One of my favorite recent movies was Moneyball, a baseball film that follows the success of the Oakland A’s. The premise was that the general manager had significantly less money than the large market teams. In order to compete, he uses sabremetrics to evaluate the usefulness of a player as opposed to traditional means of scouting, which were highly subjective. Through some great managing, he gets the 2002 A’s to the playoffs with 1/3 of the budget of a large market team. The movie gave me inspiration to look at how statistics can determine outcomes.
To give a little history about myself, I’ve always been known as the nerdy kid even by Pokémon player standards. I played the card game from Base Set to Neo Revelation and took a 8 year hiatus. I recently got into Pokémon again as a result of opening a box of Black and White. This lead me to joining a local Pokémon League and, later, the 6 Prizes community.
For some people, this whole article might seem like numbers and technical jargon, so I hope to give some practicality by giving an example of how prepared and built my deck before Regionals. Being out of the game for such a long time, I decided to go with an easier straightforward deck, ZPST.
The Stock List
I decided to go with a stock list from back in June that was in one of the previous ZPST related articles to get a feel for the general deck and play in general. My friends also gave me some general axioms for building decks such as having 4 Pokémon Collector, 4 Professor Oak’s New Theory, and at least 12 Basic Pokémon.
Here’s the decklist that I started off with.
|
Pokémon – 12 |
Trainers – 32
4 Junk Arm 1 Switch |
Energy – 16 12 L |
In deck building, many take the approach of play testing against the most popular decks and will, for the most part, reach reasonable conclusions in regard to fine-tuning a deck. One thing I like to do in particular in play testing is keep a notepad and write notes for each game I play. Each turn, I write down cards that could have helped out the situation and cards that were “dead”. If I see reoccurring cards, then I will add or drop those particular cards.
Another fun way to optimize in play testing for those last couple of slots in your deck is to play a couple of “wild” cards in your deck. When you draw them, you can play them as if they are any card. It seems rigged, but it will also give you a loose idea of what is needed in the deck.
There were many things I found that didn’t work with the deck, but for the most part it was fine tuned. Being the competitive person I am, I wanted to make sure I had some numbers to back up the validity of the deck.
Statistics, be careful!
freespirit.comThere are many subjects where you can compile as many statistics as you want, but most of it will be just numbers if it doesn’t mean anything to you. When you look at probability, it is important to set what goals you want to accomplish. The goal of ZPST is to do the following:
Start with a Tornadus or Zekrom and get multiple Energy with Pachirisu or Shaymin to charge a Tornadus and Zekrom.
To break this down into simple terms, we want the highest probability of opening a Tornadus or Zekrom and then obtaining 2-3 energy cards with Pachirisu or Shaymin in the most efficient way possible.
The starting hand is what we’ll examine.
Basics and Probability
I wanted my starting hands to be the best to combat the threats of the metagame and setup as fast as possible. With decks such as ZPST and Tyrogue being able to donk, I wanted to make sure the deck’s initial Pokémon met the following.
- Start an ideal Pokémon (Zekrom or Tornadus)
- Make sure I had at least 2 Pokémon in play (I guess this is more important for other decks that have several low HP Pokémon)
- (Lower priority) Make sure I don’t mulligan
To spare you the math that goes into this, I compiled some tables that showed this information. I know that Ness has “Basic Pokémon math” done in an article somewhere on the internet. I have formulas to determine the probability of each situation, and I will address how to do the calculations of each in another article.
For these calculations though, I am going to define some variables:
# of Basics in the deck – Pretty self-explanatory.
# of “good ideal” starters in the deck – This is what you can define. Usually, it is something with decent HP or free retreat.
In the case of ZPST, the ideal starter will always be Zekrom or Tornadus. The number of Basics in the deck totaled to be 12 Pokémon with 8 ideal starters (4 Zekrom and 4 Tornadus).
| # of Ideal Starters in Deck | ||||||||||
| # of Total Basic Pokémon in Deck | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
| 4 | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 5 | 84.2% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 6 | 73.8% | 87.6% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 7 | 66.5% | 79.0% | 90.1% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 8 | 61.1% | 72.6% | 82.8% | 91.9% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 9 | 57.1% | 67.8% | 77.3% | 85.8% | 93.3% | 100.0% | 100.0% | 100.0% | 100.0% | |
| 10 | 53.9% | 64.0% | 73.0% | 81.0% | 88.2% | 94.5% | 100.0% | 100.0% | 100.0% | |
| 11 | 51.4% | 61.0% | 69.6% | 77.3% | 84.1% | 90.1% | 95.3% | 100.0% | 100.0% | |
| 12 | 49.4% | 58.6% | 66.9% | 74.2% | 80.8% | 86.5% | 91.6% | 96.1% | 100.0% | |
| 13 | 47.7% | 56.7% | 64.7% | 71.8% | 78.1% | 83.6% | 88.6% | 92.9% | 96.7% | |
| 14 | 46.4% | 55.1% | 62.9% | 69.8% | 75.9% | 81.3% | 86.1% | 90.3% | 94.0% | |
| 15 | 45.3% | 53.8% | 61.4% | 68.1% | 74.1% | 79.3% | 84.0% | 88.1% | 91.7% | |
| 16 | 44.4% | 52.7% | 60.1% | 66.7% | 72.6% | 77.7% | 82.3% | 86.3% | 89.9% | |
Table 1: Probability of starting a good Pokémon
To use this table, simply line up the number of total Pokémon in the deck and the number of ideal starters to find the total probability of starting an “ideal starter”. In this example, we have 8 good starters (4 Zekrom and 4 Tornadus) and 12 total starters. We can see from here, that we will have a 80.8% chance with a non-mulligan hand to start a Zekrom or Tornadus. This is roughly 4 out of 5 games
With statistics, you have to be careful in balancing what you really want from your deck. I could simply drop Shaymin and Pachirisu to make sure that I start Zekrom or Tornadus 100% of the time, but that would kill the point of the deck. It is important to discern various factors in deck building. By increasing the odds of a situation, you lower the odds of another.
There were some side things I considered in testing out the deck.
1. Drop a Zekrom
pokebeach.comIn many matches, I prefer to start a Tornadus and then use hurricane to set up other Tornadus or Zekrom and maintain a balance on energy flow.
If we use Tornadus as our only ideal starter, then our chances of opening Tornadus increases from 49.4% (4 Tornadus, 12 starters) to 51.4% (4 Tornadus, 11 Starters). This seems decent right? However by doing so, our chances of having to open with a Pachirisu or Shaymin increases from 19.2% to 22.7%.
There were two things to consider the decision:
a. Do I value starting Tornadus at any cost?
b. Do I value not having to start Pachirisu or Shaymin?
For me, I preferred not having to use a Pachirisu or Shaymin early over starting the Tornadus more frequently. My matchup in the ZPST mirror also required the 4th Zekrom. This led to the decision of keeping the 4th Zekrom.
2. Adding Tech
This decision was a bit tougher for me because with a stock list, I have a significantly low chance of winning against a Trainer lock based deck. I looked into adding a combination of 1 or 2 Basics, but each tech option, unfortunately, had very low HP, so I had to research another statistic with donking becoming more of a risk.
Here’s another table to look at:
| # of Basic Pokémon | Chance of Starting 2+ Basics |
| 4 | 15.82% |
| 5 | 20.91% |
| 6 | 25.89% |
| 7 | 30.75% |
| 8 | 35.48% |
| 9 | 40.06% |
| 10 | 44.50% |
| 11 | 48.78% |
| 12 | 52.89% |
| 13 | 56.83% |
| 14 | 60.58% |
| 15 | 64.15% |
| 16 | 67.53% |
Table 2: Probability of starting two or more Pokémon
So now I have to balance two statistics, the probability of starting a good Pokémon as well as avoiding potential donks. With a tech, I believe it is too risky to just run one copy in case it is prized, so typically I would want to run at least 2 to avoid this from occurring. So let’s look at the new math.
We would have a total of 14 Pokémon (12 original + 2 tech) and 8 ideal starters.
If you refer to Table 1, this means that we decrease our chances of starting Zekrom or Tornadus from 80.8% to 75.9%, meaning that we will see a bad starting Pokémon every 4 games as opposed to 5 games. We also will only get 2 or more Basics about 60% of the time.
Let’s compare the two builds:
| ZPST | ZPST w/ tech | |
| # of Basics | 12 | 14 |
| # of Ideal Starters | 8 | 8 |
| Chance of Starting an Ideal Starter | 80.80% | 75.90% |
| Chances of Opening 2+ Pokémon | 52.89% | 60.58% |
| Chances of Mulligan | 19.06% | 13.86% |
The key statistic here was the fact that I drop my chances of starting Tornadus or Zekrom by 5%, which ultimately led me to sticking with straight ZPST. My goal was to set up turn 1 and having to find an additional energy, super scoop up, or switch would ultimately lead me to be too far behind.
On a closing note of this section, feel free to use the tables to do some of your own calculations
Supporter Draw
Ideally, in any deck, always having a Supporter is a must. Assuming that you start off with a Basic Pokémon, which leaves you 7 cards (6 cards + 1 draw) to get a Supporter. Here is another table to determine the odds of drawing at least one Supporter.
| # of Supporters and Pokégear 3.0 | Chances of opening a Supporter or Pokégear |
| 7 | 60.78% |
| 8 | 66.06% |
| 9 | 70.72% |
| 10 | 74.82% |
| 11 | 78.42% |
| 12 | 81.56% |
| 13 | 84.31% |
| 14 | 86.70% |
| 15 | 88.77% |
| 16 | 90.55% |
| 17 | 92.09% |
| 18 | 93.41% |
Table 3: Probability of opening with a draw Supporter
I included Pokégear 3.0 in this calculation because it will essentially get you a Supporter, especially in decks with higher counts, unless you just stink at drawing or your opponent flipped heads with Teddiursa TM.
The important fact to realize here is the idea of diminishing returns. As you incrementally add Supporters, the percent difference will decrease. When we go from 7 to 8 Supporters, we see an increase of 5.3%, but when we go from 17 to 18 Supporters, the probability only increases by 1.3%.
I wanted to make sure that my hand wasn’t always too cluttered with Supporters and through testing, I found that 15 was incredibly sufficient, giving me a Supporter to start the game roughly 8 out of 9 games.
Energy
Lastly, a good ZPST deck needs high energy because it needs two (1 DCE + 1 Lightning) or three Energy (3 Lightning or 2 DCE + 1 Lightning) in order to achieve the donk. With that being said, I present another table:
| Key Stats | # of Non-Energy Cards Seen | 0 Energy | 1 Energy | 2 Energy | 3 Energy |
| Opening Pokémon Collector | 6 | 14.10% | 33.63% | 33.18% | 15.88% |
| Opening Hand Refresher | 13 or 14 (PONT/Juniper) | 1.00% | 5.61% | 16.28% | 75.96% |
| Opening Hand Grower | 10 or 9 (Cheren, Sage’s) | 3.29% | 13.67% | 27.14% | 28.95% |
Table 4: Supporter and Energy Synergy (Assume 16 Energies/Energy Search in Deck)
pokebeach.comMany people saw the merits of opening Pokémon Collector and getting an instadonk with Pachirisu and Shaymin. However, in early testing, I found that Pokémon Collector would rarely ever achieve the donk for me and would often clutter my hand mid-game.
I did some calculations and Table 4 confirmed my suspicion that having 4 Pokémon Collector in the deck was not the optimal build. The 3 energy donk was incredibly hard to achieve. The statistics showed me that opening a Pokémon Collector with three energies only occurs 15.88% of the time or roughly 1 out of 6 games.
In contrast, opening the game with a hand refresher such as Professor Juniper helped my odds immensely to over 75%! Being able to start a game by attaching an Energy, Dual Balling, and then playing Professor Juniper or PONT led to significantly more T1 setups.
Now I know this isn’t completely revolutionary because many are playing 2 Pokémon Collector and 4 Dual Balls in their ZPST builds, but, at least we have some statistical justification to it! With that being said, here was my closing list that got Top 16 at Regionals.
|
Pokémon – 12 |
Trainers – 33 2 Cheren 2 Judge
2 Pokégear 3.0
4 Junk Arm 1 Defender 1 Switcht |
Energy – 15 11 L |
Mark A. HicksTo recap, I decided on the standard build with 12 Pokémon, 16 Energy (note the 1 Energy Search), and 15 Supporters/Pokégear 3.0. The combination of Trainers was done through play testing. I wanted a tool box of Trainers with the Junk Arm engine.
The only oddity you will see here is that I use 2 Judge and this was to counter other decks, especially Gothitelle and Trainer lock based deck. This helped significantly in the matchup without losing me too much consistency against other decks and was an overall solid play.
In the Trainer lock matchup, unless they haven’t used Pokémon Collector yet and benched their needed Pokémon, I would aim for a kill only after Judging them, significantly reducing the chances of them to retaliate with twins.
Anyway, I hope you enjoyed my article. This may have been one of the most boring articles you have ever read.
Lastly, I have attached the Excel document that will auto-calculate many things for you by a couple of simple inputs. I will explain how to use this in a follow-up article. Enjoy!
Now this is something I’d like to see more of.
I tried to download the excel document but we need to request access to it. Is there a way for you to fix this for others and for yourself so you don’t have to approve a bunch of people? or was this intentional?
This will be fixed soon hopefully – I couldn’t access it either. I figured I’d at least post the article now then Daniel can open up access to the file when he has a chance.
I just got to work and have changed the privacy settings for the excel document. Anyone has access to it, you can PM me if you have questions in regards to running it.
This is just my kind of article. I think on Pro Pokémon I found out about calculating Basics and it was awesome to do. This is awesome. Thanks.
Great article man, i was thinking of doing something like this for a future underground article but you beat me to it. Good job. It’s funny how moneyball is just getting main stream because of the movie when I’d read that book maybe 4-5 years ago and I’m a fan of the Tampa Bay Rays and their management because they’d taken moneyball to the next level. Oakland did it with 1/3 of the Yankees payroll but the Rays have done it with 1/5, and are even more stacked than the A’s ever were in terms of future talent.
Anyways, great job and I hope to see more of this.
I did not know the Rays did that, was that this year?
This is something I’ve been thinking about recently. I’m not super great at math, so it’s great to see a guide I can go by to work with my decks. AWESOME article!
Epic article. Thanks dude
You have to wonder how many good players take these kinds of numbers into consideration when playing a deck. I sure didn’t before reading this, hopefully this will be touched on more in the future +1 :)
I think many pros get a feel for what is good even if they don’t go heavy into the statistics. Realistically, in a more complicated deck such as PrimeTime, there are many other numbers that need to balance out besides the starting situation. Mid game and late game situations play more of a prevalent role in deck building that needs to be considered.
Statistics are huge in Pokemon. I personally don’t go into this exact detail, I’ll go for a rougher idea (instead of getting 21.2%, I’ll get 20%). I get pretty much the same information, it just helps save time.
Great article!
Great work, man. I couldn’t get the Google Doc to open (try File -> Publish to Web?).
Also: “Lastly, a good ZPST deck needs high energy because it needs two (1 DCE + 1 Lightning) or three Energy (3 Lightning or 2 DCE + 1 Lightning) in order to achieve the donk. With that being said, I present another table:”
I think you mean 3 Lightning or 2 Lightning + 1 DCE) there.
Also also, for those who want to do the math on their deck: http://www.pokepedia.net/ has a deck analyzer that allows you to see several of these statistics in there, such as your chances of opening with a certain Basic, only that Basic, etc. I think this is pretty well known but I figure it would fit in this article.
Hey Mekkah. I fixed the privacy settings. Can you try again and see if it works?
As for pokepedia, there were some discrepancies I found with the math. It does give you the probability of starting a lone basic in a non-mulligan setting. However, if you do mulligan, you simply shuffle your hand and that hand is considered dead. As a result, the odds of starting a particular basic is not 100% accurate because it doesn’t account for having to reshuffle if a mulligan occurs.
It works now. Did you manage to publish it for everyone, or did you just give me access?
I was gonna verify what you said about Pokepedia math because that would be a pretty big deal, but I can’t really be bothered. I think I get what you mean though.
I gave everyone access to it. In regards to Pokepedia, the math is correct, but it doesn’t give you a true % of the time you have to start a particular pokemon because it doesn’t take into account mulligans.
This is one of the better articles written on here in a long time.
Wow, amazing (but brain-hurting :P) article! Someone’s going to be a Mathematician :P
Now THIS is a good substitute to the probabilities of how decks stand a chance against others.
This is one heck of an article. VERY well done!
Best article I have ever seen on this site. Props
I think this sort of analysis is totally worth doing with ZPST, but you can’t argue with experience. All the odds in the world can be foiled by poor play. So, when I made up my ZPST list I tested it by loading it up and just running it on a computer (playtcg.me) a bunch of times to see how often I got the sort of start I wanted.
I was able to tally what kind of turn1 or turn2 attack I put together and weather I saw a Catcher or not (something you’ld really want to keep track of). The one curious thing I noticed was the inverse correlation of getting a Catcher and getting a turn 1/2 bolt strike. That is, when I ended up with only a T2 hurricane, I saw catcher in those scenarios more often than in others.
I was using this tactic to decide between draw supporters and ultimately went with 4 PONT 2 Juniper 2 Judge and 3 pokegear. That’s one less than this list here, but I also teched 2 Bellsprout, Seeker and Fisherman for lock matches – these 4 cards would be the first to be swapped out now.
I also discovered the power of Energy Search, which really pumped my getting 3 energy on turn 1.
What I love about ZPST is its total versatility to techs. hmmm…. think I’m going to go play it some more.
I would say, no.
This is cool & all but as much as we wish they were, not all cards are uniform in shape and weight, even in cases.
The slight weight and curvature of primes and holos is an easily citable example, as well as weight differences in reverse holos or otherwise all skew these numbers by a bit.
This math is cool on paper, but that’s where it belongs.
I’m sad to say he’s right, your non-full art reverse holo Zekrom and Tornadus are thicker than your Pachis and Shaymins. I haven’t tested this theory with Full Arts because I think of them as a waste of cash.
I’ve found that your Tornadus and Zekrom (so long as they aren’t Full Art) are thicker than your Pachirisus or Shaymins.
If your cards are sleeved (which they should be) and unmarked by the judge’s perception (which they should be) the slight weight and curve differences are a non-issue. If you’re shuffling correctly, that won’t affect your odds.
However, it’s still odds. The random nature of the game is what turns people off to statistical analysis. I think the article was amazing and exactly what needs to be done instead of “personal experience” and an author’s instincts.
It was a great article, but then how do you explain how, let’s say, I nearly always start my full art Zekrom or reverse holo Solosis when I play Gothitelle, when I only play 1 FA Zekrom and 1 RH Solosis?
you stack the deck, obvioulsy! :P
Wow, you’ve put in a lot of effort for this article! Thanks!
I want to like this, but it’s so hard to support an article that’s giving real, logical, mathematical reasons and counts for how to achieve a better donk in ZPST D= That deck is already hard enough to beat with heavy Trainers.
But +1 anyways because this is amazing and has way more evidence than most else. It’s impossible to count every single possible variable, but this is still crazy extensive.
Raw numbers. I like it.
Very interesting and very unique. I also liked the opener. The excel document also looks awesome – thanks man!
why hasnt coolestman22 trolled this yet?
Yes, He would say: “Your chances of starting with Tornadus are 80%, but with Thundurus it will be 1000000%”.
Never forget that Muldin would say too: “You have 5 Tornadus in your deck quarter-turn, your piece of CHEAT”.
i just realized that the probability of coolestman22 being the same person as muldin is >9,000%
p.s. you are now one of my favorite pokemon players for your epic reply comment!
Thanks about that! When You come here in Brazil, or we meet each other at some world, I really will enjoy play with you.
i would enjoy that too! and not just because i somehow managed to get into brazil/worlds lol : P
but seriously, i would love to play you sometime also!
Fantastic analysis. I think for a deck like ZPST this kind of in-depth calculations are very viable. But for much complicated decks, I think it will be more and more difficult as more types of cards (Evolutions, Stadiums) are incorporated. Sure its still all possible, but we’ll be looking at way more numbers…
One thing I find interesting is the diminishing returns of the probability of getting a Supporter as the number of it increases. Not a whole lot of change but still something. Kudos for the article. :D
Phenomenal. Loved the stats.
All this statistical knowledge, yet you still have 4 tech trainers (Defender, SSU, Energy Search, Switch)? Without anything to search out these trainers, it’s incredibly situational that you’ll have discarded them (to use with Junk Arm), or have them available to use when you need them. Unless you’re drawing 75-100% of your deck each game, I don’t see how this motley of trainer techs is helpful on a consistent basis.
still, though, great article.
Yea understandable.
Like I said, you let your preferences dictate the statistics an not the other way around. The toolbox tech of cards was not necessarily that important for me to obtain. Hence why I felt that 1 of each copy was needed and not multiple, regardless of the statistics
Tech Trainers are just that… Techs. With Junk Arm, you can afford to include just 1 or 2 copies of the card (especially if it’s non-essential) and still get it when the situation arises. Personally, I play 3 Defender because I feel it’s hugely beneficial to the mirror and Reshiram matchup. But the fact that it’s not required and will clutter your hand with unnecessary cards when trying to get the T1, T2 setup is a definite consideration.
Great article, it was fun to read and it was a great joy to read. Two questions though:
1: What were the techs for trainerlock you thought about including?
2: Why did you play energy search over just plain lightning energy?
thanks for complements!
a.) Bellsprout + rescue
– I found that I would need at least 2 of these to even counter gothitelle, so I figured it was not worth it
b.) Magby
– Due to the flippy nature of Magby, I needed 2 to even make this even a Goth counter
c.) Smoochum/Rotom
– This was probably my favorite tech of the 3 options. I would take early prizes off of anything a Goth player would dare to add energy too. Once a Gothitelle was out, then I would immediately switch to Smoochum and begin moving energies onto their baby or to the Reuniculus and then snipe with Rotom. The Gothitelle would never get 3 energies on it unless they played Shaymin. However, due to the sleepy/flippy nature of Smoochum, it was too inconsistent.
Energy search was used as a deck thinner and was junk armable which had some minor merits. Playing too many of these would be cumbersome because I would run out of lightning energy in longer games.
I didn’t consider this and I will definitely need to do a reanalysis on this. Thanks for the heads up.
The Smoochum/Rotom idea is beast. I never would have thought of that. I personally don’t like the other two options.
The idea of a deck thinner is good, but do consider Vileplume and Gothitelle. Sometimes Gothitelle will be out without a Reuniclus, I know because I play Goth, and Vileplume shuts it off, so that is something to consider.
I’d love to see a real world study of the thickness in cards and their effect (if any) on a random shuffle. I’d put in a few hours shuffling and reorganizing a few decks if anyone would like to put together what data would be needed.
This article is very well written and makes for a great reference. Thank you for writing it!
OMG! These kind of articles are the evidence that Pokémon TCG is far more than a simple game. Excellent article!
Do this with Reshiphlosion!
I have not seen anyone say or notice that on your closing list you have 34 trainers, making your deck 61 cards.
you know what you’re right. I think I had -1 switch for my regionals list (not 100% sure)