<h6 style="text-align: right;">(<span class="edhrecp__link"><a class="edhrecp__link-a" content="Deflecting Swat" href="#" target="_blank">Deflecting Swat</a><span class="edhrecp__link-image"></span></span> | Art by <a href="https://twitter.com/izzymedrano?lang=en">Izzy</a>)</h6>
<h1>Mana Curveball</h1>
<p>Commander differs from most other Constructed formats in that you always start the game with at least one card that you know you will have access to. Your commander dictates almost everything about the 99 cards you put around it, and so it stands to reason that it would also shape your mana curve - that is, the casting costs of each other card in your deck. But how exactly does this influence manifest itself?</p>
<p>One theory comes from, among other places, a recent episode of <a href="https://www.youtube.com/channel/UCLsiaNUb42gRAP7ewbJ0ecQ">The Command Zone</a>. Episode #453, "<a href="https://youtu.be/LB6HotI0ntI?t=1265">Advanced Deckbuilding: Mastering Your Mana Curve</a>," is all about factors that brewers should account for when crafting their deck's curve.</p>
<p>Hosts Josh and Jimmy advise considering the mana value of your commander when building your curve. Specifically, you should run <em>fewer</em> cards at your commander's mana value than you otherwise might. Their theory makes sense: you know that your commander will be available to play on a specific turn (given you've hit your land drops/ramp), so don't run other cards that you would also play on that turn.</p>
<p>So, do EDH deckbuilders actually follow this recommendation? It looks like the answer is no.</p>
<p>First, consider this "average" mana curve, built by agglomerating a large sample of decks on EDHREC:<a href="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value.png"><img loading="lazy" decoding="async" class="alignnone size-full wp-image-82515" src="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value.png" alt="" width="1200" height="675" srcset="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value.png 1200w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value-300x169.png 300w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value-1024x576.png 1024w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Average-number-of-cards-per-deck-at-each-mana-value-768x432.png 768w" sizes="auto, (max-width: 1200px) 100vw, 1200px" /></a></p>
<p>This excludes all lands, and it suggests that the modal mana value across all decks is 2. There are 15.7 2-mana-value cards per deck, and 15.4 3-mana-value cards. From this peak, frequencies drop off in both directions, tailing off at the high end -- the average deck has about 1.5 cards with mana value 8 or higher.</p>
<p>If deckbuilders, broadly speaking, adhere to The Command Zone's heuristic, we should expect decks with commanders of mana value <code>x</code> to deviate from that global curve, specifically by running fewer cards at mana value <code>x</code>.</p>
<p>Looking, for example, at all of the 4-mana-value commanders pooled together, I find that there are an average of 9.7 4-MV cards, which is actually slightly <em>higher</em> than the 9.5 cards/deck in the global curve above. This is contrary to our Command Zone expectation! What do <em>all</em> of the deviations look like, at each mana value, pooled across all commanders at a given mana value?</p>
<div id="attachment_82516" style="width: 1210px" class="wp-caption alignnone"><a href="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value.png"><img loading="lazy" decoding="async" aria-describedby="caption-attachment-82516" class="wp-image-82516 size-full" src="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value.png" alt="" width="1200" height="1200" srcset="https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value.png 1200w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value-300x300.png 300w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value-1024x1024.png 1024w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value-150x150.png 150w, https://edhrecstatic.com/articles/wp-content/uploads/2022/04/Deviation-from-average-mana-value-distribution-by-commander-mana-value-768x768.png 768w" sizes="auto, (max-width: 1200px) 100vw, 1200px" /></a><p id="caption-attachment-82516" class="wp-caption-text">You're probably going to want to click on this one to see it larger.</p></div>
<p>First, note that there are only 800 0-MV commander decks in my sample, 1,200 12-MV decks, and fewer than 10,000 1-, 9-, and 10-MV decks, although even 800 is probably a sufficient number to learn something from.</p>
<p>What is this graph telling us? Well, each panel summarizes the curve of all commanders with the mana value in the panel's title. The thin line, common to all twelve panels, reproduces the "global curve" shown in the first plot we looked at. The little line segments each end with a dot; that dot represents the actual mana curve of the commander subset, meaning that the length of the line segment reflects how much deviation there is from the global mode.</p>
<p>With all of that cleared up, what can we take away from this? The first thing that stands out is that high-MV commanders seem to run a disproportionately large number of other high-MV cards (they're red/under the global curve on the left/low side and green/above the curve on the right/high side). This is almost certainly because they are built to ramp up to cast their commander early and thus have mana available to cast other expensive spells.</p>
<p>The lower end of the commander-MV spectrum is more interesting, in that it really defies Josh and Jimmy's advice. In almost every case, <code>x</code>-mana-value commanders actually run <em>more</em> <code>x</code>-mana-value spells than expected, with the exception of the 3-MV commanders. I could probably come up with some post-hoc theory that explains all of this, but I'll leave that as an exercise to the reader (send me <a href="https://twitter.com/MtG_DS">your best theories here</a>, or in the comments below).</p>
<p>Does this mean that the folks posting online decklists are doing something wrong? Maybe, but we can't tell that from the available data. Jimmy and Josh certainly know a lot about building winning decks, but (a) we don't have game outcome data to weigh in on whether their strategy really does pay off, and (b) many EDH players aren't prioritizing winning as their only objective.</p>
<p>All I feel confident saying, after seeing this data, is that high-mana-value commander decks look different from their low- and moderate-mana-value counterparts, but perhaps this sparks some ideas for how to better understand and evaluate the connection between commander MV and that of the 99.</p>
<hr />
<h2>Thoughts? Questions? Critiques? Suggestions?</h2>
<p>Let me hear them! Do you agree with The Command Zone's advice? How do you build your curve? Do you have other ideas for how to wrangle this data to find answers? I'd love to hear what you think, and if you aren’t already, please <a href="https://twitter.com/mtg_ds">follow me on Twitter</a>!</p>


Paradigm Shift - How Your Commander's Mana Value Alters Your Curve

Price of Knowledge - EDHREC Market Capitalization

<h6 style="text-align: right;">(<span class="edhrecp__link"><a class="edhrecp__link-a" content="Archaeomancer&#039;s Map" href="#" target="_blank">Archaeomancer&#039;s Map</a><span class="edhrecp__link-image"></span></span> | Art by <a href="https://www.ovidiocartagena.com/">Ovidio Cartagena</a>)</h6>
<h1>Taking Command</h1>
<p>In <a href="https://edhrec.com/articles/rise-to-the-challenge-the-best-sets-for-commander/">my last post</a>, I looked at the specific expansions which have contributed the most to the Commander format, in terms of the popularity of cards they introduced. <a href="https://edhrec.com/articles/rise-to-the-challenge-the-best-sets-for-commander/#:~:text=focused%20Masters%20sets.-,Color%20Balance,-It%20has%20long">I also found</a>, preliminarily, that recently-printed cards in white are being added to EDHREC-tracked decks at a higher rate than white cards have been added historically.</p>
<p>Mark Rosewater has noted, "<a href="https://markrosewater.tumblr.com/post/678441421658898432/in-the-last-years-weve-seen-green-get-card#notes">White has had more gains in the color pie than green in the last year</a>," and I believe one of the things to which he is referring is the expansion of white's pool of ramp and card draw, the two primary functions most commonly cited as holding white back from being able to hold its own against other colors in EDH.</p>
<div class="edhrecp__cards"><div class="edhrecp__card-container" name="Archaeomancer&#039;s Map"></div></div>
<p>For card draw, I'm using a fairly broad definition that encapsulates functions and mechanics like pure card draw, <a href="https://mtg.fandom.com/wiki/Cantrip#:~:text=A%20cantrip%20is%20a%20slang,be%20found%20in%20all%20colors.">cantrips</a>, <a href="https://mtg.fandom.com/wiki/Reanimation">reanimation</a>, regrowth effects, <a href="https://mtg.fandom.com/wiki/Looting#:~:text=Looting%20is%20a%20R%26D%20slang,equal%20to%20what%20they%20drew.">looting, and rummaging</a>. Basically, a variety of "positive" card advantage functions. You could certainly quibble with some of my choices; if you have a different idea for how to do it, <a href="https://twitter.com/MtG_DS">tell me</a>!</p>
<p>For <a href="https://mtg.fandom.com/wiki/Ramp">ramp</a>, I'm primarily looking at cards that put you "ahead on mana" relative to what you would be able to spend had you just played one land per turn. I'll also include cards that <a href="https://scryfall.com/search?q=function%3Atutor-land+ci%3Dw+ci%3D1+o%3A%22put+it+into+your+hand%22+-o%3A%22battlefield+tapped%22&amp;unique=cards&amp;as=grid&amp;order=released">tutor lands to your hand</a>. They're not ramp, strictly speaking, but they do help ensure you hit your lands drops, and they constitute a specific form of card draw. Plus, such cards seem to be part of <em>WotC</em>'s plan to help white.</p>
<hr />
<h2>Creating Supply to Meet the Demand</h2>
<p>How is <em>Wizards of the Coast</em> responding to players' demands for better ramp and draw in white? Let's count. First, note that I am again focusing only on mono-colored cards -- a <a href="https://scryfall.com/search?q=function%3Aramp+ci%3Dwg&amp;order=edhrec&amp;as=grid&amp;unique=cards">green/white ramp card</a> is just taking advantage of green's strength. These cards aren't improving ramp in white 👇.</p>
<div class="edhrecp__cards"><div class="edhrecp__card-container" name="Mirari&#039;s Wake"></div><div class="edhrecp__card-container" name="Avacyn&#039;s Pilgrim"></div><div class="edhrecp__card-container" name="Faeburrow Elder"></div></div>
<p>For each set of cards making their debut, we can just count the number of cards that serve a ramp and/or card draw function, then divide by the total number of new cards. When you do this, and plot the smoothed trend of the proportion over time, it looks like this:</p>
<p><a href="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3.png"><img loading="lazy" decoding="async" class="alignnone size-full wp-image-81812" src="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3.png" alt="" width="1200" height="675" srcset="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3.png 1200w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3-300x169.png 300w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3-1024x576.png 1024w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Smoothed-proportion-of-cards-with-ramp-or-draw-functions-by-release-date-and-color-3-768x432.png 768w" sizes="auto, (max-width: 1200px) 100vw, 1200px" /></a></p>
<p>Blue has historically lead the way with card draw, an essential part of its strengths as a color, but all five colors have seen an influx of draw spells in recent years, with white joining the party latest but with the steepest slope. In ramp, a somewhat more niche function, green dominates and has only increased its lead in recent years, but here also white is experiencing a sharp uptick.</p>
<p>We can also think of the question this way: "How recently has this function, in this color, become a priority for <em>WotC</em>?" One way to answer that question is to look at the median debut date of cards printed by color/function:</p>
<table class="table table-striped table-hover table-condensed" style="width: auto !important; margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align: left; background-color: #ffffff;">color</th>
<th style="text-align: left; background-color: #ffffff;">category</th>
<th style="text-align: right; background-color: #ffffff;">count</th>
<th style="text-align: left; background-color: #ffffff;">median date</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #c02b28 !important;">R</span></td>
<td style="text-align: center;">draw</td>
<td style="text-align: right;">71</td>
<td style="text-align: left;">2018-10-05</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #ffffff !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #345058 !important;">B</span></td>
<td style="text-align: center;">draw</td>
<td style="text-align: right;">154</td>
<td style="text-align: left;">2017-03-10</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #e2d9bb !important;">W</span></td>
<td style="text-align: center;">draw</td>
<td style="text-align: right;">66</td>
<td style="text-align: left;">2017-01-20</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #a6bcac !important;">G</span></td>
<td style="text-align: center;">draw</td>
<td style="text-align: right;">133</td>
<td style="text-align: left;">2015-07-17</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #0897d1 !important;">U</span></td>
<td style="text-align: center;">draw</td>
<td style="text-align: right;">310</td>
<td style="text-align: left;">2015-05-22</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #e2d9bb !important;">W</span></td>
<td style="text-align: center;">ramp</td>
<td style="text-align: right;">25</td>
<td style="text-align: left;">2012-05-04</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #e2d9bb !important;">W</span></td>
<td style="text-align: center;">other</td>
<td style="text-align: right;">3315</td>
<td style="text-align: left;">2010-10-01</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #c02b28 !important;">R</span></td>
<td style="text-align: center;">ramp</td>
<td style="text-align: right;">67</td>
<td style="text-align: left;">2010-10-01</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #ffffff !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #345058 !important;">B</span></td>
<td style="text-align: center;">other</td>
<td style="text-align: right;">3218</td>
<td style="text-align: left;">2010-07-16</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #c02b28 !important;">R</span></td>
<td style="text-align: center;">other</td>
<td style="text-align: right;">3243</td>
<td style="text-align: left;">2010-07-16</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #a6bcac !important;">G</span></td>
<td style="text-align: center;">other</td>
<td style="text-align: right;">2863</td>
<td style="text-align: left;">2010-07-16</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #0897d1 !important;">U</span></td>
<td style="text-align: center;">other</td>
<td style="text-align: right;">3007</td>
<td style="text-align: left;">2010-04-23</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #a6bcac !important;">G</span></td>
<td style="text-align: center;">ramp</td>
<td style="text-align: right;">319</td>
<td style="text-align: left;">2010-04-23</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #000000 !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #0897d1 !important;">U</span></td>
<td style="text-align: center;">ramp</td>
<td style="text-align: right;">41</td>
<td style="text-align: left;">2007-10-12</td>
</tr>
<tr>
<td style="text-align: center;"><span style="color: #ffffff !important; border-radius: 4px; padding-right: 4px; padding-left: 4px; background-color: #345058 !important;">B</span></td>
<td style="text-align: center;">ramp</td>
<td style="text-align: right;">46</td>
<td style="text-align: left;">2006-10-06</td>
</tr>
</tbody>
</table>
<p>Each date listed is the date before which half of all cards were first printed in their respective color/function category. So, half of all red cards with draw functionality have been printed since the fall 0f 2018. Indeed, <a href="https://markrosewater.tumblr.com/post/676585022224039936/im-listening-to-your-podcast-on-bends-and-breaks#:~:text=much%20like%20we%20created%20impulsive%20draw%20for%20red">R&amp;D has made "impulsive draw" a priority in red</a> to help with its card advantage shortcomings. Just like in the plot above, you can see that card draw is ramping up across all colors, while ramp peaked relatively early, <a href="https://scryfall.com/search?q=function%3Aramp+ci%3Db+ci%3D1+-is%3Areprint&amp;unique=cards&amp;as=grid&amp;order=released&amp;dir=asc">especially for black</a>.</p>
<div class="edhrecp__cards"><div class="edhrecp__card-container" name="Dark Ritual"></div><div class="edhrecp__card-container" name="Cabal Coffers"></div><div class="edhrecp__card-container" name="Phyrexian Tower"></div></div>
<hr />
<h2>But Are They Getting Played?</h2>
<p>It does no good if <em>Wizards</em> prints many new ramp and card draw spells for white if they are so ineffectual as to not see play. Rather than evaluate on a case-by-case basis how effective each card is in Commander, I want to look at whether internet deckbuilders are actually building with the new tools they have.</p>
<div class="edhrecp__cards"><div class="edhrecp__card-container" name="Smothering Tithe"></div></div>
<p>Let's start with January 25, 2019, the date that <span class="edhrecp__link"><a class="edhrecp__link-a" content="Smothering Tithe" href="#" target="_blank">Smothering Tithe</a><span class="edhrecp__link-image"></span></span> was released, and let's consider mono-blue cards first. Of the 659 new Commander-legal blue cards printed since that date, 105 of them have either card draw or ramp functionality; that's about 16%. Taken together, all 659 new cards appear in EDHREC decks 2,293,503 times; the new ramp/draw cards appear in 430,837 decks. So, ramp/draw constitutes almost 19% of the recently released inclusions. Take 19% ÷ 16%, and you'll find a ratio of 1.18, which we'll call the degree to which ramp/draw is <em>overrepresented</em> in Commander decks, relative to all printed cards in blue. That ratio for red, black, and green is 1.32, 1.53, and 1.67, respectively. <strong>For white, the ratio is 2.89!</strong></p>
<p>So yes, players have responded to the printing of new tools by eagerly putting them into their decks!</p>
<p>Here is another way of looking at the same question: for any given non-reprint, what is the probability that it will appear in a deck that can play it (by color identity; what I call "color identity prevalence")?</p>
<p>For cards released since <em>Ravnica Allegiance</em>, I built a very basic model<a href="#fn1"><sup>1</sup></a> predicting each card's prevalence within color-aligned decks in the two-year EDHREC data.</p>
<p>New multicolored cards and lands are more likely to be added to decks than are mono-colored cards, generally speaking, and uncommons are more likely to see play than commons; rares and mythics more likely still.</p>
<p>First, note that the average mono-colored rare is played in about 1.5% of decks that can accommodate its color identity. I'm mainly interested, though, in what the model says about card draw and ramp in white.</p>
<p>As this plot of modeled propensities shows, the typical white card draw spell released in the last three years has a prevalence of about 3%, or about twice as high as the white baseline.</p>
<p><a href="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards.png"><img loading="lazy" decoding="async" class="size-full wp-image-81856 aligncenter" src="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards.png" alt="" width="1200" height="675" srcset="https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards.png 1200w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards-300x169.png 300w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards-1024x576.png 1024w, https://edhrecstatic.com/articles/wp-content/uploads/2022/03/Modeled-prevalence-for-recently-printed-mono-colored-cards-768x432.png 768w" sizes="auto, (max-width: 1200px) 100vw, 1200px" /></a>The small set of white ramp cards each see play in almost 7% of relevant decks!<a href="#fn2"><sup>2</sup></a></p>
<p>The sample sizes involved here mean that I wouldn't draw any bold conclusions from these modeled estimates, but I don't think it's too bold to claim that your complaints have been heard, <em>Wizards</em> R&amp;D has responded, and EDH players writ large are making use of the new functionality in white.</p>
<hr />
<h2>Thoughts? Questions? Critiques? Suggestions?</h2>
<p>Let me hear them @<a href="http://twitter.com/MtG_DS">MtG_DS</a>. I’d love to know your ideas for other ways to enumerate <em>WotC</em>'s efforts to shore up white's weaknesses and whether this data convinces you that white's needs are indeed being addressed, and if you haven’t already, please <a href="https://twitter.com/mtg_ds">follow me on Twitter</a>!</p>
<hr />
<h6><sup><a id="fn1"></a>1</sup> Specifically, a negative binomial regression, to account for the overabundance of zeros in the data.</h6>
<h6><a id="fn2"></a><sup>2</sup> Changing the pool of cards to either exclude Smothering Tithe or to stretch back to the beginning of <em>Magic</em> changes the magnitude of the coefficients, but not their order.</h6>


MtGDS

MtGDS

Paradigm Shift - How Your Commander's Mana Value Alters Your Curve

Price of Knowledge - EDHREC Market Capitalization

Invigorating Boon - Shoring Up White's Biggest Weaknesses in EDH

Rise to the Challenge - The Best Sets for Commander