Background

Your passion since you were a child was to be a Poke’mon gym leader. You have a thing for psychic Poke’mon so you plan on opening up a gym for psychic Poke’mon. In order to do so you’re going to need to have a solid team of Poke’mon to fight trainers. This analysis is going to determine the best team of six Poke’mon you should have if you’re a psychic gym leader. The analysis will only choose Poke’mon that are psychic type and are not legendary. It will also assume that the higher a Poke’mon’s stats is the better off one will be in a Poke’mon battle. There are six stats a Poke’mon can have. They are speed, attack, special attack, defense, special defense, and HP.

The data that will be used for this analysis was provided by Alberto Barradas from kaggle.com. It provides the Poke’mon’s base stats which determine how quickly a Poke’mon levels up in a specific stat. The modified data set with only psychic Poke’mon can be found here: 

datatable(Psychic, options=list(lengthMenu = c(5, 10, 20)))

Potential Mathematical Problems

Determining the best team of six Poke’mon was a difficult task. There are some variables that are random and hard to account for. For example, the stats of a Poke’mon are given by the following mathematical formula:

\(HP = \left[\frac{2 \times Base \; + IV + \frac{EV}{4} \times Level}{100}\right] + Level + 10\)

\(Other \; Stats = \left(\left[\frac{2 \times Base \; + IV + \frac{EV}{4} \times Level}{100}\right] + Level + 5\right) \times \; Nature\)

\(IV\) is a random value between 0 and 31 that is applied to every stat. Every individual Poke’mon will have have different IV’s. It makes it so that no one Poke’mon has the same stats. You could think of it like the “genes” of the individual Poke’mon. For example, one Pidgey might be faster or have higher defense than the other. More information can be found at this link.

\(EV\) is a value that ranges between 0 - 255 that can be applied to every stat. The total EV across all stats can’t be higher than 510. It starts at the value of 0. Depending on which Poke’mon your Poke’mon beats in battle it’s effort value will go up a specific amount. For example, if any of my Poke’mon were to beat a Pidgey in battle it’s effort value in speed would go up by 1. If that same Poke’mon were to beat a Psyduck it’s effort value in special attack would go up by 1. It ensures that a trained Poke’mon is stronger than it’s wild counter part. Click on this link for more information.

\(Nature\) is a number determined by a Poke’mon’s personality value. Depending on the personality of the Poke’mon it will have different nature values assigned to it’s different stats. For example a Poke’mon could be brave, impish, or lax in nature. This number is determined by a randomly generated number. More information on that can be found at this link.

Because these variables are random or impossible to determine without cheats this analysis will only look at \(Base\) for determining the best Poke’mon.

Analysis

The assumption this analysis made was a gym leader would want to have a Poke’mon that is overall well rounded, but specializes in a specific stat. The specialization will allow the your team to adapt to a range of situations. The plots below plot their overall value of a Poke’mon’s base stats with a specific stat it has. The plots and what stats that are being compared are found below:

HP

#1
plot(Total ~ HP, data = Psychic,
     ylab = "Total Base Stats",
     xlab = "HP",
     main = "Total Base Stat Vs. HP Base Stat",
     col = "gray",
     pch = 19)

text(120, 600, "Cresselia", col = "red", pos = 3)
points(120, 600, pch = 19, cex = 1.2, col="red")

Attack

#2
plot(Total ~ Attack, data = Psychic,
     ylab = "Total Base Stats",
     xlab = "Attack",
     main = "Total Base Stat Vs. Attack Base Stat",
     col = "gray",
     pch = 19)

text(165, 630, "Mega Gallade", col = "red", pos = 2)
points(165, 618, pch = 19, cex = 1.2, col="red")

Defense

#3
plot(Total ~ Defense, data = Psychic,
     ylab = "Total Base Stats",
     xlab = "Defense",
     main = "Total Base Stat Vs. Defense Base Stat",
     col = "gray",
     pch = 19)

text(180, 590, "Mega Slowbro", col = "red", pos = 2)
points(180, 590, pch = 19, cex = 1.2, col="red")

Special Attack

#4
plot(Total ~ `Sp. Atk`, data = Psychic,
     ylab = "Total Base Stats",
     xlab = "Special Attack",
     main = "Total Base Stat Vs. Special Attack Base Stat",
     col = "gray",
     pch = 19)

text(175, 590, "Mega Alakazam", col = "red", pos = 2)
points(175, 590, pch = 19, cex = 1.2, col="red")

Special Defense

#5
plot(Total ~ `Sp. Def`, data = Psychic,
     ylab = "Total Base Stats",
     xlab = "Special Defense",
     main = "Total Base Stat Vs. Special Defense Base Stat",
     col = "gray",
     pch = 19)

text(125, 618, "Mega Gardevoir", col = "red", pos = 3)
points(135, 618, pch = 19, cex = 1.2, col="red")

Speed


The Poke’mon I highlighted in red are the ones I feel are best in a particular stat without too much sacrifice in their overall stat total. It should be acknowledged that Alakazam was picked twice in both Special Attack and Speed.

Interpretation

Almost all of the Poke’mon chosen are Mega Poke’mon. That requires the Poke’mon to Mega Evolve during the battle. Also, since Alakazam was considered favorable twice I switched out the Poke’mon I would of chosen for speed for the most well rounded Poke’mon. I chose to replace speed with well roundedness since speed only determines which Poke’mon fights first. The most well rounded Poke’mon is Mega Metagross who has the highest total base stats at 700. The Poke’mon and the role in within this psychic team are listed below:

  1. High Health - Cresselia
  2. High Attack - Mega Gallade
  3. High Defense - Mega Slowbro
  4. High Special Attack - Mega Alakazam
  5. High Special Defense - Mega Gardevoir
  6. Most Well Rounded - Mega Metagross

It should be noted that these would be my recommendations. There are some possible other combinations that might prove useful. Also, this analysis didn’t include variables such as the moves a Poke’mon can learn, items it can hold, stat boosters such as vitamins, and optimal \(Natures\) for each Poke’mon and how they relate to their role on your team. A future analysis should consider these variables.