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Author Topic: Return on Investment, a concept...  (Read 7993 times)

piousflea

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Return on Investment, a concept...
« on: April 29, 2013, 10:20:23 PM »
Return on Investment: A concept

When we look at mana generator cards in MW, you spend anywhere from 4 to 6 Mana to increase your mana income by 1. Therefore, your "return on investment" (RoI) is either 1/4, 1/5, or 1/6 per round. This can also be expressed as a 4, 5, or 6 round break-even (BE).

You could argue that a 5-round BE is "average". Anything that breaks even in 4 or less rounds is an above-average investment, while anything that takes 6+ rounds is a below-average investment.

However, in the late game this assumption falls apart. If both players are low on health and could die on any given round, it is far better to blow all your mana on immediate damage or healing. Never forget that an investment that breaks even in X rounds sucks if the game ends in X-1 rounds.

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What a lot of people don't realize is that you can assess damage and actions in a similar fashion:
For example, a Fireball costs 8 Mana + 1 Quick Action to roll 6 dice and ~0.93 Burns. (approx. 9 damage vs. 0 armor, 6 damage vs. 5 armor)
Meanwhile, a Ghoul Rot on Mage costs 8 Mana + 1 Quick Action to deal 2 direct damage per round.

Looking at these numbers, Ghoul Rot takes anywhere from 3 to 5 rounds (depending on enemy Armor) to "break even" with Fireball.

So just by examining the relative value of the two spells, Ghoul Rot is an "average investment" relative to Fireball against 0 armor, but becomes a "very good investment" against high Armor. Again, whether or not Ghoul Rot is a superior play depends on the other guy's total HP. If he's got 3 HP left, a Fireball is very likely to kill instantly (0 rounds) while Ghoul Rot will still take 2 rounds. The fact that Ghoul Rot breaks even after 3 rounds is irrelevant if the enemy player is dead in 2.

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Okay, so now let's apply this concept to creatures:
A Fireball costs 8 Mana + 1 Quick Action to roll 6 dice and ~0.93 Burns. (approx. 9 damage vs. 0 armor, 6 damage vs. 5 armor)
A Skeleton costs 8 Mana + 1 Full action, and starting 1 round later it can roll 4 dice per round. (approx. 4 damage vs. 0 armor, 2 damage vs. 5 armor)

Regardless of enemy Armor, the Skeleton breaks even after 4 rounds. This makes it an "above average" investment in damage. So why use attack spells at all? Well, your opponent could kill the skeleton. He could daze or stun it. He could put an Iron Golem on Guard. All of these things would prevent the Skeleton from effectively using its damage dice, whereas a Fireball would always get its damage dice in.

In addition, the Skeleton uses a full action. If you weren't summoning, you might have used that full action to swing 4 or more damage dice (often much more). We'll talk more about this later.

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Now let's take this concept to the next level!
There are two enemy Falcons in my zone, pecking me for 3+3 dice per round. How worthwhile is a Ring of Fire?

A Ring of Fire has a 60% chance to one-shot a Falcon (it doesn't get to attack you this round). The surviving Falcons will get to attack you for at least 1 round.
- Surviving Falcons will have a 50% chance to have 1 or more Burn tokens.
- Of the Burning falcons ~67% of them will Burn to death over ~1.5 rounds.
- Overall, you will kill ~60% of Falcons instantly, ~10% of Falcons after 1 round, ~5% of Falcons after 2 rounds, and ~25% of Falcons will survive.

The traditional calculation says you're spending 9 Mana to kill an average of 1.5 Falcons (7.5 Mana) so it's not worth it. But what if we analyze it based on RoI, reducing the enemy's damage dice?
- On average, a Falcon struck by Ring of Fire will deal 1.2 damage dice the first round, 0.9 damage dice the second round, and 0.75 damage dice every round afterward.
- Compared to an unharmed Falcon, this is a 1.8 damage dice savings on the first round, 2.1 on the second, and 2.25 on the third.
- 9 mana is 1 more than a Fireball, which against an unarmored Mage would deal ~9 damage over 2 rounds. So for the purposes of our break-even analysis, let's assume that casting Ring of Fire allows your opponent to nuke you for ~10 damage dice.
* By the end of round 1, the Ring of Fire "saves" you 3.6 damage dice.
* By the end of round 2, the Ring of Fire "saves" you 7.8 damage dice.
* By the end of round 3, the Ring of Fire "saves" you 12.3 damage dice.

So even against just 2 Falcons, Ring of Fire has an extremely rapid 3-round BE! Because Falcons have a very high ratio of damage to health, you really want to kill them quickly, even if you have to use a "non mana efficient spell" to do so. But does this mean we should always use a zone-attack every time there are 2 Falcons in a zone?

Don't be silly! Ring of Fire may have a 3 round BE, but there are much less expensive ways to kill Falcons! If you can kill the Falcons with a Lash of Hellfire instead, you don't need to worry about "breaking even" because you never spend any mana in the first place.

Always remember: You can calculate break-even points for an investment, but achieving an objective for no cost is always superior to spending mana on an investment.

=============
Can we place a relative price on Quick Actions, and Full Actions?

The answer is: Sort of.

Compared to a Mana Crystal (+1 channeling with no action), a Battleforge or Thoughtspore has 1 channeling and 1 quick action, but costs 8 mana instead of 5. This is a +60% relative mana cost.

Does this mean that a quick action is worth 0.6 Mana? Don't be silly. A spawnpoint or familiar usually doesn't use its action every single round. Spawnpoints are additionally limited by range, and familiars are easily killed.

My best guess is that Quick Actions can be "priced" at ~2 Mana, while Full Actions are "priced" at around 4 Mana. Using these numbers makes Spawnpoints and Beastmaster passive seem vastly more mana efficient than you'd usually think.

However, you also have to realize that actions cost Mana. If you are mana starved, all the spawnpoints and familiars in the world are useless. Players are only willing to give up Mana for Actions if they have enough Mana to take those actions.

============
What does this all mean?

Many times in Mage Wars, a player has the opportunity to choose between an action with immediate effects (such as a Battle Fury or Fireball) and an action with delayed effects (such as summoning a creature or casting an enchantment). Taking the latter action is like making an investment toward later rounds of the game.

In each of these situations, you should try to think about the following:
1) Is the game about to end? If not, then:
2) Is there a way to achieve the same objective without an investment? If not, then:
3) If you make an investment, will it pay off in a reasonable timeframe? If so, then:
4) Does your opponent have an investment with a stronger payoff than yours?
5) If so, then focus on destroying his investments. If not, then focus on making your own investments.

For example, for a Wizard paying 4 mana per mana crystal sounds like a pretty sweet RoI. However, if an enemy Beastmaster is summoning Foxes in your face, 3 dice per round is even sweeter for him than 1 Mana per round is for you.

Instead of focusing on your own investment, your best strategic option is to focus on destroying your opponent's investments. Throw out a Ring of Fire, a Suppression Cloak, a Circle of Lightning or a Darkfenne Hydra, and you'll rapidly cut his dog swarm down to size.

On the other hand, if your opponent is investing in 5-mana Crystals while you are investing in 4-mana Crystals, you are definitely coming out ahead. You should feel comfortable sitting back and continuing to build up - investing for a future full of big creatures and attack spells.

sdougla2

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Re: Return on Investment, a concept...
« Reply #1 on: April 29, 2013, 11:34:37 PM »
Nicely written.

I often think about creatures, equipment, enchantments, and conjurations as investments, but I hadn't compared them in as much detail to immediate effects like Fireball, and I hadn't done an explicit RoI or BE analysis aside from direct mana generators.

I definitely think many players undervalue Quick Summoning.

When would you say a spawnpoint has broken even? Lets say you play a Lair, and use it to summon a creature every turn. It generates 2 mana per turn, and if you value full actions as ~4 mana, then it will break even in 3 rounds. That seems a little fast. Is that how you regard it? I tend to value spawnpoints and familiars much more for the action advantage they allow than for the mana they generate, but I haven't put a specific value on those actions when I was evaluating those cards.
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ringkichard

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Re: Return on Investment, a concept...
« Reply #2 on: April 30, 2013, 12:00:31 AM »
There's a lot of work to be done in pursuit of a systematic structure for this game, but this looks like a good start; I appreciate what you're doing here.

Some thoughts

1.  I really like using a benchmarking system to establish efficiency: the way you're comparing fireball and ghoul rot. I was working on a (brute force) comparison of all the creatures, but the tables got so large that excel crashed. What do you think good bench marks for creatures and attack spells would be? Hurl boulder? Adramelech? Bitterwood Fox?


2.  To me, measuring actions in mana currently seems like an over-reach of abstraction. Can you give some examples where evaluating actions like this is useful in play? This is one area I've struggled with, and now I try to keep my theoretical ideas pertinent to play or deck design.

For now, I favor an orthogonal 4 currency model; actions, mana, spellbook, and damage. Of course, eventually, you need some way to evaluate an exchange rate between these, but I don't think we're there yet.

3.  I think what you're getting at with your Lash of Hellfire alternative to Ring of Fire is the idea of Opportunity Costs, maybe? The opportunity cost of using a Ring of Fire is that you can't use your Lash of Helfire. Ring of Fire may be able to break even against an opponent's fireball, but does anything break even against the Lash?

4. You're going to have to introduce some sort of marginal utility concept, maybe? If I have 30+ mana, spending 9 mana for 3 extra damage is probably a good play, even if it looks really inefficient.
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ringkichard

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Re: Return on Investment, a concept...
« Reply #3 on: April 30, 2013, 12:09:53 AM »
And, one more...

5. Can you use this system to evaluate the efficiency of using Banish on a Lord of Fire?
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Preacher

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Re: Return on Investment, a concept...
« Reply #4 on: April 30, 2013, 03:39:26 AM »
I think you guys need to get out more :)

Snotwalker

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Re: Return on Investment, a concept...
« Reply #5 on: April 30, 2013, 08:07:50 AM »
Interesting read...  However, I'd like to point out that in Mage Wars, it isn't always about what's the best analytically-correct action to take, after crunching the numbers... it's also about a nifty concept called Psychological Warfare!   :angry:

Maybe it's true that it's more cost-effective, mana-wise, to utilize an attack spell this round instead of summoning another creature... but I happen to know that my opponent really hates those Gorgon Archers, and will become very distracted from my mage in his efforts to kill that snakey lady.   B)  This creature distraction will accomplish two things... 1)  give me more actions per round, and 2) take up my opponent's actions in his attempts to destroy the creature.  

And perhaps nailing the opposing mage with a fireball is also a better ROI than a ghoul rot, but I also know from experience how painful, psychologically, those curses can be whilst hanging out on your beloved mage...  often leading one to use up their own actions to try to rid themselves of the curse, hence handing the game's momentum over to their opponent by going reactive instead of proactive, as well as using up their limited number of dispells.

Now don't get me wrong... I certainly think about ROI before putting any mana flowers/crystals/etc., in my spell books, but outside of that, I think my actual gameplay tends to run more towards trying to get my opponent to react to what I'm doing, so as to grab onto and maintain the initiative.  Hmmm, is there a ROI regarding game momentum and proactive vs. reactive playstyles?

Koz

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Re: Return on Investment, a concept...
« Reply #6 on: April 30, 2013, 10:44:46 AM »
This is an excellent write up and something I've spent a lot of time thinking about.  Namely, the question of how much mana is each action worth is something I've been wracking my brain over for months now.  It's a very hard question to answer, but I think you've put a lot of good ideas down to get us started.

This thread makes me think about the recently spoiled Meditation Amulet.  That card costs 4 mana and then you can take a full action to gain 3 mana.  That just seems...awful...to me.  It takes you two full actions to gain 2 mana...yuck.  Seriously, that seems like the worst card they've ever printed and I have to question what they were thinking on that one.  

Anyway, as to the OP, this is a good thread and I will have other thoughts later when I have more time to write them up (i.e. when I'm not at work lol)

sdougla2

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Re: Return on Investment, a concept...
« Reply #7 on: April 30, 2013, 04:08:02 PM »
The other thing you could consider in this analysis is how much it costs your opponent to deal with something. If it costs them the same amount to deal with it as it cost you to play it, but it gave you something in the meantime, you're coming out ahead. If they devote more resources than you invested in order to deal with it, you also come out ahead. A Ghoul Rot that procs once and then gets Dispelled has broken even if you include the cost your opponent payed to deal with it.
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reddawn

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Re: Return on Investment, a concept...
« Reply #8 on: April 30, 2013, 05:25:43 PM »
Good analysis.  This article deserves a sticky, but I will say some parts could be a bit clearer for the less math-inclined.  And yes, I realize the math in question is not terribly complicated, but for folks like myself who see math as a foreign language, it could help out some.

I think a good majority of this article flows directly with my own article on aggro, though yours looks at the numbers much more than mine does and explains game flow in a grittier way.  This kind of investment theory definitely plays an integral part in higher level MW play and I'm glad you dissected it.

For those looking for the key lessons in this article, these are them:

4) Does your opponent have an investment with a stronger payoff than yours?
5) If so, then focus on destroying his investments. If not, then focus on making your own investments.

This is one of the most important lessons in this game.  Period.   Knowing when you are fundamentally out-gunned in the early game in a specific matchup is absolutely critical to knowing what you need to do for the rest of the game.  It is the deciding factor between in determining, as Shadow expressed in a MTG article I am well acquainted with, "Who is the Beatdown?"  

If your investments are more immediately going to pay off, you are the beatdown.  If they are not, you are the control.  If you are the beatdown, press the issue and improve your current investments, and if you are not, destroy your opponents' investments.  This is very simply why "big one" or "big two" creature beatdown works; it is the fastest way to gain the superior investment/board advantage with which to end the game.  It's effectively the same thing as dumping out a ton of small creatures early on in a MTG match; however, because of the different structures of each game, MW expresses aggro as very large, expensive creatures rather than a bunch of small, efficient ones.  This is also fundamentally why using "creature swarm" strategies that use many small critters are not aggro strategies in MW; they are extremely mana-efficient, but very action-inefficient, and thus are suited more for control/midrange strategies that need to cast early channeling bonuses in order dominate the late-game, but still need some sort of board presence so as not to get totally crushed early on.

In a nutshell, as your initial creatures get bigger and bigger, that's a good indication that you are playing aggro and are the beatdown, so press your opponent with your superior early board.  As your initial creatures get smaller and smaller, that most likely means you are the control, and need to do what you can to make sure you destroy your opponent's superior early board and delay him/her enough that your frugal mana-use pays off in the mid-late game.
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piousflea

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Re: Return on Investment, a concept...
« Reply #9 on: April 30, 2013, 07:45:08 PM »
Quote from: "sdougla2" post=12042
A Ghoul Rot that procs once and then gets Dispelled has broken even if you include the cost your opponent payed to deal with it.


That's true, and it's another source for my "quick action = 2 mana" napkin math. If you want to get rid of a Ghoul Rot (2 damage per turn) or Regrowth Belt (2 healing per turn) or Essence Drain (2 mana per turn) but you have to wait until next round because of an action shortage, you lose 2 damage or 2 mana.

However, as previously stated, just because an investment is mana-efficient does not make it a smart gameplay move. Ghoul Rot is usually a mana-efficient play. However, if I spent my quickcast putting Ghoul Rot on you, and you spend your quickcast Battle Furying for 7+7 dice and instakilling my Dark Pact Bloodreaper, you have most definitely come out ahead.

Shad0w

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Re: Return on Investment, a concept...
« Reply #10 on: May 01, 2013, 08:23:24 PM »
It is nice to see people starting to pickup on thing we noticed when we started play testing. Keep up the great work all.
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MrSaucy

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Re: Return on Investment, a concept...
« Reply #11 on: May 18, 2013, 05:01:53 AM »
I appreciate all the time you guys are putting into this post but I honestly don't see the point of it. A lot of it just seems to be common sense and intuitive. Plus, you don't need to calculate everything out using return of investment formulas and whatnot to know if a decision makes economic sense. Finally, Mage Wars has loads of strategy, but it also has loads of luck. Part of the fun is making risky "not-by-the-book" decisions and being thrilled if/when they pay off. Just my opinion. 
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reddawn

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Re: Return on Investment, a concept...
« Reply #12 on: May 22, 2013, 09:35:31 PM »
I appreciate all the time you guys are putting into this post but I honestly don't see the point of it. A lot of it just seems to be common sense and intuitive. Plus, you don't need to calculate everything out using return of investment formulas and whatnot to know if a decision makes economic sense. Finally, Mage Wars has loads of strategy, but it also has loads of luck. Part of the fun is making risky "not-by-the-book" decisions and being thrilled if/when they pay off. Just my opinion.

To be honest, I don't think the OP needed to be as in-depth to get across the fundamental ideas that I previously pointed out.  For me, the less numbers the better...but some people, especially vocal minorities that arise in online gaming communities, often enjoy the nitty-gritty knowledge that those numbers bring.

Of course, you are right that MW has luck in it, but that is not terribly relevant.  Pretty much every game has luck in it and really, MW has a lot less luck than some given the control a player has over choosing what to do and when.  In fact, there is so much player control aside from rolling attack dice that I would argue that MW would be far less fun without dice...it's really the only part of the game that is somewhat unpredictable, and its this sprinkling of unpredictability on top of very heavy player control that allows for some of the more memorable gameplay moments, for better and worse.

That said,  there definitely are baseline strategies that are simply more competitive than others.  Pit a player who knows good openings against a player who is unfamiliar with competitive openings and it wont be a close match.  That isn't to say you cant play casually but you will certainly see rewards for applying some of the concepts this article and some others discuss.
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Re: Return on Investment, a concept...
« Reply #13 on: May 27, 2013, 08:27:48 AM »
Wow! Great breakdown, very helpful.

@Koz I had the same thought about the Meditation Amulet almost the moment I saw it. The only builds that it might make sense in I think are those that employ significant boosts to number of casting actions. I'd be curious to see if it could be beneficial in a Forcemaster buiild with multiple Thoughtspores, a Warlord Swarm build with Goblin Builder and Barracks, or a Beastmaster build with Lair (you could still summon two creatures per round and just make one of them beefier while gaining the 3 mana).

Since you need the mana to make casting actions valuable it makes sense that there would be a certain trade-off point where using an action to gain mana would increase in value because you had more action potential then you could properly utilize otherwise.

Xilos of the mana temple

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Re: Return on Investment, a concept...
« Reply #14 on: September 30, 2015, 04:53:09 PM »
OH MY!!!  ALL OF THE FORUM BROWSERS SHOULD LOOK UP TO THIS GUY!!! HE IS UNBELIEVABLE