"Moveset RNG: The statistical case for a Move Tutor"

#PokemonGO: TL;DR The probability for rolling a preferred moveset (1 in 6) is only greater than 90% after 13 evolutions. Equivalently: 10% of all players are not expected to receive their preferred moveset after each evolving/hatching 13 of the same pokemon.For extended TL;DR: see summary at the bottom of the post.First things first, although spurred by recently rolling a bunch of terrible movesets this post was motivated by a desire to move the conversation about move tutors into a more productive space than just complaining, bashing RNG, or wild speculation on how to implement them. For those unfamiliar, a move tutor is simply a way to change your pokemon's moves.Even if you belong to the school of thought that movesets are irrelevant for defenders, they are still vitally important to attackers and even more so for presitigers. That said the following assumes that you care about which moveset you roll; given the amount of time devoted in this subreddit to spreadsheets and min/maxing I think most of us care.I’ve now evolved 25 Lanturns without getting a single Charge Beam + Thunderbolt one. This mythical and ever-elusive Lanturn I hope to use to prestige against Dragon Tail Gyarados. I wanted to bash my head against the wall in frustration but at the same time I started wandering what exactly was the chance of this occurring.1. Probabilities of rolling a specific moveset: RNGezus (mostly) hates you.1 in 6 doesn’t seem like terrible odds until you’ve rolled your 3rd or 4th Dragonite with Steel Wing + Hyper Beam and you keep telling yourself that good luck is overdue, but it isn't. Somewhat counterintuitively it doesn’t matter what your previous rolls were, the chance that the next pokemon you evolve gets the moveset you want is always 1 in 6. Yet, while the probability of a specific roll never changes from 1 in 6, over many evolutions the probability that a specific moveset isn’t rolled will decrease; e.g. flipping a coin is always 50:50 but if a coin is flipped 1000 times the chance that a single head isn’t observed is vanishingly small.This type of probability distribution (where you either get what you want or don’t) is called the binomial distribution, and we can use it to model the probability that we don’t get the moveset we want after a certain number of evolutions/hatches.No. of EvolutionsChance to get specific moveset116.7%230.6%342.1%451.5%559.8%666.5%772.1%876.7%980.6%1083.8%1186.5%1288.8%1390.7%1492.2%1593.5%1694.6%1795.5%1896.2%1996.9%2097.4%2197.8%2298.2%2398.5%2498.7%2599.0%I think it can be strongly argued that the probability of getting the moveset you want is not high enough, especially considering the cost of 125 candy evolutions and the rarity of Snorlax/Lapras hatches. The probability for rolling a preferred moveset (1 in 6) is onlygreater than 90% after 13 evolutionsgreater than 95% after 17 evolutionsgreater than 99% after 25 evolutionsSo whilst I am unlucky with Lanturns about 1% of players can also expect not to evolve a specific movest after 25 evolutions of a specific mon.Would you quit playing the game after not evolving a single DT/O Dragonite after 13 evolutions ? Because you would expect that to happen to 10% of all players.2. The case for Move TutorThe key problem here is that the number of evolutions required to get good probabilities of certain movesets can be far below the amount of rare pokemon a player will expect to receive or evolve, even over exceptionally long time frames.Summed up: many players will max out at level 40 before having a good chance to roll preferred movesets for many important mons. The probabilities calculated above mean than unless you are swimming in rare candy it is very unlikely that you will evolve enough of these mons to guarantee good probabilities of rolling your preferred moveset.Example: At level 35 and just shy of 7 million xp I have hatched 3 Lapras, 4 Snorlax, and have only just scraped together enough candy to evolve 2 Muk. At my current rate of hatching/evolving I can expect to have probabilities of 77%, 87%, and 60% respectively of getting the specific moveset I want for each of these mons by the time I reach level 40.A good quality Machamp can be extremely important for solo players planning to take out a Blissey. Many Machamp movesets compare terribly with Counter + Dynamic Punch. At 7 million xp I have collected almost exactly 400 Machop candy. At my current rate of collection I can expect to have enough candy to evolve 9 Machamps by the time I reach level 40 in more than a year’s time. This only gives me an 80.6% chance of evolving a Counter + Dynamic Punch Machamp after almost 2 years of playing. This excludes the candy cost of powering it up.I am not trying to conflate the issues of pokemon availaibility (especially in rural areas) and moveset rolls. These are my specific examples, and almost all players will have their own unique to the biome they live in.The point I have hopefully made is that as a very active player, I don’t want to invest 2 years of playing to only have an 80% shot at obtaining a key counter to a meta-defining pokemon. As bad as these probabilities are, they will only get worse as new generations of pokemon are introduced to further dilute the candy pool.Niantic’s answer so far has been to close the gap between better and worse movesets, including a greater balancing between moveset types (i.e. boosting fighting type moves in general). However, these efforts might seem a little lacking if you’re the type of player who has only ever evolved or hatched a single Snorlax or Dragonite with a terrible moveset.I’ll finish with an example probably relevant to all players. I will gain enough xp to get to level 40 more than twice before I will get enough candy to guarantee a 90% chance at rolling a Poison Jab + Gunk Shot Muk. Something is broken here.Low probabilities are not necessarily a problem by themselves, in fact they are central to the grinding style of gameplay that is PoGo. However, low probabilities can be troublesome when they are layered on top of each other. The low chances of first obtaining rare candy/pokemon, getting good IVs, possible evolution items, (don’t even mention shininess), and then rolling good movesets make the probabilities of obtaining some particular pokemon beyond the reach of many players.I’m not saying the PoGo grind should be easy, but it shouldn’t be dishearteningly difficult either.3. Move Tutor: ProsOk so hopefully I’ve established that the low probabilities of rolling specific movesets, coupled with the rarity of certain mon’s candy, means that many players will have very low chances at rolling desired movesets. Introducing a move tutor can address this problem whilst adding other benefits to the game:A more competitive gym sceneIncreased player satisfaction/retentionFirst and foremost a move tutor would enable rural and causal players get a solid chance at evolving the most competitive movesets. As I stated previously this may be of less importance for defenders but is crucial for key attacking pokemon such as Macahmp and Lapras which have some truly terrible attacking movesets. Alternatively, for city players the guarantee of obtaining a particular moveset could make the choice of powering up specialist attackers, like Scizor, much more alluring. In both cases, if players can more easily assemble an effective attacking team then this will hopefully help with gym stagnation.Secondly, one of the central themes to the anime and the main series games is the special connection between trainer and pokemon. Obviously PoGO is a difference beast where the vast majority of caught pokemon are ground into candy. However, many players keep pokemon with uncompetitive movesets for sentimental reasons (eg. starters, first/one-of-a-kind, 100% IV, Lvl 1 Dex, caught at a special location, etc…) and it would mean a lot to players if they could find a use for these mons.Whether intentional or not Niantic have shifted the relationship to your pokemon away from pure candy grinding with the implementation of the buddy system. More than just Pikachu hopping on your shoulder there is a connection made with pokemon that many people walk many hunderds of kms.I’ve personally walked a Chansey more than 650km. Yes I did it for the candy, but I would grind all other pokemon I have into dust before I touched a whisker on her head. A move tutor would mean that the special pokemon you’ve walked for weeks just to get enough candy to evolve won’t be ruined if they evolve a bad moveset.A move tutor would increase the connection to your pokemon and reduce the frustration of rolling bad movesets; both of which can only be good for player retention.Hopefully now we’ve covered the why and can move onto the how of implementing a move tutor. If you don’t agree with these motivations feel free to skip ahead to the criticisms section.4. Implementation of a Move Tutor: Important ConsiderationsPokemon Go is a game of grinding and RNG. Sometimes the best way to overcome bad RNG is to grind. However, good game design will mean that casual players (and hardcore players with bad luck) don’t give up in frustration. Niantics move to include evolution items in the 7th day spin is a very clear example of good game design helping casual players whilst not disadvantaging hardcore players.As part of good game design any step to introduce a move tutor must first address the following questions:Does it exacerbate the rural/city imbalance?Does it adversely affect the gym scene?Can it be exploited by bots or spoofers?Will it adversely affect Niantics economy?Is the likely programming/server load high?Does it clash with The Pokemon Company’s ideas for the game?Does it clash with Niantics vision for the game?Do enough people care?Is it future proof?If implementation of a move tutor (or any other game mechanic for that matter) fails too many of these hurdles it will be very unlikely to ever be implemented. Therefore….5. Resource cost for a Move Tutor: NOT CANDYImagine that the tower of botted Blisseys down the street can all easily switch their movesets to Zen Headbutt + Dazzling Gleam. Keeping in mind the above design goals I think it should be clear enough that any move tutor mechanic cannot rely on candy or stardust for its resource costs. Doing so would disproportionately benefit botters and spoofers, further worsen the rural/city imbalance, and adversely affect the gym scene.If the resource for re-rolling moves cannot be stardust or candy then it still leaves us with many options:Buddy Distance RequirementBuddy Time RequirementEnemy Gym Prestige RemovedFriendly Gym Prestige AddedPokestop ItemRe-roll on TradingOthers I haven’t thought of e.g. breeding/hatching tokensI feel that it is unlikely in the current game to be able to implement any mechanic relying on gym interaction without overwhelmingly benefiting botters and spoofers. The same is most likely true for pokestop items unless they only appear in the 7th day bonus. Arguably it makes most sense, from an in-game world perspective, for buddy or traded pokemon to learn new moves. This has the added benefit of eliminating the possibility of re-rolling moves of pokemon currently in gyms.From a balance perspective the cost of a moveset re-roll should be such that players can re-roll a few favourite/rare mons but not their entire stable of defenders/attackers. It should be important to have a trade-off between investing the resource to re-roll a moveset versus simply evolving a new pokemon from scratch. Therefore, you should only be able to re-roll movesets at a rate lower than you accumulate maxed-out pokemon, to keep some element of grind to the game. From this perspective a moveset re-roll every week should be considered too frequent, whilst a rate of about once-a-month is probably closer to being sensible; the resource cost will need to balanced to reflect this.Whatever the specific resource cost of a re-roll, the exact mechanics of a re-roll need to be determined first as this will influence the overall cost of obtaining a moveset, i.e. a guaranteed choice of moveset should be comparatively resource-intensive compared to a random 1 in 6 re-roll of moves.6. Re-roll Mechanics: Neither pure RNG nor guaranteed choiceThe specific re-roll mechanics will influence the actual resource cost of obtaining a desired moveset. Say, for example, there is a 100km buddy distance requirement for a re-roll: this may sound great, but if the re-roll mechanic doesn’t change from a random 1 in 6 chance that means that our originally poor moveset probabilities don’t change. We should therefore expect that 10% of players will walk 1300 km trying to get a Frost Breath + Ice Beam moveset for their sole Lapras.The ways in which a moveset re-roll could occur are the following:Re-roll of both quick and charge move, i.e. 1 in 6 chanceRe-roll of either the quick or charge move, i.e. 1 in 2 and 1 in 3 chancesEither of the above options excluding rerolling the currently known move (or previously known moves).Choosing both the quick and charge moves.For reasons that should be obvious now a random 1 in 6 re-roll is going to be just as disheartening as the current evolution potluck. However, it can be argued that a guaranteed moveset choice (like the main games) goes against the spirit of the grind. Ideally we want a situation where the likelihood of not getting your desired moveset quickly drops to zero after some initial random rolls. Looking at individually re-rolling the charge or quick moves looks like it could be a good option. At least on face value 1-in-3 and 1-in-2 chances for respectively rolling the charge and quick move sound a lot better than 1-in-6. But we can use the binomial distribution to show the required number of evolutions to get minimum probabilities of evolving your desired moves:Chance to get specific moveQuick Move Re-Rolls (1 in 2)Charge Move Re-Rolls (1 in 3)Greater than 90%46Greater than 95%58Greater than 99%712These are better odds than 1-in-6 but we cannot escape that fact that due to RNG some unlucky 1% of players will still not get their desired movesets before a significant amount (7 or 12) of re-rolls. Statistically speaking there is a small but finite chance that there will be a player that never gets the moveset they want.Therefore, I think a move tutor needs to step away from pure RNG and guarantee some sort of maximum cost before getting your desired moveset, i.e. an option where rolling the currently known (or previously known) moves is disallowed. In this case we can map out a decision tree whereby we obtain our desired quick and charge moves over several re-rolls. This results of this decision tree can be summarised in the following:1 in 6 players get their desired mon on the initial hatch/evolve1 in 3 players get their desired mon after 1 re-roll1 in 6 players get their desired mon after 2 re-rolls1 in 6 players get their desired mon after 3 re-rollsThis sets a maximum cost of 3 re-rolls to obtain our desired moveset, i.e. worst-case-scenario of no desired moves on hatch, one re-roll to get desired quick move, two more re-rolls to get desired charge move. More importantly we see there that if a pokemon is evolved/hatched without the desired moveset that the expected/average cost of obtaining a desired moveset is 1.75 re-rolls. Having a well-defined average (of 1.75) for the number of re-rolls is important for determining and balancing the re-roll resource cost, i.e. if we would like a rate of one optimal moveset pokemon re-rolled per month, we should set the resource cost at 1.75 re-rolls per month.7. Move Tutor: CriticismsWriting this has actually been a great way for me to deal with the disappointment of rolling bad movesets, so honestly I don’t even know how I fell about the issue anymore.Nevertheless, there are several extremely valid reasons why a move tutor would be bad for the game:Introduction of new moves (see Dragonite) keeps the grind somewhat freshTrading becomes less important/valuable with move tutors.This is a grinding game, so git gud grinding.This is a different game from the main series, so we shouldn’t expect to re-roll moves.1 in 6 gives bad odds but many pokemon have multiple usable movesets.Move Tutors will promote homogeneity and make gyms even more boringMovesets are irrelevant when attacking in numbers, this is primarily a team gameIt may not be possible to implement Move Tutors within the current game codeUnforeseen and possibly OP move combinations (e.g. Dragon Breath + Outrage Dragonite ?)Gym Rebalance is coming so just wait and seeThese are all valid criticism of move tutors and many of them do not have strong counterarguments.However, for a key criticism let’s look at how the grind affects two pokemon that are most likely to cause frustrations with bad movesets: Dragonite and Tyranitar. Both are strong meta pokemon because of their epic stats. These epic stats will mean that they remain CP-relevant a long time into future generations of pokemon. Indeed, Tyranitar has the 3rd highest CP of any non-legendary pokemon across all generations of pokemon games. Even with a gym or CP re-work it is likely that they will remain important pokemon, due again to their epic stats. If newer, better movesets aren’t added for these pokemon then the scene will stagnate and there will be no new resource sink for excess candy/stardust. If it becomes easy to re-roll moves then there is no incentive to evolve new Dragonites and therefore no incentive to get out and hunt/hatch Dratinis. Here you can clearly see the argument that player retention is improved by the need to get out and grind; a move tutor may remove this need.If they are other criticisms of a move tutor that I haven’t thought of please do leave a comment.8. ConclusionsDespite several valid criticisms, I think there is still room in the game for a move tutor. Many of these criticisms are only valid if move tutors become cheap or easy to obtain. I would argue that a high-cost move tutor could add to the grind and further incentivise play.The grind must be a balance between not being too easy, nor too frustrating. The example being that the odds of hatching a Snorlax or stumbling across a wild Mareep are so small that they are unlikely to factor into player’s daily motivations. On the contrary, hatching a Lick + Earthquake Snorlax or evolving a Charge Beam + Focus Blast Ampharos will cause almost any player deep frustration. Having some gameplay element to correct for this can get players out and give them motivation to play.If we take the long-term view then we have at least 5 more generations of pokemon to go, but no guarantee that the game has the legs to get that far. The most important factor to PoGo’s long term survival will be player retention. Obviously, care must be taken to not invalidate the grind, but a high-cost move-tutor need not necessarily do so. If implemented well a move-tutor can reduce frustration, strengthen emotional investment in your pokemon, and therefore increase player retention.9. Summary / Extended TL;DRI originally wrote this with the aim off furthering an objective discussion. However, I have come across several unavoidable conclusions based on the current game environment:1) Current 1 in 6 moveset roll mechanics offer statistically poor chances of desired movesets2) Many players will evolve only a handful of rare pokemon, with correspondingly poor chances of obtaining desired movesets3) Move tutors could increase player retention by reducing frustration and increasing (emotional) investment in pokemon4) There are many important considerations for a Move Tutor with regards to good game design (e.g. 7th day evolution item)5) The prevalence of botting/spoofing will most likely limit the implementation of a move tutor to a buddy distance/time requirement.6) To equally respect both the grind and a maxiumum re-roll cost:the mechanics of a re-roll should not be entirely random nor a guaranteed outcome.the most likely mechanic is therefore a random re-roll without the possibility of rolling the currently known move/moveset.the cost/rate of moveset rebalancing should be lower than the rate at which high level players max out pokemon.7) Criticisms are that a move tutor might worsen the gym scene, disincentive the grind and/or team play, devalue trading, and may not be possible within the game code.8) However, a strong statistical case remains for move tutors. Furthermore, a well-designed move tutor could increase player retention/satisfaction without major side effects, but it must be made with careful consideration of the grind, gym balance and future trading.I look forward to discussion/criticisms and any suggestions on move tutors below. I didn’t want to undermine my efforts to be objective in this post so I’m going to leave my suggestion for a move tutor somewhere in the comments.See you on the road fellow travellers via /r/TheSilphRoad http://ift.tt/2pECBJQ