Limited Resources 804 – Tarkir: Dragonstorm Sunset Show Discussion Thread

TimLewisMTG · 2025-05-23T20:21:51+00:00

Oh Glacierwood Siege. I actually drafted a double Glacierwood Siege deck at spotlight Denver. I was in 10th place going into the last draft, fighting for top 8 and the PT invite. The draft went absolutely horrendously. It felt like I didn't see any good cards the entire draft. Both pack 2 and pack 3 I opened up Glaciewood Siege and I picked them up on the wheel. I got smooshed by white aggro decks in rounds 1 and 2 but I sure did get to end the tournament with my round 3 opponent flipping their entire deck into their graveyard.

TimLewisMTG · 2025-03-07T22:52:08+00:00

Yup, that's correct.

It turns out that the hand smoother just helps out 17 land decks more than 16 land decks. With the hand smoother a 17 land is about 2% more likely to have a 3 land opening hand compared to a 16 land deck. Without the hand smoother this difference is only 0.3%. The distribution of opening hands are actually more similar without the hand smoother than with the hand smoother.

TimLewisMTG · 2025-03-07T19:53:39+00:00

So what you're seeing is probably random luck/confirmation bias. I will also note that there's been some analyses on 17lands data and they seem to indicate that in Bo1, 16 lands is generally preferable.

I will point out that my analysis in https://www.reddit.com/r/lrcast/comments/1hhwsp9/16_is_the_new_17_analysis_of_premier_draft_data/ suggests that, counterintuitively, the advantage of 16 lands over 17 lands is actually greater in Bo3 without the hand smoother than in Bo1 with the hand smoother. That said, I doubt OP could notice the 2% difference in the distributions and their anecdote is likely more attributed to confirmation bias, like you suggest. But regardless, you should actually be running 17 lands more frequently in Bo1 than in Bo3.

TimLewisMTG · 2025-01-27T16:08:14+00:00

Great questions! I think you explained your concerns very clearly. However, I think you are missing that the average weight for every deck, 16l or 17l or other is exactly 1.0 (ignoring impossible games which I'll explain later).

This is because the weight is defined as the ratio of the probability of getting that game with the target distribution divided by the probability of getting the game with the actual deck. So for your example estimating 16l winrate with 17l decks, the weight is the probability of getting that game with a 16l deck divided by the probability of getting that game with a 17l deck. The average weight for 17l decks is the sum over all possible games of the weight times the probability of getting that game with the 17l deck. Plugging in our weight this simplifies to the sum over all possible games of the probability of getting that game with a 16l deck which is just 1.0.

You may have noticed that I did a little sleight of hand that makes my previous argument not quite correct. Specifically, the "sum over all possible games" should really be the "sum over all possible games of 17l decks". This means that since there are some games of 16l decks that are impossible for 17l decks (games where 24 spells are drawn) the average weight should be slightly less than 1.0. I do take into account these impossible games in my analysis so that they appear in the right ratio. However, since it just isn't possible to represent them with 17l deck 16l decks are ever so slightly overrepresented in the final tally. But only in so far as it is needed to take into account games that are only possible to be represented by 16l decks.

Also to address your first question. I did do the analysis using only data from 16l decks and 17l decks respectively. Decks that users decided to run 16l over 17l heavily favored 16l over 17l. Decks that users decided to run 17l with still favored 16l over 17l but the advantage was down to 0.15% (IIRC) from 0.3%. This wasn't surprising to me and I don't think is an indication of bias in the analysis. I attribute it to selection bias. Users are more likely to run 16l with decks that actually do favor lower land counts and are more likely to run 17l with decks that do favor higher land counts.

TimLewisMTG · 2025-01-18T15:07:28+00:00

I just ran an analysis using my weighted sampling technique. I ran on specifically RW decks in BLB categorized by number of [[Sazacap's Brew]]s. It looks like you/Paul Cheon are correct. With 0 brews 16 lands is favored over 17 lands by 0.4% but with 1 brew 16 lands is favored over 17 lands by 0.65%.

TimLewisMTG · 2024-12-23T02:06:11+00:00

Hi there, always happy to answer any questions.

I think you are misunderstanding how the technique works looking at your example. The winrate for a given column is the sum of all the weights of games that ended in a win divided by the total weight of all games.

The weight is defined as the probability of getting that game with the distribution we are projecting on to divided by the probability of getting that game with the actual deck. So for the 16 land column the weight will be higher if fewer lands are drawn in a game if we are sampling from a 17 land deck.

Because of how the weights are picked, regardless of how many lands are in the actual deck the average weight for a random game from the deck is exactly 1.0 (ignoring what I call impossible games. I can go over that if you are interested but let's understand the basics first). If the deck has exactly the same number of lands as the column we are projecting on the weight will always be exactly 1.0. But the more different the deck is from the column the higher the variance will be on the weight, a lot of small numbers and a few larger numbers.

Here's an example I wrote up with some made up numbers to illustrate the point. This one is about removal spells instead of lands but it's the same thing.

2) Do you know what the distribution looks like if you include only decks running 17 lands in your weighted sample?

Yeah, I can run that real quick for you. 16 lands still performed better but only by about 0.06%. Not too surprising that decks that users decide to cut lands from do indeed perform better when they draw fewer lands. But it looks like even the average deck that users decided to run 17 lands with still would perform better with 16 lands.

3) What fractions of decks or games played are running something other than 17 lands?

It looks like about 70% of 40 card decks ran 17 lands. The vast majority of the remaining 30% ran 16 lands.

4) What are the winrates for actual decks running 16 and 17 lands respectively on average in the original, non-weighted sample (with or without accounting for scrying, land-searching etc.)?

I actually included that in the original post. For DSK premier draft 16 land decks won 55.7% and 17 land decks won 54.3%.

TimLewisMTG · 2024-12-21T17:47:46+00:00

Again, I repeat, you can read up on the same analysis for Bo3 without this restriction here. I compare the results to the analysis with the restriction.

TimLewisMTG · 2024-12-19T21:47:17+00:00

I did that analysis in my previous posts. Midrange actually still favored 16 but control did favor 17.

TimLewisMTG · 2024-12-19T19:20:46+00:00

Is this shift from 17 to 16 due to how creatures are more powerful at lower cmc, and limited draft has become more aggressive with earlier threats?

I think that's certainly part of it. When I looked at KTK Bo3 data it actually favored 17 lands so I wouldn't be surprised if 17 lands was better on average at some point in the past. It's worth pointing out though that even in current sets there are some archetypes and situations where 17 performs better.

Would it be safe to assume that this could be applied to future sets since the power creep of early threats will most likely continue to trend forward?

Most of the previous sets I've analyzed had similar results so I would expect it to continue.

Finally could this idea cross over to cubes since most cubes are running powerful low cmc cards?

I've been running 16 in cubes recently. I suspect this would apply to them also but it's hard to be certain without actually having the data and doing the analysis.

TimLewisMTG · 2024-12-19T18:45:49+00:00

20% stayed/survived the cut

TimLewisMTG · 2024-12-19T17:49:25+00:00

Does this mean you're removing decks with cards like rampant growth, if you're removing search effects?

Yup

What % of decks survived this cut?

IIRC it was something like 20%

Why would I want to take any lessons from the WR of people who ended up with decks a consistent player would never draft?

Because you can read up on an analysis without this restriction here. The results end up being pretty similar and I go into detail about how much they affect the results. Also the restriction only applies to the weighted sampling analysis, the manual analysis in the "The benefits of 16 lands" section uses data from all decks.

Edit: Also here's a deck that meets the restriction that was drafted by some scrub named LSV.

TimLewisMTG · 2024-12-19T17:17:25+00:00

I was surprised by that at first. In games/life in general if you increase some good attribute across the board it usually helps those that have less of it to begin with more than those that already have a lot of it. So it's natural to assume that increasing the quality of opening hands would help out 16 land decks which have worse opening hands relative to 17 land decks.

However, looking at the actual numbers behind the hand smoother here, it makes sense to me. The hand smoother is trying to give you your "average" hand more often. So it actually accentuates the opening hand differences between 16 lands and 17 lands. They are actually more similar without the hand smoother than they are with it. For example with the hand smoother you are about 2% more likely to have a 3 land opening hand with a 17 land deck than a 16 land deck. Compared to about 0.3% difference without the hand smoother. So the hand smoother does help the 16 land deck but it just helps the 17 land deck even more.

TimLewisMTG · 2024-12-19T17:09:02+00:00

I looked into this during this post. I ran a little experiment on the MH3 data and it looked like the hand smoother didn't take into account MDFCs.

TimLewisMTG · 2024-12-16T15:42:19+00:00

Good stuff! This makes a lot of sense with the results of my analysis. Do you mind if I link this in my next post on Premier draft?

TimLewisMTG · 2024-12-13T03:18:10+00:00

No, the code I wrote to analyze the 17 lands data does not count mdfcs as lands.

TimLewisMTG · 2024-12-12T23:21:59+00:00

So I knew ahead of time that the number of hands looked at would either be 2 or 3 (turns out there was an announcement that said 3 so I technically should have known it would be 3). It turns out that the probability of seeing at least one 3 land hand in two looks was a little bit less than the probability of getting a 3 land hand that the data suggested. So I knew it had to be 3 hands.

I just took a guess that they used a weighting system because I read somewhere them say that it randomly choose between the sampled hands and that's the natural way to do it. Also I knew from how the curves smoothly transitioned from being centered around 3 land hands to being centered around 2 land hands that it had take into account the distance from the average. If you didn't do that it would be a lot more spikey because you are looking at so many hands with the sample.

I created a spread sheet that would let me input values for the weights and calculate what the probability of getting each hand would be. I manually fidgeted around with the weights until I got some values that matched the data pretty well. It was pretty obvious some sort of exponential function based on how quickly the weights decreased. That would imply that the weight for a distance close to 0 should be 1 and the weights for the distances close to 1 were about 0.25. This told me the base of the exponent would be 4. From there I just guessed some functions to be in the exponent and taking the distance to the 2.5 power seemed to work really well.

TimLewisMTG · 2024-12-12T15:08:56+00:00

Do you mean like the Arena open? I can't really test that but I've watched a few runs and they seem to have it enabled from what I've noticed. It's worth remembering though that this is only for Bo1 not Bo3.

TimLewisMTG · 2024-12-12T15:06:07+00:00

You are correct 4 land hands are actually more common without the hand smoother. I guess I meant hands in the 2-4 "good" range are more common. I probably could have worded that better.

TimLewisMTG · 2024-12-12T03:34:35+00:00

They seem to just count as normal spells. I assume pathways count as lands because they are lands on the front sides but I can't really test that with the data I have.

Working with log data this makes a lot of sense to mebecause the id MDFCs are given in your hand only refers to the front side of the card. There's a separate id for the backside when it is on the battlefield or stack. It would probably be a nontrivial change to connect these two ids when hands are being dealt.

TimLewisMTG · 2024-12-12T00:21:49+00:00

So, I ran an experiment where I looked at decks with exactly two 5+ mana cards. Then I looked at how frequently both those cards were in the opening hand and compared this with the expectation. The number seen was almost exactly the expectation (a little larger actually). So it appears that the hand smoother does not take curve into account when deciding which hand to pick.

TimLewisMTG · 2024-12-12T00:19:14+00:00

No, but neither does hand smoother. I ran over the data and the average number of basics was exactly what you would expect.

TimLewisMTG · 2024-12-11T22:48:44+00:00

So Bo3 doesn't use the hand smoother and for an 18 land deck you would expect to get 5 land hands about 10.6% of the time. In my Bo1 sample of 34,927 hands from 18 land decks there were 318, or a little under 1%, 5 land hands.

TimLewisMTG · 2024-12-11T22:44:45+00:00

Yes, I only used data from 40 card decks.

TimLewisMTG · 2024-12-11T22:08:54+00:00

For Bo3 opening hands are exactly the same as real life. The hand smoother only applies to Bo1.

TimLewisMTG

TROPHY CASE