Mana Curve Analysis
By Kitty · June 2020 · In DepthBack to guides
Mana. As explained at length in the complete guide and the deck building guide, mana management is everything in a Stormbound battle. The game essentially boils down to who can make the most out of their mana.
Making an efficient deck from a mana standpoint is not that trivial however. There are a lot of things to take into consideration, and it is sometimes difficult to assess the effect of a card and its cost on the overall deck.
“Lower your mana curve and add a finisher.”
— Every deck advice ever
In this short guide, we will demystify the so-called “mana curve”, see how to analyse it and how to improve it. By the end of it, you should be able to understand where mana-related problems lie and how to solve them.
To analyse the mana curve of your deck, compose it in the deck builder, then follow the “Insights” link in the navigation to switch to the detail view. You will be offered a graph representing the mana curve, as well as some suggestions to improve your deck.
Anatomy of the graph
A mana curve graph is made of two lines: the mana line (in blue), which represents the likelihood of spending all the available mana on a given turn and the cards line (in green) for the likelihood of playing all 4 cards on a given turn.
This likelihood is represented as a percentage on the Y axis, from 0 to 100%. On the opposite axis, the X axis, are the turns, from 3 mana onwards.
The intersection of the two lines marks a decisive point in the reading of such graph, as we will see more in detail in the next few sections.
The mana line
The mana line (in blue) represents the likelihood of spending all the available mana. As the game progresses and the allocated mana becomes greater, it becomes less and less likely to be able to spend it all. This is because at some point, one has too much mana for the cards in hand.
The best—not to mention theoretical—mana line is a horizontal line at the 100% mark. That would mean spending all the available mana on every turn of the game without having any leftover at any turn, regardless of how long the game lasts. The only card in the game making it possible to spend an infinite amount of mana is Lady Rime, and it is a) impossible to have her at every turn and b) not taken into consideration in this simulation.
The ideal mana line stays high for as long as possible. The higher it stays, the most mana is being used every turn, which translates into better board control or speed.
In the next graph, the mana line is steady and very high in the first 5 turns, which is very good. It means the first few turns will almost always use all the available mana, which is what one would want.
However, we see that starting turn mana 8, the likelihood of having too much mana is getting greater and greater. This is indicative of a rush deck, which will perform increasingly worse as the game progresses.
In this graph, the mana line is incredibly spiky. This is a bad sign, as it means one turn out of two will have a high chance of wasting some (possibly a lot) of mana.
There is virtually no way to spend all mana on the first turn, which is not great. The 2nd turn, at 4 mana, is actually great, with virtually no way not to spend all mana. Turn 5 however, which is a critical turn to assert board dominance, is fragile and subject to randomness.
The cards line
The cards line (in green) represents the likelihood of playing all 4 cards from the hand in a given turn. It is impossible for it to be non-null on the 3-mana turn since it would imply one or more of the 4 cards cost 0 mana (which can happen in Brawl as we will see later). As the game progresses and the allocated mana becomes greater, it becomes more and more likely to be able to play all 4 cards from the hand.
There again, the best and theoretical cards line is straight and sticking to the 100% line, since it would imply being able to play the full hand on every turn of the game, since the very beginning of the game.
The ideal cards line gets high as quick as possible. This translates into playing a lot of cards, which is usually critical for board control and speed.
In the next graph, the cards line is stuck at 0% for just a few turns, then starts going up increasingly fast.
By turn mana 7, it becomes possible—albeit unlikely—to play the full hand. Every turn from there makes it more and more likely to be able to do so.
From turn mana 10 on, the chances of being able to play all 4 cards are passing over 50% and reach over 90% by turn 13, which might potentially be a little late depending on the randomness of the cards.
In this graph, the cards line is close to null on turn mana 7, and jumps to the 40% mark by turn mana 8 thanks to Gift of the Wise which grants free mana. This makes it more likely to be able to play all cards on that turn and the subsequent ones.
It increases relatively slowly, as the ability to play all these expensive cards truly relies on Gift of the Wise to begin with. In a deck like this, turn mana 8 is decisive and likely make or break for the game. That’s why the simulation never cycles Gift of the Wise at turn mana 7 if it is in the hand.
Both the following graphs are for the same deck (with a single card change).
On the first one, we notice a very awkward turn mana 4, with a high chance of wasting mana, which is not ideal that early in the game. This is indicator of having too many cards costing an odd number of mana (namely 3- and 5-drops).
By changing a single 5-drop for a 4-drop, we have greatly smoothened the early mana line making for a less random early game.
It is important to remember that this data visualisation is still just an approximation of the real picture. A game of Stormbound involves many different mechanics which cannot be efficiently represented with a simplistic algorithm.
Here are the mechanics that are currently implemented in the representation of the mana curve:
- Cycling the most expensive card when there is not enough mana to play the full hand. While this is a little reductive, cycling the card with the highest mana cost is not an uncommon move, especially in early game where board control is critical.
- Rimelings and Gift of the Wise granting mana. Both of these cards have been properly implemented, and their mana gain is taken into account in the evaluation of these chances.
- Not cycling Gift of the Wise at turn mana 7 to make for high-value combos at turn mana 8. There again, maybe a little reductive as this is situational, but for heavy/mana-ramp decks, having Gift of the Wise at turn mana 8 is quite critical to come back from an early push and take the board back.
- Cards which cannot be played on the first turn. This includes Icicle Burst, Confinement, Unhealthy Hysteria and Broken Truce due to lack of enemies, as well as Toxic Sacrifice, and other potions (which are cheapened in Brawl) due to lack of friendly units.
This leaves us with the following mechanics yet to be implemented for a more accurate depiction of the mana curve: Frozen Core and Dawnsparks for mana-ramp Winter decks; Counselor Ahmi for Satyr decks; pirates and particularly Freebooters; Collector Mirz and Harvesters of Souls for larger-than-12 decks; and finally Archdruid Earyn for free plays.
A certain amount of Brawls decrease the mana cost of some cards (Dwarves -2 mana, Pirates -2 mana, Structures =2 mana, Spells -2 mana, Toads =2 mana, Knights -2 mana, and Unspent mana is carried over). The spell Brawl in particular makes for very interesting graphs which are interesting to look at.
The graph on the left for Frostkhan’s Eye Tempest deck is pretty astonishing, because both lines almost intersect on turn mana 6, which is incredibly early due to Gift of the Wise only costing 6 mana in that Brawl.
This means on turn mana 6, it is likely to have played all cards and have leftover mana. Other notable point is that it is already possible—although very unlikely—to play all 4 cards at turn mana 4.
In the graph on the right from The_mirc’s spell Brawl deck, the cards line does not start at 0, which is particularly interesting.
That means that as the first player, on the very first turn, it is already not only possible but also not highly unlikely to play the full hand. This is due to the high number of 0-, 1- and 2-mana cards in the deck.
How it works
This graph relies on being able to compute the odds of being able to spend all available mana, and to play all cards on a single turn. It then determine these odds for every turn from 3 until one of them reach its extreme (0% for the mana line, 100% for the cards line).
For a given turn, it computes all the possible unique hands there can be for the deck, which yields 495 sequences of 4 cards. For each hand it checks whether it is possible to spend all mana. If it is not because there is not enough mana, it cycles the most expensive card (with the exception of Gift of the Wise at turn mana 6). From there, it gets 8 new hands, and see how many can spend all mana. Eventually, we get to retrieve how many hands out of the initial 495 can spend all the available mana on a given.
Computing the chances of being able to play all 4 cards are very similar, and takes account cycling in the same way.
Special thanks to Troxyz#5675 for the original idea and implementation draft, and 123499#2723 for their help with the underlying logic and algorithms.
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