Optimization of Search - A Rational Approach
Andrew C. Kolbert, Ph.D., M.T.M.
As most of these articles start with a Pokemon resume, here it is – I won a Regionals once, top 16nd in another, and top cutted in a couple of cities and BR/League challenges. Not particularly impressive, I’ll admit, but my greatest accomplishment has been as a master trainer and coach for my son, a multiple city, State, Regional’s champion, Top 16 at Nats, Top 32 in Worlds in Juniors and Seniors.
I spend a great deal of time optimizing decks including goldfishing (setups against a non-interfering opponent) and playtesting and I’ve come to realize that at times subtle optimization of decks requires a massive amount of setups in order to reveal 1-2% statistical improvements that in aggregate may become important. Surely there must be a better way. I’ve come to use Excel as a tool to optimize deckbuilding and I’d like to share a part of that today, the optimization of search.
Pokemon deck builds have a large variety of search options and there are often multiple ways of building decks to get out your Pokemon. The approach many players have to deck build optimization is extensive playtesting, however I believe there is a rational approach based on statistics that can shed clarity on choices that could only otherwise be revealed by testing dozens to hundreds of games with each build. Let’s think about deckbuilding principles that lead to optimized search.
- We need a high number of ways of getting out our attackers and support Pokemon
Overall, decks need to stream attackers and the inability to get attackers out is a failure of deck search that will lead to inconsistent performance.
- The ways that different Pokemon can be searched for must be somewhat in balance. If you have an excessive number of ways to get out a stage 2, but much less ways to get out a basic, this excess search capability will be ineffective and wasted. It is likely that being able to search out basics is a higher priority and there should be slightly more search for basics than the corresponding higher stage Pokemon.
A few ground rules for this exercise
- The examples I examine will be from NXD to Flashire as it is somewhat richer in search than a format that just lost 4 sets while gaining one.
- I’m just going to examine swapping search cards for other search cards. We will not be messing with the Supporter lines as they are assumed to be adequate. Obviously removing Supporters for extra search will appear to optimize search at the expense of draw and overall deck functioning.
- Finally, this will be a zero order approximation, as we say in chemistry. Many cards have costs and interact with other cards and it would be far too complex to consider all the possible cross-interactions. It is my belief that conclusions drawn from this zero order approximation still hold regardless of these secondary considerations.
Let’s look at the search profile of a deck that constantly needs search to stream attackers, Trevenant/Accelgor from the format that just ended.
Trevenant/Accelgor uses Accelgor and Mew to Deck and Cover, putting its attacker back into the deck every turn while bringing up Trevenant for trainer lock. The failure to search and setup a new attacker to Deck and Cover or keep bringing up Trevenants is a deck fail and needs to not happen more than a couple of times a game or you will likely lose. A sample Pokemon lineup with its search resources is summarized below.
total searches 133
RSD of all searches 15.4%
total attacker searches 76
RSD attacker searches 18.3%
The Pokemon lineup is in column 1 with the counts under the column headed Direct. This particular list runs 4 Skyla, 4 Level Ball 4 Ultra Ball, 1 Computer Search, and 2 Evosodas. There are a number of ways to get each Pokemon out, including direct draw. In the columns we have each way of getting out each Pokemon. I include Skyla as a search card as it can get any of the others, eventhough the combo uses two cards. The far right column totals the ways of searching out each Pokemon. The total of all searches is 133 ways.
The RSD is the standard deviation of all ways divided by the average of all ways, expressed as a percent. This is a “relative standard deviation” and represents the spread of the numbers. A small number means the ways of searching the various Pokemon are close to equal. A high number represents imbalance. The RSD of the overall search of this build is 15.4%. If we drop the Dusknoir line as well as the tech Sigilyph from consideration, we have a total of 76 “attackers” (including the Trevenant line) with an RSD of 18.3%.
This build has a high total search number, and reasonable balance, however, there are more ways of getting out Accelgor than Shelment, which is not optimal.
Let’s compare this to some other builds. Let’s drop an Ultra Ball and add in another Evosoda.
total searches 128
RSD of all searches 16.8%
total attacker searches 73
RSD attacker searches 20.3%
The total ways of searching Pokemon has dropped from 133 to 128 while the Trevenant/ Accelgor/Mew components have dropped from 76 to 73. The RSD of both the total search as well as the search for the Trevenant /Accelgor/Mew lines has gone up, not the right direction.
Let’s look at another, more significant, change. From the first list let’s drop a Skyla, a Level Ball, and an Ultra Ball for 3 Heavy Balls.
total searches 118
RSD of all searches 16.9%
total attacker searches 69
RSD attacker searches 20.1%
The total ways of searching all Pokemon has dropped to 118, a significant change from the 133 of the first list. This list has 69 ways of searching out Trevenant/Accelgor/Mew line components, as compared to the 76 of the first list.
Let’s look at the first list again, but swap the Evosodas for Heavy Balls.
total searches 131
RSD of all searches 15.4%
total attacker searches 76
RSD attacker searches 18.3%
The total search number is only down by 2, with little else changing except that now Shelmet/Accelgor is 18/16 as opposed to 16/18 as in the first list. Weighing the merits of +2 greater search over having a bit more searching for Shelmets I leave to the reader. The first and final list seem to be the best of all these choices.
Let’s look at a different deck, Ishaan Jagiasi’s National’s winning Empoleon/Miltank list.
total searches 103
RSD of all searches 9.9%
total attacker searches 48
RSD attacker searches 11.8%
The Piplup/Prinplup/Empoleon line is nicely pyramided at 14/11/12 with 48 ways to get out the attacking Pokemon. There is a 9.9% total RSD of Pokemon searches and 11.8% of the attacking lines. Can this be improved at all?
Let’s consider swapping a single Level Ball for a 4th Ultra Ball.
total searches 106
RSD of all searches 9.3%
total attacker searches 50
RSD attacker searches 10.3%
The Empoleon line is now at 14/11/13. There are now 50 ways to get out attackers from 48, the RSD has dropped from 9.9% overall to 9.3% and 11.8% on attackers to 10.3%. The total search ways has increased from 103 to 106. More specifically, it is a relative 9.1% easier to search for a Miltank and 8.3% easier to search for an Empoleon. It is difficult to argue that this is not an improvement, however slight it may be.
These sort of changes are the type that would only be apparent from playtesting after dozens of trials and would be subject to psychological interpretation bias. This process and tool is objective and does not allow for self delusion. Hopefully this will be another tool in the reader’s arsenal for optimizing his decks.
Andrew C. Kolbert, Ph.D., M.T.M.
As most of these articles start with a Pokemon resume, here it is – I won a Regionals once, top 16nd in another, and top cutted in a couple of cities and BR/League challenges. Not particularly impressive, I’ll admit, but my greatest accomplishment has been as a master trainer and coach for my son, a multiple city, State, Regional’s champion, Top 16 at Nats, Top 32 in Worlds in Juniors and Seniors.
I spend a great deal of time optimizing decks including goldfishing (setups against a non-interfering opponent) and playtesting and I’ve come to realize that at times subtle optimization of decks requires a massive amount of setups in order to reveal 1-2% statistical improvements that in aggregate may become important. Surely there must be a better way. I’ve come to use Excel as a tool to optimize deckbuilding and I’d like to share a part of that today, the optimization of search.
Pokemon deck builds have a large variety of search options and there are often multiple ways of building decks to get out your Pokemon. The approach many players have to deck build optimization is extensive playtesting, however I believe there is a rational approach based on statistics that can shed clarity on choices that could only otherwise be revealed by testing dozens to hundreds of games with each build. Let’s think about deckbuilding principles that lead to optimized search.
- We need a high number of ways of getting out our attackers and support Pokemon
Overall, decks need to stream attackers and the inability to get attackers out is a failure of deck search that will lead to inconsistent performance.
- The ways that different Pokemon can be searched for must be somewhat in balance. If you have an excessive number of ways to get out a stage 2, but much less ways to get out a basic, this excess search capability will be ineffective and wasted. It is likely that being able to search out basics is a higher priority and there should be slightly more search for basics than the corresponding higher stage Pokemon.
A few ground rules for this exercise
- The examples I examine will be from NXD to Flashire as it is somewhat richer in search than a format that just lost 4 sets while gaining one.
- I’m just going to examine swapping search cards for other search cards. We will not be messing with the Supporter lines as they are assumed to be adequate. Obviously removing Supporters for extra search will appear to optimize search at the expense of draw and overall deck functioning.
- Finally, this will be a zero order approximation, as we say in chemistry. Many cards have costs and interact with other cards and it would be far too complex to consider all the possible cross-interactions. It is my belief that conclusions drawn from this zero order approximation still hold regardless of these secondary considerations.
Let’s look at the search profile of a deck that constantly needs search to stream attackers, Trevenant/Accelgor from the format that just ended.
Trevenant/Accelgor uses Accelgor and Mew to Deck and Cover, putting its attacker back into the deck every turn while bringing up Trevenant for trainer lock. The failure to search and setup a new attacker to Deck and Cover or keep bringing up Trevenants is a deck fail and needs to not happen more than a couple of times a game or you will likely lose. A sample Pokemon lineup with its search resources is summarized below.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Comp Search | Evosoda | Total |
| Phantump | 4 | 4 | 4 | 4 | 1 | 17 | ||
| Shelmet | 3 | 4 | 4 | 4 | 1 | 16 | ||
| Accelgor | 3 | 4 | 4 | 4 | 1 | 2 | 18 | |
| Trevenant | 3 | 4 | 4 | 1 | 2 | 14 | ||
| Mew | 2 | 4 | 4 | 1 | 11 | |||
| Duskull | 2 | 4 | 4 | 4 | 1 | 15 | ||
| Dusclops | 1 | 4 | 4 | 4 | 1 | 2 | 16 | |
| Dusknoir | 1 | 4 | 4 | 1 | 2 | 12 | ||
| Sigilyph | 1 | 4 | 4 | 4 | 1 | 14 |
total searches 133
RSD of all searches 15.4%
total attacker searches 76
RSD attacker searches 18.3%
The Pokemon lineup is in column 1 with the counts under the column headed Direct. This particular list runs 4 Skyla, 4 Level Ball 4 Ultra Ball, 1 Computer Search, and 2 Evosodas. There are a number of ways to get each Pokemon out, including direct draw. In the columns we have each way of getting out each Pokemon. I include Skyla as a search card as it can get any of the others, eventhough the combo uses two cards. The far right column totals the ways of searching out each Pokemon. The total of all searches is 133 ways.
The RSD is the standard deviation of all ways divided by the average of all ways, expressed as a percent. This is a “relative standard deviation” and represents the spread of the numbers. A small number means the ways of searching the various Pokemon are close to equal. A high number represents imbalance. The RSD of the overall search of this build is 15.4%. If we drop the Dusknoir line as well as the tech Sigilyph from consideration, we have a total of 76 “attackers” (including the Trevenant line) with an RSD of 18.3%.
This build has a high total search number, and reasonable balance, however, there are more ways of getting out Accelgor than Shelment, which is not optimal.
Let’s compare this to some other builds. Let’s drop an Ultra Ball and add in another Evosoda.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Comp Search | Evosoda | Total |
| Phantump | 4 | 4 | 4 | 3 | 1 | 16 | ||
| Shelmet | 3 | 4 | 4 | 3 | 1 | 15 | ||
| Accelgor | 3 | 4 | 4 | 3 | 1 | 3 | 18 | |
| Trevenant | 3 | 4 | 3 | 1 | 3 | 14 | ||
| Mew | 2 | 4 | 3 | 1 | 10 | |||
| Duskull | 2 | 4 | 4 | 3 | 1 | 14 | ||
| Dusclops | 1 | 4 | 4 | 3 | 1 | 3 | 16 | |
| Dusknoir | 1 | 4 | 3 | 1 | 3 | 12 | ||
| Sigilyph | 1 | 4 | 4 | 3 | 1 | 13 |
total searches 128
RSD of all searches 16.8%
total attacker searches 73
RSD attacker searches 20.3%
The total ways of searching Pokemon has dropped from 133 to 128 while the Trevenant/ Accelgor/Mew components have dropped from 76 to 73. The RSD of both the total search as well as the search for the Trevenant /Accelgor/Mew lines has gone up, not the right direction.
Let’s look at another, more significant, change. From the first list let’s drop a Skyla, a Level Ball, and an Ultra Ball for 3 Heavy Balls.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Comp Search | Evosoda | Total |
| Phantump | 4 | 3 | 3 | 3 | 1 | 14 | ||
| Shelmet | 3 | 3 | 3 | 3 | 3 | 1 | 16 | |
| Accelgor | 3 | 3 | 3 | 3 | 1 | 2 | 15 | |
| Trevenant | 3 | 3 | 3 | 3 | 1 | 2 | 15 | |
| Mew | 2 | 3 | 3 | 1 | 12 | |||
| Duskull | 2 | 3 | 3 | 3 | 1 | 12 | ||
| Dusclops | 1 | 3 | 3 | 3 | 1 | 2 | 13 | |
| Dusknoir | 1 | 3 | 3 | 3 | 1 | 2 | 13 | |
| Sigilyph | 1 | 3 | 3 | 3 | 1 | 11 |
total searches 118
RSD of all searches 16.9%
total attacker searches 69
RSD attacker searches 20.1%
The total ways of searching all Pokemon has dropped to 118, a significant change from the 133 of the first list. This list has 69 ways of searching out Trevenant/Accelgor/Mew line components, as compared to the 76 of the first list.
Let’s look at the first list again, but swap the Evosodas for Heavy Balls.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Comp Search | Evosoda | Total |
| Phantump | 4 | 4 | 4 | 4 | 1 | 17 | ||
| Shelmet | 3 | 4 | 4 | 4 | 2 | 1 | 18 | |
| Accelgor | 3 | 4 | 4 | 4 | 1 | 16 | ||
| Trevenant | 3 | 4 | 4 | 2 | 1 | 14 | ||
| Mew | 2 | 4 | 4 | 1 | 11 | |||
| Duskull | 2 | 4 | 4 | 4 | 1 | 15 | ||
| Dusclops | 1 | 4 | 4 | 4 | 1 | 14 | ||
| Dusknoir | 1 | 4 | 4 | 2 | 1 | 12 | ||
| Sigilyph | 1 | 4 | 4 | 4 | 1 | 14 |
total searches 131
RSD of all searches 15.4%
total attacker searches 76
RSD attacker searches 18.3%
The total search number is only down by 2, with little else changing except that now Shelmet/Accelgor is 18/16 as opposed to 16/18 as in the first list. Weighing the merits of +2 greater search over having a bit more searching for Shelmets I leave to the reader. The first and final list seem to be the best of all these choices.
Let’s look at a different deck, Ishaan Jagiasi’s National’s winning Empoleon/Miltank list.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Dowsing Machine | Evosoda | Total |
| Piplup | 4 | 4 | 2 | 3 | 1 | 14 | ||
| Prinplup | 1 | 4 | 2 | 3 | 1 | 11 | ||
| Empoleon | 4 | 4 | 3 | 1 | 12 | |||
| Miltank | 3 | 4 | 3 | 1 | 11 | |||
| Duskull | 2 | 4 | 2 | 3 | 1 | 12 | ||
| Dusclops | 1 | 4 | 2 | 3 | 1 | 11 | ||
| Dusknoir | 2 | 4 | 3 | 1 | 10 | |||
| Exeggute | 1 | 4 | 2 | 3 | 1 | 11 | ||
| Jirachi | 1 | 4 | 2 | 3 | 1 | 11 |
total searches 103
RSD of all searches 9.9%
total attacker searches 48
RSD attacker searches 11.8%
The Piplup/Prinplup/Empoleon line is nicely pyramided at 14/11/12 with 48 ways to get out the attacking Pokemon. There is a 9.9% total RSD of Pokemon searches and 11.8% of the attacking lines. Can this be improved at all?
Let’s consider swapping a single Level Ball for a 4th Ultra Ball.
| Ways to get Pokemon | Direct | Skyla | Level Ball | Ultra Ball | Heavy Ball | Dowsing Machine | Evosoda | Total |
| Piplup | 4 | 4 | 1 | 4 | 1 | 14 | ||
| Prinplup | 1 | 4 | 1 | 4 | 1 | 11 | ||
| Empoleon | 4 | 4 | 4 | 1 | 13 | |||
| Miltank | 3 | 4 | 4 | 1 | 12 | |||
| Duskull | 2 | 4 | 1 | 4 | 1 | 12 | ||
| Dusclops | 1 | 4 | 1 | 4 | 1 | 11 | ||
| Dusknoir | 2 | 4 | 4 | 1 | 11 | |||
| Exeggute | 1 | 4 | 1 | 4 | 1 | 11 | ||
| Jirachi | 1 | 4 | 1 | 4 | 1 | 11 |
total searches 106
RSD of all searches 9.3%
total attacker searches 50
RSD attacker searches 10.3%
The Empoleon line is now at 14/11/13. There are now 50 ways to get out attackers from 48, the RSD has dropped from 9.9% overall to 9.3% and 11.8% on attackers to 10.3%. The total search ways has increased from 103 to 106. More specifically, it is a relative 9.1% easier to search for a Miltank and 8.3% easier to search for an Empoleon. It is difficult to argue that this is not an improvement, however slight it may be.
These sort of changes are the type that would only be apparent from playtesting after dozens of trials and would be subject to psychological interpretation bias. This process and tool is objective and does not allow for self delusion. Hopefully this will be another tool in the reader’s arsenal for optimizing his decks.