TTC - Modern Draft Statistics

Graham · Super Moderator

The crew shares some fascinating statistics on the winningest (and crappiest) cards in Modern Masters draft.

Lurkon · **Posted:** 11 Jul 2013, 14:06

It is really fun listening to you guys dance around trying not to tell us that running a card will win us games.
This was a lot of fun to listen to, I'd love to see these kinds of statistics for sets I've actually played with.

Graham · Super Moderator

Well, we didn't want to intentionally misinterpret the data.
It's very easy to see how Tromp has a high win percentage, because if you can't win with it, you don't cast it. Still a powerful card.

danbopes · **Posted:** 11 Jul 2013, 15:38

Just saw the video, and wanted to pop in and say thanks for the compliments. I enjoyed the statistics, and glad you put them to good use =)

-Daniel

tamaness · **Posted:** 11 Jul 2013, 19:10

I'm pretty sure that's Crovax on Volrath's Motion Sensor.

Lord Hosk · **Posted:** 11 Jul 2013, 19:37

I would love to see if they could get stats of "winner" of a drafts rating and "average draft rating" my sample was Very small compared to theirs I assume it was massively automated.

Drecon · **Posted:** 11 Jul 2013, 22:46

Yay, more TTC!
Loved the episode, the stats and the stories. Great as always.

Also: the whacky thing for Organ Harvest is that your teammates can sacrifice creatures to get the effect, which is pretty awkward as they are usually in completely different games...

mtgratingtester · **Posted:** 12 Jul 2013, 00:11

Lord Hosk wrote:

I would love to see if they could get stats of "winner" of a drafts rating and "average draft rating" my sample was Very small compared to theirs I assume it was massively automated.

Here you go.
A graph of user count v rating over the sample supplied to Graham.
http://imgur.com/WFWe1B4

bunched to the left as added <1500 together

Graham · Super Moderator

I can confirm that ^^ mtgratingtester ^^ is the source for these delicious stats

Lord Hosk · **Posted:** 12 Jul 2013, 04:42

What I mean is that I went in and manually looked at all the RTR drafts 4 times over 2 days, and typed !rating (name) of everyone in the draft then averaged it to get this.

Average rating of:

Swiss
Top two: 1642
Whole Field: 1630

4-3-2-2
Top two: 1680
Whole Feild: 1642

8-4
Top Two: 1737
Whole Field: 1653

Could you set it up to check ALL the data like you did here for the rating of the Winner of the draft, the top two of the draft and ALL participants of the draft? Or something like that? My data was only from the limited number of drafts I could do by opening the draft, typing the name, writing down the number moving on... I would love to see if it holds up over the massiveness you are able to grab.

Utilitarian · **Posted:** 12 Jul 2013, 15:07

I object to Tromp being called the most ridiculous Overrun effect

That status goes to Overwhelming Stampede, which I can't believe was ever printed.

It's in DotP 2014 ^_^

mtgratingtester · **Posted:** 13 Jul 2013, 02:42

Lord Hosk wrote:

What I mean is that I went in and manually looked at all the RTR drafts 4 times over 2 days, and typed !rating (name) of everyone in the draft then averaged it to get this.

Average rating of:

Swiss
Top two: 1642
Whole Field: 1630

4-3-2-2
Top two: 1680
Whole Feild: 1642

8-4
Top Two: 1737
Whole Field: 1653

Could you set it up to check ALL the data like you did here for the rating of the Winner of the draft, the top two of the draft and ALL participants of the draft? Or something like that? My data was only from the limited number of drafts I could do by opening the draft, typing the name, writing down the number moving on... I would love to see if it holds up over the massiveness you are able to grab.

You were very close for most of them. This is over the 20k games:

8-4
Avg 1731
Top2 1740
STDEV 76

4-3-2-2
Avg 1683
Top2 1701
STDEV 80.5

Swiss
Avg 1671
Top2 1698
STDEV 86.2

Lurkon · **Posted:** 13 Jul 2013, 05:58

Interesting. As one would expect, there's an increase in player rating when you jump up to 8-4, but there isn't much of a difference between the ratings of players of Swiss and 4-3-2-2.

Graham · Super Moderator

The same folks play Swiss and 4-3-2-2 because they don't have the confidence to face the 8-4.
But if you're winning Swiss matches, it's much better value to try the 8-4 queues.

qrpth · **Posted:** 13 Jul 2013, 13:43

I made a script that estimates some of the statistics using Bayesian probability theory.

Results:

Code:

Cloudgoat Ranger: 1169 wins, 604 losses
        Probability of being in a winning deck: 65.915%
                90% confidence interval: [64.055%; 67.755%]
        Probability of being a good card: 100.000%
Progenitus: 4 wins, 3 losses
        Probability of being in a winning deck: 55.556%
                90% confidence interval: [28.924%; 80.710%]
        Probability of being a good card: 63.672%
Bridge from Below: 0 wins, 6 losses
        Probability of being in a winning deck: 12.500%
                90% confidence interval: [0.730%; 34.816%]
        Probability of being a good card: 0.781%
Blood Moon: 0 wins, 3 losses
        Probability of being in a winning deck: 20.000%
                90% confidence interval: [1.274%; 52.713%]
        Probability of being a good card: 6.250%
Bonesplitter: 2650 wins, 2371 losses
        Probability of being in a winning deck: 52.777%
                90% confidence interval: [51.618%; 53.935%]
        Probability of being a good card: 99.996%

'90% confidence interval' means that the model is 90% certain that the true value is in that range.
Measure of being a good card: appearing in winning decks.

mtgratingtester · **Posted:** 13 Jul 2013, 21:03

qrpth wrote:

I made a script that estimates some of the statistics using Bayesian probability theory.

Results:

Code:

Cloudgoat Ranger: 1169 wins, 604 losses
        Probability of being in a winning deck: 65.915%
                90% confidence interval: [64.055%; 67.755%]
        Probability of being a good card: 100.000%
Progenitus: 4 wins, 3 losses
        Probability of being in a winning deck: 55.556%
                90% confidence interval: [28.924%; 80.710%]
        Probability of being a good card: 63.672%
Bridge from Below: 0 wins, 6 losses
        Probability of being in a winning deck: 12.500%
                90% confidence interval: [0.730%; 34.816%]
        Probability of being a good card: 0.781%
Blood Moon: 0 wins, 3 losses
        Probability of being in a winning deck: 20.000%
                90% confidence interval: [1.274%; 52.713%]
        Probability of being a good card: 6.250%
Bonesplitter: 2650 wins, 2371 losses
        Probability of being in a winning deck: 52.777%
                90% confidence interval: [51.618%; 53.935%]
        Probability of being a good card: 99.996%

'90% confidence interval' means that the model is 90% certain that the true value is in that range.
Measure of being a good card: appearing in winning decks.

not exactly sure how you calculate Probablility of being a good card?
Full data available here
http://ge.tt/5Rdvfgl/v/0

qrpth · **Posted:** 14 Jul 2013, 01:09

mtgratingtester wrote:

not exactly sure how you calculate Probablility of being a good card?

Integral of the posterior probability density function from 0.5 to 1.0.

mtgratingtester wrote:

Full data available here
http://ge.tt/5Rdvfgl/v/0

I ran my script on the full dataset and here are the top 30 cards:

Code:

  1:                Vedalken Shackles (rating: 100.00000000000000%; win prob: 72.836%; rarity: M)
  2:               Vedalken Dismisser (rating: 100.00000000000000%; win prob: 62.509%; rarity: C)
  3:                Tromp the Domains (rating: 100.00000000000000%; win prob: 85.366%; rarity: U)
  4:               Tidehollow Sculler (rating: 100.00000000000000%; win prob: 62.365%; rarity: U)
  5:                 Skeletal Vampire (rating: 100.00000000000000%; win prob: 69.407%; rarity: R)
  6:                 Sanctum Gargoyle (rating: 100.00000000000000%; win prob: 57.291%; rarity: C)
  7:                   Rude Awakening (rating: 100.00000000000000%; win prob: 78.500%; rarity: R)
  8:              Riftwing Cloudskate (rating: 100.00000000000000%; win prob: 60.647%; rarity: U)
  9:                       Pestermite (rating: 100.00000000000000%; win prob: 57.560%; rarity: C)
 10:                 Murderous Redcap (rating: 100.00000000000000%; win prob: 59.760%; rarity: U)
 11:                      Mulldrifter (rating: 100.00000000000000%; win prob: 59.636%; rarity: U)
 12:                    Marsh Flitter (rating: 100.00000000000000%; win prob: 63.798%; rarity: U)
 13:                  Latchkey Faerie (rating: 100.00000000000000%; win prob: 58.289%; rarity: C)
 14:                      Imperiosaur (rating: 100.00000000000000%; win prob: 58.588%; rarity: C)
 15:                 Faerie Mechanist (rating: 100.00000000000000%; win prob: 57.407%; rarity: C)
 16:                 Errant Ephemeron (rating: 100.00000000000000%; win prob: 59.480%; rarity: C)
 17:                 Cloudgoat Ranger (rating: 100.00000000000000%; win prob: 65.915%; rarity: U)
 18:                      Amrou Scout (rating: 100.00000000000000%; win prob: 58.692%; rarity: C)
 19:                       Æthersnipe (rating: 99.99999999999999%; win prob: 57.915%; rarity: C)
 20:              Thundercloud Shaman (rating: 99.99999999999979%; win prob: 61.179%; rarity: U)
 21:           Oona, Queen of the Fae (rating: 99.99999999999964%; win prob: 65.979%; rarity: R)
 22:               Sporesower Thallid (rating: 99.99999999999946%; win prob: 58.369%; rarity: U)
 23:                   Stir the Pride (rating: 99.99999999999913%; win prob: 65.854%; rarity: U)
 24:        Sword of Light and Shadow (rating: 99.99999999999429%; win prob: 68.039%; rarity: M)
 25:               Incremental Growth (rating: 99.99999999999137%; win prob: 63.525%; rarity: U)
 26:                      Electrolyze (rating: 99.99999999999069%; win prob: 59.060%; rarity: U)
 27:                      Flickerwisp (rating: 99.99999999998536%; win prob: 58.796%; rarity: U)
 28:                Sporoloth Ancient (rating: 99.99999999983821%; win prob: 56.418%; rarity: C)
 29:        Meloku the Clouded Mirror (rating: 99.99999999976612%; win prob: 63.551%; rarity: R)
 30:            Sword of Fire and Ice (rating: 99.99999999976504%; win prob: 66.828%; rarity: M)

And the bottom 30:

Code:

                  Crush Underfoot (rating: 2.24002136580020%; win prob: 47.043%; rarity: C)
                Arcbound Wanderer (rating: 1.98343091713762%; win prob: 43.986%; rarity: C)
                       Fury Charm (rating: 1.52030239592511%; win prob: 45.032%; rarity: C)
                 Festering Goblin (rating: 1.43924037588680%; win prob: 47.658%; rarity: C)
                Bridge from Below (rating: 0.78125000000000%; win prob: 12.500%; rarity: R)
                 Greater Gargadon (rating: 0.74163412990679%; win prob: 42.807%; rarity: R)
                        Extirpate (rating: 0.63629150390625%; win prob: 22.222%; rarity: R)
                  Summoner's Pact (rating: 0.50316666327932%; win prob: 37.500%; rarity: R)
              Reach Through Mists (rating: 0.28426579246221%; win prob: 47.061%; rarity: C)
                  Greater Mossdog (rating: 0.26329227955340%; win prob: 45.822%; rarity: C)
                    Sylvan Bounty (rating: 0.20124226759130%; win prob: 40.891%; rarity: C)
                    Angel's Grace (rating: 0.04561170935631%; win prob: 20.690%; rarity: R)
                Perilous Research (rating: 0.04241730067842%; win prob: 44.763%; rarity: C)
                       Lava Spike (rating: 0.03768397384116%; win prob: 45.574%; rarity: C)
                       Æther Vial (rating: 0.02145202542113%; win prob: 41.996%; rarity: R)
                     Manamorphose (rating: 0.01284628212620%; win prob: 44.989%; rarity: U)
                  Paradise Mantle (rating: 0.01156059400594%; win prob: 44.634%; rarity: U)
                 Arcbound Stinger (rating: 0.00632045415149%; win prob: 46.586%; rarity: C)
              Relic of Progenitus (rating: 0.00572821815057%; win prob: 39.016%; rarity: U)
                    Stingscourger (rating: 0.00172395455853%; win prob: 46.124%; rarity: C)
                       Narcomoeba (rating: 0.00171781182065%; win prob: 36.596%; rarity: U)
                    Stinkweed Imp (rating: 0.00067637976677%; win prob: 46.458%; rarity: C)
              Jhoira of the Ghitu (rating: 0.00013366427432%; win prob: 28.814%; rarity: R)
                   Rift Elemental (rating: 0.00008952249253%; win prob: 41.898%; rarity: C)
                      Syphon Life (rating: 0.00006509801909%; win prob: 42.128%; rarity: C)
              Squee, Goblin Nabob (rating: 0.00003111605357%; win prob: 39.114%; rarity: R)
               Hammerheim Deadeye (rating: 0.00000415762164%; win prob: 42.230%; rarity: C)
                        Hana Kami (rating: 0.00000133099942%; win prob: 37.576%; rarity: C)
                 Runed Stalactite (rating: 0.00000006253135%; win prob: 41.698%; rarity: C)
           Stinkdrinker Daredevil (rating: 0.00000000005429%; win prob: 42.377%; rarity: C)

mtgratingtester · **Posted:** 14 Jul 2013, 03:59

more data
http://ge.tt/1MWbjhl/v/0

Code:

Total Games   20928
   
Avg Turns   9.0
Avg Lands   6.2
   
Win % on Play   49.9%
Win % on Draw   50.1%

Mulligan to   6          5          4
Win% Average   36.4%   21.6%   14.8%
Win% on play   35.9%   19.0%   16.7%
Win% on draw   36.9%   24.6%   13.3%
         
Name        Played % of Field   Win%
WUB (Esper)   908   2.5%   52.6%
UGR           870   2.4%   51.1%
BGR (Jund)   533   1.5%   48.2%
WGR           906   2.5%   46.9%
WUG           817   2.2%   54.1%
UBG           671   1.8%   50.4%
WBR           473   1.3%   51.8%
WR (Boros)   4173   11.5%   51.0%
WUR           1134   3.1%   49.6%
UBR (Grixis)   827   2.3%   52.5%
BR (Rakdos)   2641   7.3%   48.5%
BG (Golgari)   1589   4.4%   48.6%
WBG           666   1.8%   48.3%
UG (Simic)   2031   5.6%   50.8%
WG (Selesnya)   3099   8.5%   49.8%
WU (Azorios)   3596   9.9%   55.2%
GR (Gruul)   1950   5.4%   45.0%
UR (Izzet)   2843   7.8%   48.8%
WB (Orzhov)   2902   8.0%   55.3%
UB (Dimir)   3702   10.2%   52.1%

Lord Hosk · **Posted:** 14 Jul 2013, 19:15

Graham wrote:

The same folks play Swiss and 4-3-2-2 because they don't have the confidence to face the 8-4.
But if you're winning Swiss matches, it's much better value to try the 8-4 queues.

When I ran all my games I had much better return on the 4-3-2-2. in 16 drafts of each I got back 46 packs in 4-3-2-2. 39 packs in swiss, but only 32 in 8-4.

There is a definite jump in skill level to the 8-4s which explains why I got back almost a pack less on average.

Lord Hosk · **Posted:** 14 Jul 2013, 19:18

mtgratingtester wrote:

You were very close for most of them. This is over the 20k games:

8-4
Avg 1731
Top2 1740
STDEV 76

4-3-2-2
Avg 1683
Top2 1701
STDEV 80.5

Swiss
Avg 1671
Top2 1698
STDEV 86.2

Thank you very much! is that RTR, MM or all drafts? I dont know if it would matter im just curious about stats.

phlip · **Posted:** 14 Jul 2013, 19:40

Lord Hosk wrote:

Thank you very much! is that RTR, MM or all drafts? I dont know if it would matter im just curious about stats.

This is what I was just about to ask, too... If you have the data for a "normal" (non-MMA) draft format, like RTR block, I'd love to run some analysis on it re: the 4-3-2-2 EV debate... (I could do the same analysis for MMA figures, but it would be less likely to be widely applicable, since I suspect the format drew more better players.)

Lord Hosk · **Posted:** 14 Jul 2013, 20:09

That was exactly what I was thinking, Modern Masters had a different group of players than "standard" "current" stuff.

My big complaint about the bad EV arguments for 4-3-2-2 because "You are just throwing away a pack because they pay less" There is a clear skill difference and skill matters in magic the gathering, meaning that slightly less skilled players have a better chance of winning and a much better chance of getting packs back in a 4-3-2-2 than a 8-4.

It is extremely unlikely that you will be able to go infinite on 4-3-2-2's no matter how good you are, and next to impossible to come out ahead. If you are very good either are possible in 8-4's.

My experience would show that you can slow you bleeding and get many more games in for the investment though if you are below the "play forever" skill level.

mtgratingtester · **Posted:** 14 Jul 2013, 20:45

That depends on whether the LRR guys want to do a show on the DGR data first, but happy to publish it after.

Lord Hosk · **Posted:** 15 Jul 2013, 06:27

So those ratings numbers are for Modern Masters?

ecocd · **Posted:** 15 Jul 2013, 09:10

These data are pretty cool. I'm not going to take the time to dig them out, but there was 1 common that was never cast, 6 uncommons, 5 rares and no mythics.

In 19,243 drafts, each draft saw about 16750 (+-240) copies of each common (fudging for foil lands), 7700 (+-56) of each uncommon, 2540 (+-22) of each rare and 1280 (+-9) of each mythic. Recall even though mythics are 1 out of 8 packs, there are only 15 mythics compared to 53 rares which accounts for the counterintuitive result.

It may be possible to back out an estimate on the proportion of times each card was included in a deck, but it would be a pretty wild estimate making some pretty strong assumptions.

Other fun statistics:
11 games were won by a player having played only 1 land
56 with 2 lands
402 with 3 lands
1638 with 4 lands
3917 with 5 lands
5269 with 6 lands
...
21 games with 15 or more lands
4 games with 19 or more lands

And Zempre won a game on turn 25 having played 20 lands.

@qrpth if those are Bayesian estimates, they're credible intervals, not confidence intervals. What does "Measure of being a good card: appearing in winning decks." mean, anyway? What was your prior distribution that gave you credible intervals extending well above 0 when the empirical evidence was Bridge From Below was 0-for-6?

TTC - Modern Draft Statistics

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