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 Pokemon player standards. I played the card game from Base Set to Neo Revelation and took a 8 year hiatus. I recently got into Pokemon again as a result of opening a box of Black and White. This lead me to joining a local Pokemon League and, later, the Six 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 Pokemon Collector, 4 Professor Oak’s New Theory, and at least 12 Basic Pokemon.
Here’s the deck list that I started off with.
|
Pokemon – 12 |
Trainers – 32
4 Junk Arm 1 Switch |
Energy – 16 12 Lightning |
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 regards 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!
There 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 Pokemon met the following.
- Start an ideal Pokemon (Zekrom or Tornadus)
- Make sure I had at least 2 Pokemon in play (I guess this is more important for other decks that have several low HP Pokemon)
- (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 Pokemon 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 Pokemon with 8 ideal starters (4 Zekrom and 4 Tornadus).
| # of Ideal Starters in Deck | ||||||||||
| # of Total Basic Pokemon 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 Pokemon
To use this table, simply line up the number of total Pokemon 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
In 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 Pokemon | 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 Pokemon
So now I have to balance two statistics, the probability of starting a good Pokemon 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 Pokemon (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 Pokemon 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+ Pokemon | 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 Pokemon, 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 Pokegear 3.0 | Chances of opening a Supporter or Pokegear |
| 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 Pokegear 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 Pokemon 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)
Many people saw the merits of opening Pokemon Collector and getting an instadonk with Pachirisu and Shaymin. However, in early testing, I found that Pokemon 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 Pokemon 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 Pokemon 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 Pokemon 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.
|
Pokemon – 12 |
Trainers – 33 2 Cheren 2 Judge
4 Junk Arm 1 Defender 1 Switcht |
Energy – 15 11 Lightning |
To recap, I decided on the standard build with 12 Pokemon, 16 Energy (note the 1 Energy Search), and 15 Supporters/Pokegear 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 Pokemon Collector yet and benched their needed Pokemon, 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!
