a combo deck may often find themself in situations where they have 2 of 3 combo pieces in hand, but need the last one. In this case, only the missing combo piece may be relevant to our situation, and cantrips increase the likelihood of finding the relevant cards.

The cantrip component of brainstorm fulfills a major glue-mechanic in which decks can more consistently run and play with higher quality cards with different functions and values in different circumstances.

Brainstorm is a cantrip, and will it will give this effect.

2.) [Library Manipulation]–This is a more straight foward effect to consider. Think of this as Sage Owl. How many cards do you have left in your library? To what degree do the individual cards in a deck deviate from the mean win-condition value of cards in a deck? The higher this deviation, and the lower your library count, the more effective library manipulation becomes. Bare in mind, the mean win-condition value and deviations vary per metagame, per deck, per matchup, and per specific game circumstance. This makes it incredibly difficult to calculate, but it highlights the variance we see in even the mean values across a spectrum of conditions. Library manipulation, like a cantrip, helps isolate and condense the average variance from the mean value of win-condtions across the spectrum of play-conditions.

Sage Owling into a 40-card library with nothing but Lightning Bolts isn’t going to net you anything. However, Sage Owling into a 40-card library that has only three or four relevant card in the deck (perhaps you MUST Wrath of God next turn or you lose) increases your likelihood of seeing relevant cards sooner. Like the cantrip, library manipulation benefits the deck that has higher variance in card value from the average card value.

Let’s take a basic example:

If you had 36 cards left in your library, 3 WoG’s in the library, and Wrath was the only relevant card, what does a 4-card Library manipulation effect do for you?

Without the library manipulation you have a 1 in 12 chance to draw Wrath of God next turn.
With a 4-card library manipulation you have a 1 in 9 chance to draw Wrath of God next turn.

Library manipulation is still very good even beyond looking for 1-of a specific card in your deck. It lines up your deck plays too. It could be as simple as counting your land drops drops for the next several turns and making sure relevant spells are on top with land being placed exactly where you would need to draw it so you could make a land drop for the next several turns.

Library manipulation allows you to order cards in their relevance to your current game position. If you need a counterspell before you need a land, then go ahead and put the land under the counterspell. The land may be relevant, but maybe it is less relevant than the counterspell. Library manipulation increases the quality of your future draws. A basic permutation grid of a 4-card library manipulation ensues.

Actual Card1 (in Slot1) — Value at Slot1=1, V@S2=6, V@S3=8, V@S4=5
Actual Card2 (in Slot2) — Value at Slot1=3, V@S2=5, V@S3=4, V@S4=6
Actual Card3 (in Slot3) — Value at Slot1=0, V@S2=5, V@S3=6, V@S4=2
Actual Card4 (in Slot4) — Value at Slot1=4, V@S2=2, V@S3=3, V@S4=3

Card1 moves to Slot3, Card2 moves to Slot4, Card3 moves to Slot2, Card 4 moves to Slot1.

Originally, we have a top 4-card value of 15. After a 4-card library manipulation we have a top 4-card value of 23.

The permutation grid is actually much more complicated than I’ve provided. For example, what if Card 3 only has a value of 5 in Slot2 if and only if Card 4 is in Slot1? Multiply this type of value calculation, and you see that identifying the value specifics cards, even in a very specific circumstances, can be quit complicated. These are the sorts of mental calculations that we make on the fly. It seems obvious, but drawing out the reason why we do what we are doing is more complex than we initially thought.

Shuffle effects has a specific effect right here too. You know the value of the top X cards of your library. Is that value below the average value of X cards in your library? If it is below, then a shuffle effect increases the value by [Average Value of X cards]-[Value of Current X cards].

Decks with higher variations of value per slot make the most use of library manipulation. Again, perfectly rounded decks with zero variance from the mean value per card would not want library manipulation. It must be noted that this perfect balance might not be found at 60 cards in a specific format and metagame, and thus a perfect deck without cantrips might not be possible in many circumstances.

Brainstorm have a 2-card library manipulation value. However, it’s 3rd effect is the game-breaking ability that twists library manipulation into relevant and immediate card advantage and quality.

3.) [Hand+Library Manipulation] This is a very odd effect in magic. This is the effect that makes brainstorm more than just a mere cantrip and library manipulation. This ability might be seen as an extension of library manipulation, but we must distinguish this component of brainstorm from a Sage Owl effect because of the influence this mechanic has upon an active hand. This effect alone can make brainstorm as good as Ancestral recall + 1/2 a Sage Owl or as bad as 1/3 an Ancestral Recall + 1/2 a Sage owl. That’s right, I said it: Brainstorm can be BETTER than Ancestral Recall. There is a two card quantity difference between the worst brainstorm and the best possible brainstorm, and most of the math behind understanding the value of a specific resolution of Brainstorm, as found between that spectrum, relies upon this mechanic.

Given the cantrip effect, the Hand+Library Manipulation effect is only a count of 2 cards. The value differences

To look at the Hand+Library Manipulation effect itself, we will neglect the cantrip and library manipulation components of Brainstorm for now.

Hand:
Card in Hand1 — Value in Hand=2, Value in Library=2 (in not particular order on library, just with X cards from the top)
Card in Hand2 — Value in Hand=3, Value in Library=0
Card in Hand3 — Value in Hand=1, Value in Library 1

Library
Card on Library1 — Value in Hand=3, Value in Library 1
Card on Library2 — Value in Hand=1, Value in Library 0

Current value of Hand+Library=7.

After a 2-card Hand+Library manipulation, where Hand1 is replaced with Library1 and Hand3 is replaced with Library2, the value of Hand+Library=10

This is rudimentary, but it shows the basic principle.

Echoing truth against a High-tide/Reset deck is a useless card. Hand-Library manipulation increases your current hand value by putting echo onto your library. This, of course, is at the expense of future draw values. However, when you add shuffle effects, it turns dead cards into average card value. Essentially, Hand-library manipulation is a 3-fold utility:

1.) Gives immediate hand value increase equal to [Cards put into hand from library] - [Cards put on top of library].
2.) Combined with shuffle effect, increases library value to [Average library card value of X cards] - [current top X card library value]
3.) Hiding valuable cards that you don’t want discarded.

Brainstorm does this effect like no other card for such a cheap cost.

Card value–

I’ve talked alot about card value. But, I haven’t given any good definition for it. Here goes:

Cantrips, Hand and Library manipulation are difficult to evaluate because it requires a system of identifying the exact of value of each card in a library average circumstance/metagame and the mean variance of value in those circumstances/metagame. This is a good starting place, and it gives us a common language to better understand where and why we use or do not use Brainstorm in a deck.

Card values vary per metagame, but are static to any one specific metagame. Yawgmoth’s Will is inherently stronger in a format that is better at getting cards into the graveyard. Basic land is inherently stronger in a format that doesn’t have better alternatives.

Universal Metagame=
Specific Metagame=

For the purposes of deckbuilding, card values are determined by their degree of influence on the offense/defense ratio of a deck. You are attempting to quantify how essential a card is to your win condition (having a higher offense/defense ratio than your opponent).

A deck or card is meaningless without an opponent or metagame to interpret its value. Against a metagame/opponent with a 60-land deck, the best deck will be the one that has the highest average win condition. It isn’t just whether you won, it is the margin by which you win or lose that helps form the value of the cards in your deck against a 60-land deck metagame. The win-condition to be met, in this metagame, is simply reaching the stage where an opponent has 20 lifeloss, has been milled and can’t draw, or loses through a straight “win-ability” (Door to Nothingness, etc.). Whichever deck has the highest average chance of reaching that win-condition is the best deck in that metagame.

What if you went against a 60-FoW deck metagame? Perhaps the deck that was the best in a 60-land deck metagame would not be the best in this specific 60-FoW deck metagame. The combo deck that probably evolved in the 60-land deck metagame was not prepared to deal with permission. You might say it wanted “speed” at all costs. But, in reality, the deck is only as good as it matches against a specific metagame.

Value of a card has those two values, value in the universal context and the specific. Do not be confused into thinking this isn’t calculable. You just need to see how to go about looking for its value in the first place.

This game is calculable and finite. Please remember that.

In conclusion:

Brainstorm is a pretty awesome card. Add in a shuffle effect, and I think it is next to broken.

December 22nd, 2007 by gdoghomes

28// Mana
4 Mishra’s Workshop
2 Mishra’s Factory
1 Tolarian Academy
4 Wasteland
1 Strip Mine
3 Mountain
4 B-Ring
5 Moxes
1 Black Lotus
1 Sol Ring
1 Mana Vault
1 Mana Crypt

24// Disruption
1 Trinisphere
4 Sphere of Resistance
4 Thorn of Amethyst
4 Tangle Wire
4 CoTV
4 Smokestack
3 Crucible of Worlds

8// Creatures
4 Goblin Welder
2 Trike
2 Mox Monkey

// Sideboard
SB: 4 Jester’s Cap
SB: 4 Leyline of the Void
SB: 3 Rack and Ruin
SB: 4 Juggernauts

Control.

This pile drops lockpiece after lockpiece. Look at it: 9-sphere effects, wire, Cotv, stacks, and LD recursion a la CoWorlds all of which are accelerated by a souped up mana accel engine. This thing locks games down.

December 22nd, 2007 by gdoghomes

The purpose of this article is for us to better understand the meaning and value of resilience as it relates to your average PvP circumstances. I will give the equations context.

What is resilience?

Resilience is a 3-part stat.

A.) x% reduction in an opponent’s critical strike rate (henceforth variable resA)
B.) 2x% reduction in an opponent’s critical strike damage (resB)
C.) x% reduction in an opponent’s DoT damage (resC)

X = [Resilience rating * 0.025]

e.g. 100 resilience rating = 2.5% reduction in an opponent’s critical strike rate
5% reduction in an opponent’s critical strike damage
2.5% reduction in an opponet’s DoT damage

What is the purpose of resilience?

Resilience is a survivability stat which exists to mitigate the effectiveness of burst damage and randomness in the game. Unlike armor, it does not strictly mitigate all incoming damage like a blanket protection, however, it does serve to mitigate the random crit streaks and intensity of crits in the game while blanket-mitigating all DoT damage. Resilience eliminates variance in damage taken. Resilience, essentially, exists to make a more fair and predictable fight in PvP through increased consistency in survivability gains.

Beautifully, resilience mitigates nearly all sources of damage to some extent.

How valuable is this stat?

The best way to measure the effects of resilience is to understand its equivalence in HP. How much survivability does resilience add per itemization cost-unit as compared to the survivability gains of HP/Stamina of equivalent itemization costs? The truth of the matter is that several PvP circumstances exist in which resilience is the wrong stat in which to invest. Most players fail to recognize this fact.

HP, like AP is to melee damage, is a static and linear gain in survivability. Resilience, like most forms of damage reduction, functions exponentially, with geometric gains in survivability. Specifically, against targets that resilience can effect (assuming they have crit rating or use DoTs), resilience increases the value of each point of health.

To give a workable example, consider personA with 10k hp who faces a melee opponent with a 30% crit rate. If personA has one open gemslot, should he use a 12 stamina gem, 8 resilience gem, or 4 resilience/6 stamina to maximize his survivability against said opponent? 120hp vs. 0.2%/0.4% reduction vs. 0.1%/0.2%/60hp.

Without even looking too closely at the math, it is easy to see that the highest initial survivability (time to live) gains come from investment in HP/stamina. But, at some point, in cases where a person has enough [virtual HP] (actual HP + actual Healing received), exponential survivability stats overcome the utility of straight HP/Stamina investment in itemization costs. Where is the point of inflection? Where does resilience become greater in value, per itemization cost, than HP/stamina?

This is a somewhat complicated question to answer. It depends on several variables. Resilience rating, total virtual health, proportion of DD and DoT damage types, crit bonus, and crit rate are the fundamental variables you need to know. As each of these variables scale up or down, we’ll see shifts in the comparative values of resilience and stamina. In our case, we want to ask ourselves what the average quantity will be for each of these variables.

What calculations must be made?

We need to take a look at the very meaning of critical strike chance and how it effects survivability and opponent’s damage in order to fully understand what resilience is doing for us.

Take personA:

It takes 10,000 1-damage non-crit strikes to consume personA’s survivability.
If personA’s opponent (personB) has a 30% crit rate (and 100% crit damage bonus), then it will take ~7,692 strikes, or ~2307 2-damage crit strikes and ~5384 1-damage non-crit strikes, to consume personA’s survivability.

Moving from 0% to 30% crit chance on personB’s 1-damage strikes has a dramatic effect on personA’s time to live. 23.1% less effort is required of personB to get the same effect as striking without crits, and essentially, personA loses 23.1% survivability because of personB’s gain in crit chance.

+30% crit chance buff for personB is the same as a -23.1% debuff of personA’s HP.

10,000 * (1 - 23.1%) = 7,692 HP
7,692 1-damage non-crit strikes

Your opponent’s offense and your defense are mathematically translatable concepts. Because of this, you may even think of this situation as each point of personA’s 10,000 health is worth 23.1% LESS because of an increase in personB’s crit chance. Time to live ratio’s remain the same, regardless of how you look at the problem.

Damage enhancement is not directly the same loss in survivability for an opponent.

([HP] / (1 + [Damage Modifier])) = [Surivability Post Damage Modifier]
10,000 / (1 + .1) = 9,090
10,000 / (1 + .3) = 7,692
10,000 / (1 + .6) = 6,250
10,000 / (1 + 1.0) = 5,000
10,000 / (1 + 2.0) = 3,333

You’ll also notice that there is diminishing returns to increases in [Damage Modifer], but an exponential returns in mitigating [Damage Modifier]. Moving from 200% [DM] to 100% [DM], a 100% difference, is merely a 1,666 gain in survivability, while moving from 10% [DM] to 0% [DM], a 10% difference, is a whopping 910 survivability. The less crit your opponent has, the better resA’s effect will become.

Resilience effect A (resA) becomes better and better with each point (I’m not going to deal with the other two effects just yet), assuming that each percentage point of resilience has a corresonding degree of crit rating. If an opponent doesn’t have a great deal of crit rate, then resilience is obviously the stat to stack. Taking crit chance to near zero is preferred. Unfortunately, a character can only get so much resilience (capped in itemization), while crit rates are much easier to maximize. If high enough (beyond resilience correspondence cap), the higher your opponent’s crit rating, the less valuable resilience becomes in this respect. In some cases, crit ratings may soar so high that stamina provides greater benefit in survivability itemization.

Think about it: it takes 400 resilience to lower just 10% crit rate (and 400 resilience is a fairly large chunk). If an opponent has only 10% to begin with, then you are gaining 910 survivability. But, if the opponent had 35% crit rate (definitely possible), then you only move from 7407 to 8000 survivability, a 593 survivabilty gain. You would need a currently unreachable amount of resilience to cover that amount of crit rate. As such, you start at the low end of the curve when calculating how resilience negates crit rate, and you receive fewer actual time-to-live benefits. While resB attempts to curb this effect, it does not negate the strength of crit stacking beyond the reach of resilience itemization possibilities. In any case, the scaling needs of resilience promotes an all-or-nothing mentality (admittedly, itemization is limited, and you’re going to definitely have some degree of resilience in your gear if you PvP; however, a good portion of enchants/gems/trinkets have more variance to choose from).

The problem for the case for resilience may be worse. We need to convert the survivability gains of resilience to the flat survivability gains of stamina/HP in equivalent itemization costs.

Even if you used 400 resilience against an opponent with 10% crit rate, gaining 910 survivability, a 10% (9,090/910) increase in the value of your HP, you could do the same thing by just adding (10,000*10%) 1,000 HP.

10,000 * 10 = 11,000 / (1 + .1) = 10,000
10,000 / (1 + .1 - [400 resA or .1]) = 10,000

In this case, where playerA has 10,000 HP, a 1,000 HP gain, or 100 stamina, is the equivalent of the survivability gains of 400 resilience against an opponent with 10% crit chance. But, which is easier to reach in itemization costs, 100 stamina or 400 resilience?

Looking at gems, 100 stamina = 66.67 Resilience rating. For the itemization cost of 400 resilience, you would gain 600 stamina or 6,000 HP. It is simply obvious that 16k hp is going to have more survivability than 10k hp with 400 resilience against an opponent with a 10% crit rate.

10,000 / (1 + .1) = 9,090
16,000 / (1 + .1) = 14,545
10,000 / (1 + .1 - [400 resA or .1]) = 10,000

Using stamina in your itemization instead of resilience will net a player 5,455 survivability, while the equivalent itemization costs in resilience (400) only nets a player 910 survivability. Stamina is 500% better than resilience at 10,000 HP with an opponent at 10% crit rate. Stamina, as well, never capped, and resilience’s effect A capped because you can’t lower crit rate beyond 0%. This could exist if people were stacking enough resil and dropping every bit of crit rating possible for linear damage gains like AP/+spell/etc.

Again, as we saw before, resilience becomes even worse against targets with higher crit rates where our exponential gains of resilience are set back in the curve.

10,000 / (1 + .35) = 7,407
16,000 / (1 + .35) = 11,851
10,000 / (1 + .35 - [400 resA or .1]) = 8,000

Stamina = 11,851 - 7,407 = 4,444 survivability gain
Resilience = 593 survivability gain.

It would seem that Stamina is 649% better than resilience in this case. Ah, but now we have a crit rating that is not matched by resA, and we have not included the second effect of resilience, resB, in our calculation. Here, resB will curb the effects of rising crit rates that resA cannot negate. In this case, there is 25% crit chance left to be affected by resB’s effect. Essentially, the effects of any crit chance left over is reduced by resB.

[HP] / (1 + (([Crit rate] - [resA rate]) * (1 - [resB rate]))) = [Survivability Post Resilience] (resA and B’s effect)
10,000 / (1 + ((.35 - [.1]) * (1 - [.2]))) = 10,000 / (1 + (.25 * .8)) = 10,000 / (1 + .2) = 8,333

Notice a 333 survivability gain because of resB against an opponent with 35% crit rate.

ResA=593 survivability gain
ResB=333 survivability gain
Resilence nets 926 survivability
Stamina nets 4,444 survivability

Stamina is 380% better than resilience when including ResB’s effect with 10k hp and a 35% crit rate opponent.

There are several forces at work. The higher initial crit rate, the less we benefit from lowering it. However, the higher the crit rate, the better resilience becomes, proportionately, as compared to stamina.

We do not play in a world where everone has exactly 10k initial HP. In some cases, for example, heavy-healing based arena circumstances, whereby a person might recieve 50k healing throughout the game in addition to their natural 10k (we might say they have 60k virtual HP), resilience is extremely valuable stat. Resilience scales with your HP. It makes each health point worth MORE; stamina cannot do this.

So, taking our example at a 35% crit rate:

60,000 / (1 + .35) = 44,444
66,000 / (1 + .35) = 48,889
60,000 / (1 + (([.35] - [.1]) * (1 - [.2]))) = 50,000

Hello, resilience.

Stamina: 48,889 - 44,444 = 4,445 survivability
Resilience: 50,000 - 44,444 = 5,556 survivability

Resilience is 25% better than stamina here. Make it 590,000 Healing + 10,000 starting HP.

600,000 / (1 + .35) = 444,444
606,000 / (1 + .35) = 448,889
600,000 / (1 + (([.35] - [.1]) * (1 - [.2]))) = 500,000

Stamina: 448,889 - 444,444 = 4,445 survivability (hrmm…I swear i’ve seen this number before…linear gains look small with enough virtual HP)
Resilience: 500,000 - 444,444 = 55,556 survivability

400 Resilience is 1,149% greater than 600 Stamina with 600k virtual hp against a target with 35% crit rate.

Stamina, a linear survivability stat, becomes outclassed quickly in fights where there are high crit rates and a lot of healing.

Where is the point of inflection, whereby stamina=resilience in itemization costs?

As stated, it depends on several variables: resilience rating (converted to resA,B, and C rates), total virtual health, ratio of DoT and Direct Damage, crit bonus, and crit chance. We need to define these variables more to understand the process.

[Initial HP] + [Actual Healing received] = [Virtual HP] (or [VHP] for short)

This cannot include overhealing. It must include all buffs to your HP that are not dispelled.

Crit bonus is an important factor. Some classes have higher damage bonuses than others with a critical strike. This influences the value of resB. The higher the bonus, the more effect from resB. This show how crit bonus and resB operates inside a resilience calculation:

[Damage] + ((([Damage] * ([Crit chance] - [ResA])) * [Crit Bonus]) * (1 - [resB])) = [Damage Post Crit and Res]

Take: 1000 1-damage swings, 30% crit chance, 0% crit bonus, 10% resA and 20% resb

1000 + (((1000 * (30%-10%)) * 0%) * (1 - 20%)) =
1000 + (((1000 * 20%) * 0%) * 80%) =
1000 + ((200 * 0%) * 80%) =
1000 + (0 * 80%) = 1000

Take: 1000 1-damage swings, 30% crit chance, 50% crit bonus, 10% resA and 20% resb

1000 + (((1000 * (30%-10%)) * 50%) * (1 - 20%)) =
1000 + (((1000 * 20%) * 50%) * 80%) =
1000 + ((200 * 50%) * 80%) =
1000 + (100 * 80%) = 1080, would have been 1100 without resB. 20 damage reduction from resB

Take: 1000 1-damage swings, 30% crit chance, 100% crit bonus, 10% resA and 20% resb

1000 + (((1000 * (30%-10%)) * 100%) * (1 - 20%)) =
1000 + (((1000 * 20%) * 100%) * 80%) =
1000 + ((200 * 100%) * 80%) =
1000 + (200 * 80%) = 1160, would have been 1200 without resB. 40 damage reducton from resB

ResB’s effect scales with crit bonus. This also means that resB affect melee classes much worse, in general, than casters. With crit bonus in mind, we have to rewrite the [Survivability Post Resilience] formula:

[HP] / (1 + ((([Crit rate] - [resA rate]) * [Crit Bonus]) * (1 - [resB rate]))) = [Survivability Post Resilience] ([SPR])

ResC’s effect has yet to be discussed. This is very straightfoward. It has the same value as resA against DoTs, and it is a strict mitigation of all DoT damage (no randomness involved). The problem with calculating ResC’s effect is that we need to know the proportion of damage that is DoT and DD over an average fight. Resilience will have a more profound effect upon DD, and thus, including this ratio of DD and DoT in our equation will bring our numbers more in line with the actual average value of resilience. Unfortunately, this gives us yet another factor of variance. Some circumstances will have heavy DoT damage and others none.

At 400 resilience you will reduce all DoT damage by 10% (just as you would reduce all crit chances against you by 10%). Assuming you were taking 100% DoT damage, the survivability value of resC is exactly 10%.

It takes 10,000 1-point DoT ticks to consume the survivability of someone with 10k HP. Let’s look at what adding 400 resilience, or 10% damage reduction of DoT’s can do:

What happens in the reduction, where X is the end survivability:

X * (1 + (-10%)) = 10,000.

11,111 * (1 + (-10%)) = 10,000

so:

[HP] / (1 + ([Damage modifier]) = [Survivability]

10,000 / (1 + (-10%)) = 11,111 survivability, or a 1,111 gain in survivability.

So, to include ResC, just see it as a negative Damage modifier on DoT damage.

[HP] / (1 - [ResC]) = [Survivability Post ResC]
10,000 / (1 - 10%) = 11,111

The total equation becomes uglier by including resC’s effect. We have to include the ratio of DD and DoT damage. They will serve as two different halves of survivability.

Proportion of damage that is Direct (critable) = [PDD]
Proportion of damage that is damage over time (affected by resC) = [PDOT]

[PDD] + [PDOT] = 100% — always.

(([PDD] * [HP]) / (1 + ((([Crit rate] - [resA rate]) * [Crit Bonus]) * (1 - [resB rate])))) + ([PDOT] * [HP] / (1 - [ResC rate])) = [Survivability Post Resilience] (Res A, B, and C)

Solving the point of inflection problem:

The base inflection problem is already in front of us. We’ve dissected how this equation works and how variables impact our outcome. We need to calculate our current survivability and then consider the value of additional stamina or resilience. This means that resA, B, and C’s rates will need to be shown as conversions. Resilience points or rating (as seen in itemization), rather than percentage or rate = [Res].

(([PDD] * [HP]) / (1 + ((([Crit rate] - ([Res] * 0.00025)) * [Crit Bonus]) * (1 - ([Res] * .0005))))) + ([PDOT] * [HP] / (1 - ([Res] * 0.00025))) = [Survivability]

1 Resilience = 1.5 Stamina

We have to solve the problem from the perspective that we have a certain amount of itemization cost available to spend.

X = itemization cost spent on resilience

(([PDD] * ([HP] + (X * 15))) / (1 + ((([Crit rate] - ([Res] * 0.00025)) * [Crit Bonus]) * (1 - ([Res] * .0005))))) + ([PDOT] * ([HP] + (X * 15)) / (1 - ([Res] * 0.00025))) = [Additional HP Survivability]

(([PDD] * [HP]) / (1 + ((([Crit rate] - (([Res] + X) * 0.00025)) * [Crit Bonus]) * (1 - (([Res] + X) * .0005))))) + ([PDOT] * [HP] / (1 - (([Res] + X) * 0.00025))) = [Additonal Resilience Survivability]

(([PDD] * ([HP] + (X * 15))) / (1 + ((([Crit rate] - ([Res] * 0.00025)) * [Crit Bonus]) * (1 - ([Res] * .0005))))) + ([PDOT] * ([HP] + (X * 15)) / (1 - ([Res] * 0.00025))) = (([PDD] * [HP]) / (1 + ((([Crit rate] - (([Res] + X) * 0.00025)) * [Crit Bonus]) * (1 - (([Res] + X) * .0005))))) + ([PDOT] * [HP] / (1 - (([Res] + X) * 0.00025)))

Solve for X.

If you don’t feel like doing it, I have an excellent spreadsheet available. Put in your stats, how much itemization you have available, and it will show you what you can gain in your specific circumstance.

Conclusions:

Resilience extends your survivability in long-term, healing intensive and high crit rate battles. The shorter the battle, the less effective resilience will be.

Melee classes are affected the most by this stat.

Healers that are self-healing will draw the greatest gains from resilience. You need only enough HP to get the next heal off. For a common Focus Fire target, with a full-time heal bot, and a very high virtual HP, resilience is a bomb stat.

For classes that aren’t focus fired as often, HP DOES offer higher initial survivability. But, why stack HP at all if you aren’t even being focus fired? We can pour our itemization into damage, because we know we aren’t going to be focus fired. This, of course, makes us better targets to hit, because we are easier to kill than everyone else.

It stands that resilience acts as a bluff stat on a non-focus fired target in a team with a healer. It basically allows you to pour most of your points into damage, enough resilience to act as a deterent to being FFed, and almost no HP/stamina.

For classes with low or no-healing circumstances, as found in 1v1, 2v2, and several 3v3 groups, HP/stamina is strictly a better survivability stat. The question becomes: is survivability important for those circumstances? Perhaps, due to your class matrix or circumstance, you find yourself never being FF’d until you’ve already lost the battle. Maybe it is rogue/priest and the priest is FF’d every single game. Would the rogue really care about his survivability? If FFing the rogue from the beginning of a fight is an autoloss for a team (because tactically it would enable the priest to do his thing), then the priest will be the FF target. Therefore, the rogue is free, in itemization to stray away from survivability in favor of damage. You want to create teams where every target is a bad target to focus. But, you want to know who they will focus and bluff in your itemization.

Several teams don’t even heal (2 or 3 DPS matrices) enough for resilience to matter enough. Stack stamina.

November 1st, 2007 by gdoghomes

The word “Community” has a positive connotation. It is a warm, safe, and responsible expression. It is an object of caring complexity. Community serves as a step up, apart from the individual, to allow us to think of a group of individuals, usually in regards to needs, beliefs, and behaviors. This is a word we throw around a lot, perhaps to our injury.

Community is a word, I feel, that is slowly being twisted by post-moderns. It is a word twisted to the benefit of the post-modern, as if it lends credibility to their arguments. Community, as a meaning, is beginning to refer to a less logical construct and a more emotional one. Touchy-feely arguments are persuasive; and regardless of the lacking logical merit of the post-modern arguments, the relativists wield these words to great effect and influence. Arguments imbued with egalitarian, humanist nonsense, as found in the twisted use of the word “Community”, are dangerous and deform the proper perceptions of our purpose and identity. We must isolate and distinguish the exact meanings of weasel words, and I will start with this word: Community.

Current definitions are neither clear, nor completely tainted by the post-modern perspective. They are changing though, and they are being infected with the thoughts of the moral relativists. Our perception of the definition of community affects how we act within that context, and so we must be careful how we define it. The chosen must extract Community-ness if we wish to protect its truth-purity and disable the relativists’ attempt to convert us. If you have no idea what I mean by the post-modern undercurrent that is subverting the very nature of our understanding of community and our purpose, leading to the subversion of our communities and purpose themselves, then start with “Spheres of Justice”, with the subtitle “In defence of pluralism and equality”, a book written by Michael Walzer. Here you will be opened to a dangerous world of thought, one that denies the fundamental concept of absolute value and truth. It is here that the elite post-moderns begin their argument. This is the birthplace of the viral memes of relative-thinking that contaminate corporate and individual responsibility and value.

To arms, chosen slaves of the Word! We must win the thought-war if we are to survive and grow.

The word community is derived from the Latin communitas (meaning the same), which is in turn derived from communis, which means “common, public, shared by all or many”. Communis comes from a combination of the Latin prefix con- (which means “together”) and the word munis (which has to do with performing services).

Ironically, the original meaning is untainted and so very close to community-ness that it is scary. The modern world, even with the benefit of time which can often improve our understanding of a word or concept, has not distinguished this concept or brought us closer to the form of community; instead, the modern world has clouded the truth and even hindered us from reaching the meaning and purpose of this word. The ancient people, at least in this case, have a better handle on the meaning of the word than we do (where did progress go?…yes, we have congressed).

Generalized, a community is any number individuals or objects that share something or some set of things in common. Community-ness is the sameness found in particulars. It is the act of grouping commonality.

This seems fairly basic, as if it is too easy. However, some basic truths don’t necessarily simplify the world, they can help us to even make sense of the world in the first place. In this case, the actual number and types of communities that exist is actually very, very complex. This should remind you of Venn Diagramming.

Consider the people who live in Kentucky. This community is a sub-community/group of two sets. All that is contained in Kentucky and all people are combined to narrow and limit the meaning of both larger communities into a smaller one.

Now, consider the fat people in KY.

All Objects in Kentucky (A community itself)

All People

All Fat Objects

Narrowed into: Fat people in Kentucky.

Sadly, this is not too much different from “People in Kentucky”. Speaking of which, “People in Kentucky” and “Fat People in Kentucky” are two different communities, even if one is contained within the other.

In general, community acts as an identifier. Community gives us the logical relations between objects. Community, of course, is not bound by region or anything, but it requires at least a single commonality. Communities can be large or very, very small. They rely upon sameness in grouping, and that is the first concept to understanding community.

Community, at this point, sounds way too much like Venn Diagrams, the Forms, and just basic grouping. And, of course, it does rely upon these logic and definition systems. But, for “Community” to mean more than just “group”, and retain any useful meaning, it must be distinguished from just “group”. Community is distinguished from those logical grouping mechanisms in that it deals with a very specific type of group, a group so relevant to our discussions of purpose and value that we distinguish it and give it its own name.

The revised and more relevant definition becomes: A community is any number of morally culpable individuals that share something or some set of things in common.

‘The Community’ is comprised of all free individuals that are morally responsible for their actions and beliefs. All sub-communities are spawned from the commonalities found between members of The Community. The Community is more than just a group, it is special and set apart from all other groupings.

A community is a grouping of sameness as found in moral beings. It is here that we will find that a community becomes its own object. So, just as we can distinguish smaller communities from the larger ones by adding other commonality factors to limit the membership, we can also add up and group similar communities to form a new community obviously.

[Fat people in Kentucky] + [not-Fat people in Kentucky]=[People in Kentucky]

It is here, that Community develops its third requirement for relevant meaning. A community becomes its own object. Specifically, a community becomes its own morally culpable object or entity. A community derives a corporate moral responsibility from the morally responsible individuals that form the group. A community, at the very least, is the sum of the responsibilities of the individuals inside it. And, perhaps, moral synergy exists in a community in which even greater responsibility is required beyond the base sum. So, it may be the case that the total sum of moral responsibility of a community is greater than the sum of the individuals’ moral responsibility.

The revised and more relevant definition becomes: A community is any number of morally culpable entities that share something or some set of things in common.

Entity, of course, could be an individual or a sub-community. From this, we can logically conclude that there exists a:

Conjunction of All sub-communities that equates to “The Community”. It is the WHOLE of all possible morally culpable entities that comprise “The Community”.  The Community is an INDEX of all moral responsibilities in existence. This gets us to our final point.

Community is a measurement of moral responsibility and a required degree of value-seeking. Community-ness is relevant in distinguishing Individual and Corporate responsibility to rationally pursue value.

Community exists for the sake of rationally pursuing value, for being virtuous, and in virtue of the moral responsibility entailed with free beings and groups of free beings.

Neo-rationalists, Chosen people, Slaves of The God…you are a Community with a specific purpose and moral responsibility. Know your identity.

October 26th, 2007 by gdoghomes

One of the most elusive words today is the concept of relevance. What is relevance?

A dictionary says: the relation of something to the matter at hand.

This is fairly broad, fairly odd, but you can see that the dictionary’s definition is at least getting where we want to be going. However, the existence of a relationship between two things is not enough. Relevance is not just any old relationship, relevance must be more. It must be a specific measurement or degree of a specific relation.

As usual, I like to look at the synonyms of words to get a better feeling for what it is and is not. Context becomes fairly important. And, it could be the case that synonyms shows paths of relevance of a word. (Yes, the word “relevance” gets me giddy).

Synonyms include: applicability, cogency, connectedness, connection, connexion, materiality, pertinence, pertinency, point, reference to, regard to, relation to, respect to.

Further inquiries into these synonyms results in circular definitions all pointing towards relevance and relation (whether concerned with ‘practical’ application or semantical connection). We’ll just say that the world in general “thinks” they know what is meant by relevance, even if they can’t define it.

Don’t worry, even the elite are confused.

For example, many philosophers and word scientists have suggested that it is a relation such as: q is relevant to p if q is implied by p. Logical implication still may not draw out the *ahem* relevant characteristic of relevance. There are problems with such a theory. For example, while [”Circles are round”] may be eventually logically implied by [”Cats are mammals”] in the long chain of deductions that we call the “conjunction of truths”, the logical implication, however “close” the relation, simply does not seem actually relevant. Relevance just isn’t captured by logical implication, it misses the point. The philosophers, who turn to man-made language, predicate logic, etc, to solve their problem, will not find solace in such a definition.

It was a nice try, but like the dictionary’s argument, it does not reveal the form of relevance. Perhaps, *cough, their definitions are not as relevant to the discussion of the meaning of “relevance” as these sources would hope. The missing piece to the logic puzzle is simple and elegant–maybe even too obvious.

Relevance is about importance–relevance is about value. Relevance is a value calculation. Let us see why.

First, I commend the sources of truthiness for pointing out a very relevant characteristic of relevance. The most concrete thing we can understand about relevance is that–

Relevance calculate a relations of two variables:

1.) The matter/object at hand (often misidentified and more complex that initially conceived).
2.) The relevant object (”").

There is only one specific type of relation (of the many that can exist between two objects) that we can call relevance. It is a value-linking relation, one of value-contributor and value-receiver or sum, that enables “relevance” to have any meaning at all. Relevance is a scaling term. Some things are more relevant than others to a matter/object at hand. To the degree that an object is necessary, fundamental and important to the matter or object at hand is the degree of its relevance. Explicitly:

Relevance is the value of the relevant object as related to the object at hand (not necessarily perceived by, rather actually contributed to ‘the object at hand’)

When I ask, “what is relevant?”, I am actually asking, “What things have value?” Relevance cannot be understood outside a value-system. Relevance is more than a causal relation or logical implication. Relevance is meaningless outside of value. How an object contributes value to another is the calculable relevance of the contributing object to the object at hand. Let us go through a series of relevance questions to better understand it.

What is the relevance of cats to mammals? -> What value does “cats” contribute to “mammals”? Take the sum value of “cats” and that is what it contributes to the value of mammals. Insofar as mammal increases in value because of cats’ value contribution to it, cats are relevant to mammals.

[Value of Cats]+[Value of non-cat Mammals]=[Value of Mammals]

Relevance percentile would look like:

[value of Cats]/[Value of Mammals]=Percentile relevance of Cats to Mammals.

These are basic (very basic) relevance-object and object-at-hand, with an easy to understand relation, and one of the easiest types of questions to understand relevance. The relevance-object and object-at-hand can become as complex and specific as any particular characteristic of anything. It can also be mundane and obvious. Regardless, all of them follow this formula. Relevance questions become slightly more difficult to understand when we ask more universal ones because we have to really accept the notion of universal value to make any sense of it at all (and that isn’t an easy task). Consider the question:

What is relevant about boats?

There is a hidden statement in this question, namely, while we have the relevance-object (boats), we lack an explicit object at hand. The object at hand, in general and in this question, is “the universe” (all existence, this actual world, etc.). The question should actually be read:

What is the relevance of boats to the universe?

The answer, of course, is that boats are only relevant insofar as they contribute to the sum total value of the actual world. We presume that the total value of boats is fairly small, but remember kids: it all adds up. Assuming the hidden variable’s value is the total sum value that could ever be considered, then the answer to [what is relevant about boats?] is the exact same question as [what is the value of boats?].

Notice that defining a hidden variables makes our job easy. Defining variables can become even more complex. We could, for example ask:

What is the relevance of [the value of boats] to [the answer to the question “What is the relevance of boats to the universe?”]?

Obviously, ‘the value of boats’ itself is really the key knowledge. We would say that [the value of boats] has 100% relevance to [the answer to the question “What is the relevance of boats to the universe?”].

No matter how complex or simple the two objects or relations they hold, as long as you define the variables exactly, you can calculate relevance.

Essentially, the solution of any relevance problem requires the prior identification of the relevant elements from which a solution can be constructed. If you don’t perfectly identify your relevance-object and object-at-hand variables, then you can’t even form a true relevance question. Even when we can identify, we must evaluate each variable. Here we run into our lacking capacity to properly evaluate an object and knowing whether or not our perceptions of an object’s value conform to its actual value. That, however, is not the point of this article (even if it is a relevant issue).

[Value of Relevance-Object]/[Value of Object-in-hand]=Relevance

This is the fundamental equation to calculate relevance. Whether you show a relevance-objects value-relation to a particular object-in-hand or even the Universe in general, the equation gives you the mathematical framework to make a meaningful statement about the proportional value contributes of any one thing to another.

How valuable is P to Q? P/Q=the rate of value. Again, two types of relevance questions can be asked. I’ll give an example.

How relevant was [George Washington] to [the American Revolution]?

How relevant was [George Washington] to [the universe]?

Notice how the ratios change. George Washington’s relevance goes from fairly high to fairly low depending upon the amount of value of the object-in-hand. GW might have been 20% of the Am. Rev’s value, and thus he retains 20% relevance to AR. As for the universe, GW might not have much relevance at all. Of course, he probably retains more relevance, proportionately, than some average Joe. Both types of relevance questions have their uses…that is to say, both types of questions remain relevant types of questions among the body of questions that could be asked.
I think the topic of ‘relevance’ is…highly relevant to us because it demonstrates the mathematical strategy model and mental mode from which we can understand and calculate the comparative advantage of one value pursuit over others. It is the basis of our psychological decisions. When we choose one thing instead of another, we are making relevance and value-based calculations. Knowing how we go about making decisions through a clarified definition of relevance gives us an insight into both our responsibility and, more importantly, how we can be more virtuous. We must, therefore, be exceedingly careful in our use of the term “relevant” so as not to misattribute value to objects. Basic distinctions of perceived relevance and actual relevance must be brought to the forefront of dialogue if we wish to bring the former closer to the latter. Our minds are too easily clouded with misinformation and ‘well-intentioned’, relativistic non-sense to waste time with irrelevant definitions and choice-systems of “relevence”.

In the end, it is important that we attempt to answer: “How am I relevant to the universe?”

To answer such a question we must use this definition of relevance. And, we will notice from our relevance calculations that we will also ask: “How relevant SHOULD I be to the universe?” (explicitly: “What is the relevance of [the person I should be] to [the universe]?)
These are distinctly different value calculations. The actual ME is different that what I ought to be. Thus, the first is asking what about my current value, while the second is asking what value I should make myself (through spiritual-value growth–becoming virtuous). This shows the degree of a sinnerhood. We can subtract the AM’s value from the SHOULD BE’s value, and realize how much we need God’s grace.

Anytime you look at something’s relevance, remember to do so from the perspective of a value-based paradigm. When you make relevance calculations, you must do so from the perspective of value-based morality exclusively. You will be asking: How this X relevant to God’s Will?