"Analysing Speed: How inaccurate is it?"

#PokemonGO: TL;DR: Speed is balanced for most pokemon. High speed pokemon lose on average only 9% damage compared to traditional games. As an example Alakazam loses 20% damage from the attack formula versus losing 4% due to speed if you accept the current attack formula or 9% if you ignore the inaccurate attack formula.Intro and ResultsAs a statistic speed presents a unique challenge when converting from the original pokemon games to Pokemon Go. Simply put, speed on its own offers no damage to a pokemon in battle. What matters is the speed ranking (is it faster or slower than the opposing pokemon?) and the impact a single turn has on the battle.To illustrate look at a simple battle (no EVs, natures, items, statuses, stat boosts, moves impacted by speed etc) between a pokemon with a base speed of 130 and one with a base speed of 120. The pokemon with 120 speed is still very fast – but in this battle it will get absolutely no value from these stat points. Similarly increasing the faster pokemon to 1000 base speed will make no difference; he’ll still be faster. This is different than every other stat in the game where increasing that stat will always increase your combat ability.In the case of Pokemon Go all we have is simple battles as outlined above. What this means is that we can easily compare how much the damage is increased due to speed between the original games (using the assumption of a simple battle) and Pokemon Go. Using the Pokemon Go gym simulator and nugget bridge’s damage calculator tools I have calculated the damage due to speed for both games for a variety of combinations of stats. (Note that I haven’t looked at defence because of the unique defender system of Pokemon Go).Stats CategoryOriginal Game Damage Bonus Due to SpeedPokemon Go Speed Bonus Using Bubble/HPDifferentialLA/AS7%16%8%AA/LS2%9%7%LA/HS13%18%4%BA/LS3%6%3%HA/LS3%5%2%LA/LS1%4%2%AA/AS12%13%1%BA/AS14%11%-3%AA/HS21%13%-9%HA/AS17%6%-10%BA/HS26%12%-14%HA/HS30%7%-23%Note that LA = Low Attack (40), AA = Average Attack (80), BA = Bonus Attack (100), HA = High Attack (120), LS = Low Speed (40), AS = Average Speed (80) and HS = High Speed (120).Those at the top of the table (Low attack, average speed) are benefiting the most from the Pokemon Go formula while those at the bottom are the worst off. Those around the middle are actually balanced remarkably well – these are where the attack and speed stats are opposed (high attack/low speed, low attack/high speed) or are equal (average attack and average speed). Bonus attack was added as an alternative to high attack as High attack turned out to be mostly unachievable with the Pokemon Go attack formula.What you can see is the impact of the two different systems – one in which the speed is multiplicative on the damage done and another where it adds a flat bonus to the attacking stat. Interestingly Niantic did make sure that that speed had diminishing returns like the original games but it didn’t decrease the value of low levels of speed. By this I mean that speed is most valuable around the average speed – going from 79 base speed to 81 base speed results in an increase in 25 up the speed ranking. You can see the distribution of speed among all fully evolved pokemon in this graph. Speed is less valuable at the top end in both Pokemon Go and the normal games, but it is also less valuable at the bottom end too in the original games – this is not the case in Pokemon Go.The other significant aspect between the two types of games is damage due to speed being multiplicative (between attack stat and speed) in the original games but additive in Pokemon Go. In the original games if you go first you get an extra attack. The impact of your speed stat is equal to how much damage that extra attack does multiplied by how often you get that extra attack. In Pokemon Go the value of speed is +(2*Speed.5) to your attack stat. So in that case the value of speed is the same for pokemon with high attack values and low attack values – even though their speed stats have traditionally had a very different impact.The other big issue that I have not yet addressed is that the Pokemon Go attack stats do not match up with the traditional games. Alakazam for example has a huge Special Attack stat of 135 (even higher than my High Attack category) but his Pokemon Go Attack Without Speed stat is 164 – or just above the average of 160. If he had equal Attack and Special Attack this would equate to 82 each in the original games. If we adjust for this in the traditional game calculation, we can see the impact of speed is much smaller – down to a 4% damage loss. As a guide this was tested on a few of the popular pokemon.Damage due to Speed – Traditional GamesDamage due to Speed – Traditional Games (adjusted attack stat)Damage due to Speed – Pokemon GoDifferentialDifferential (adjusted stats)Jolteon29%23%14%-15%-9%Dragonite18%16%10%-8%-6%Alakazam33%22%18%-15%-4%Snorlax1%1%8%7%7%Parasect1%1%13%12%12%If we’re willing to accept the conversion of attack stats from the original games to Pokemon Go the impact of speed is not huge. A difference of +12% appears to be around the maximum impact, and although this still creates a noticeable imbalance between those positively affected and those negatively affected it is limited to extreme cases and hardly game-breaking. For reference an Alakazam with /u/shinewend’s new attack formula would do 39% more damage, and with /u/mathchamp93’s formula would do 20% more damage. The attack stat conversion is having a much bigger impact than speed on some pokemon not living up to their traditional selves.Method:In the original games having a higher speed is equivalent to a single extra attack landed on the enemy pokemon. Since you get 0 damage due to speed if you have lower speed. I have calculated the bonus speed damage to be equal to the pokemon’s % speed ranking (1 minus the number of pokemon that are faster than it divided by the entire number of pokemon; considering only fully evolved pokemon from the entire series) multiplied by the damage they would do in a single hit to the chosen defender. This represents the average damage bonus from speed as it is the damage dealt to the average defender multiplied by the % chance of them going first - ie the chance of going first.The defender was chosen based on the median base stats to see how much damage the average pokemon would take. The median relevant stats for all fully evolved pokemon are HP=76, Defence = 80 and Special Defence = 80 (and Speed = 80). For this reason, Glalie was chosen as the defender as he has base 80 in every stat.Each pokemon was considered to be half the max level (50 and 20 for nugget bridge and gym simulator respectively), with max IVs but 0 EVs. The moves chosen for Pokemon Go were Bubble and Hydro Pump. Bubble was chosen to limit the impact of rounding on the results (however I believe that the LA/LS results were still heavily impacted by this) and hydro pump was chosen to represent the most accessible high tier charge move. To use a move of similar power in the traditional games Hyper Beam was used to determine a conversion rate: 150 base power to 24dps equals 6.25 base power per dps. With there being 4 Bubbles to 1 Hydro Pump at a converted base power of 68 and 148 respectively this results in an average base power of 84. Hence Return with base power 84 was used. STAB and Type Effectiveness were not considered in any case – even when it required changing the type of the move/pokemon.The gym simulator was run twice for each case, once with the attack stat including the benefit due to speed and once without the speed benefit. The total damage dealt over the time until the death of the defender was used to determine an average dps for each case. In the instance that one case had an extra charge move, both instances were run for the same length of time to normalize the impact this had on the overall dps. The percentage difference between dps with speed and dps without speed calculated to measure the impact speed had. Results will obviously vary with different attackers and defenders as well as moves - particularly because rounding can play a large part in how much damage is dealt - this is most obvious with low-average attack pokemon so their results are the least accurate. As such these results should be used as a guide of the trend and average impact of speed not as a damage guide.Conclusion:Speed is pretty balanced for most pokemon. The speed formula results in less than +/- 10% difference in damage dealt for the categories that the vast majority of pokemon fall in to. The only non-legendary exceptions are Charizard, Gengar and Dragonite. A change to the speed formula would benefit these pokemon the most, however it would assist in making some slower pokemon more balanced: Snorlax, Slowbro and Parasect in particular. If you accept the current attack conversion formula as being accurate then speed becomes even closer to being accurate/balanced.It is my opinion that correcting the speed formula to match the traditional games would not fix the meta/pokemon identity problems. Instead a change to the attack formula would have much greater results on balancing the meta and could impact a Pokemon’s damage by 20% or more such as with Alakazam. Speed needs to be reassessed and if balanced it should either be with real game impact in mind (less benefit to slow pokemon, multiplicative gains) or it needs to be more like the anime where speed changes how combat takes place (faster moves/faster dodging etc).If you made it this far the basis for this analysis is available here with some additional stats available here. As a warning it's very messy. I did everything in Excel before importing to Google Sheets so let me know if something doesn't work (or just confuses you) and I'll see what I can do. via /r/TheSilphRoad http://ift.tt/2cYIHut