gbwead

Getting back to your original post. I agree. I only presented the dirty math in the first place to present the issue of what Berto did when he talked about mirror matches by comparing mons of non equivalent usage. This remains a big no no for me. I never claimed the ceiling was the main reason that explains the higher win %. I even said it surely had a minor impact, but an impact nonetheless. Let's look at the month of March where the average usage for the top 10 in UU is 18.51% and in NU, 21.06%. This means on average NU mons will have a win rate influenced more by the mirror matches than the UU mons. For NU, if the number of mirror matches are exactly equal to usage, we would therefore have: a win% ceiling of 0.2106(0.5) + 0.7894(1) = 89.47% a win% floor of 0.2106(0.5) + 0.7894(0) = 10.53% a win% (60%p) mon of 0.2106(0.5) + 0.7894(0.6) = 57.89% a win% (55%p) mon of 0.2106(0.5) + 0.7894(0.55) = 53.95% For UU, if the number of mirror matches are exactly equal to usage, we would therefore have: a win% ceiling of 0.1851(0.5) + 0.8149(1) = 90.75% a win% floor of 0.1851(0.5) + 0.8149(0) = 9.26% a win% (60%p) mon of 0.1851(0.5) + 0.8149(0.6) = 58.15% a win% (55%p) mon of 0.1851(0.5) + 0.8149(0.55) = 54.07% Like I said, I don't think the difference in the win% ceiling would have a big impact, it's quite minor really, but I don't think it's nothing. Overall, the difference looks like 0.2% for mons between 55% to 60%p. The difference of Win Rate between UU and NU is around 2.5% in March. So 0.2% of 2.5% gives us a 8% impact roughly. 8% is quite minor, but it's still something. I'm not denying UU mons have a higher win rate, just that 8% of the reason for that is the win% ceiling. We agree on this.

Oh nvm, I get it @Lilyrain. I think your method is correct.

In order to have a Mirror Match, 2 conditions need to be met: Player 1 must have Lucario in his team and Player 2 must have Lucario in his team. The odds that player 1 will have Lucario in his team is equal to usage so 34.3%. The odds that player 2 will have Lucario in his team is 34.3% as well. However the odds that both players have Lucario in their team is 34.3% x 34.3%. So the odds of having a Mirror Match is the square of usage. With that being said, if you want to know the exact point in your example where we no longer agree is when you say the following sentence: 34.3% of those matches are mirror matches I do not think 34.3% of those matches are mirror matches. I think 11.76% of those matches are mirror matches.

The way I calced the 56.07 was by doing exactly what you did, but instead of using 34.3% usage, I'm using the square of 34.3% usage. (1 - 0.3432)p + 0.3432(0.5) = 0.5536 0.8824p + 0.0588 = 0.5536 0.8824p = 0.4948 p = 0.4948/0.8824 = ~0.5607 *100 =56.07

The Win Rate provided by PokeMMO shows is for all the games played by that specific pokemon. The amount of Mirror Matches that specific pokemon played can be estimated with the method I described (usage square). If we were to automatically consider the pokemon is played when looking at the win rate of that pokemon, the amount of Mirror Matches would be disproportionally high. Let's take 5 games with the same two players. Player 1 always plays Lucario to make it easier. Player 2 plays Lucario 3 times out of 5. We end up with Lucario being played 8 times out of 10 teams, so 80% usage. With that being said, if we use my method we would use the usage square to estimate the amount of mirror matches, so 80%x80%=64% of Mirror Matches and for 5 games that would give us 3.2 Mirror Matches. If we used your method, we would estimate the amount of mirror matches as simply 80%, so for 5 games that will give us 4 Mirror Matches. In this example, there are 3 Mirror Matches, so my 3.2 estimation is closer than your 4 estimation. At least, that's how I understand it and I haven't read everything from ChatGPT that you posted and it looks coherent with what I understand as well.

Before I address everything else, what do you mean with we need to assume 1 of the team MUST contain Lucario. If I'm looking at the data for the entire month of March, what I am interested in is when I spectate a duel in March what are the odds I will see a Lucario Mirror Match, no? And the odds of that happening is the square of Lucario's usage, just like ChatGPT explained. We need to either agree on this or agree to disagree. I can't really reply without this getting clarified.

@Zokuru @Ziiiiio @loveyun @ArtOfKilling @YJos

To start off, I would like to say I agree with most of your post and thank you for providing the data. This is what I replied to berto when I showed my dirty math. My point was simply that looking only at the top 10 the way he did (without considering usage) is wrong, because when usage is considered it doesn't work. You're correct that UU sticks out, but there is some aspects to be considered. You'll see in spoilers the tables I made to explain this: A basic average for win rate doesn't take into account the importance of usage. What I mean here is that when doing a basic average, the win rate of the #1 mon is given the same importance as the win rate of the #10 mon. This should be addressed by weighing Win Rate based on Usage. Also, Usage is what causes Mirror Matches that centralizes a mon win rates around 50%. Since we have a lot of data to work with, we can calculate what are the odds of finding a Mirror Match based on usage (Odds of Mirror) and then readjust what the win rates should be theorically by taking out Mirror Matches. This gives us the Theorical Win% Without Mirror Colum in the tables I linked. As you can see the the Adjusted Win Rates are even more extreme, so I'm not posting them because they suit what I want. The tricky thing with usage is that high usage mon will have a lower win rate ceiling compared to low usage mons simply because of Mirror Matches. We can see that because usage is so low in UU that the odds are Mirror Matches are also lower and therefore UU mons have a higher Win Rate ceiling than other tiers. So even if this has a minor impact on Win Rates, it does explain to some degree why we see higher win rates in UU and it shouldn't be ignored. Also, you started talking about it, but it's extremely important to mention that UU also sticks out in top 10 representation. UU average usage for the top 10 is extremely low compared to the other two tiers and that means a lot of things, mostly postitive. When the top 10 most used mons are less important based on representation, we're usually looking at less centralization because players have more options. We can also note that there are more mons in UU compared to other tiers when using 4.25% (usage cutoff point median for all 3 cycles) and that reinforces my previous point. So yes, in UU, win rates of high usage mons or high, but usage overall is also looking very low. However, I don't think the high win rates are that high, certainly not that extreme and can also be explained to some degree because of the higher win rate ceiling in UU because of low usage. To me, I don't think moderately high win rates by top usage mons is a sign of an unhealthy meta. It's expected imo that the top usage mons to have positive win rates because otherwise they wouldn't be played. If the most spammed mons have low win rates, I would seriously question the abilities of the players of the tier since it would indirectly mean they understand little about their own metagame and are using mons ineffective against the vast minority of mons that are barely played. I believe from statistics alone, having a large amount of mons by usage in a tier and having the top usage mons represent a small part of the overall usage are clear indicator of an healthy metagame. People should want options to built with and that's what we have. People often complain that there are too many threats in UU, but that's to be expected when we have so many options. And the thing is, we have so many mons in UU, so we might have a lot of threats to deal with, but those threats also have a shit ton of answers to deal with as well.

Berto didn't input anything into a spreadsheet. He took multiple screenshots and edited them together. When you were accusing me of only looking at February, can you see why that is now? I simply didn't want to input 6 months of usage data into a spreadsheet and chose to just look at the most recent month we had instead. You are very welcome to look at other months and make your own formulas. I just wanted to point out that it's pretty unfair that you accuse me of being biased for only inputing one month of data when you chose for yourself to not input any. I don't think we're talking about the same thing at all. I'm not opposed to anyalizing metagames trends, viabilities, archetypes, playstyle, etc. when discussing if a mon is potentially banworthy or not. The problem is that there is a big part of subjectivity in these analysis and those are not really relevant when making an argument that is purely based on statistics. When making an argument based on statistics, we're using numbers to make claims, this way we can make claims based on something objective in order to reduce the subjectivity of those claims. However, if we start making claims to explain the numbers to then go back to making claims, we're reducing the objectivity of the numbers used to make claims and therefore these claims will end up more subjective. That doesn't mean the argument is bad, just that it wouldn't be very objective. If the original implication was that UU mons have high win rate for high usage, this needs to get verified based on the actual numbers, not with the naked eye based on the usage rankings. A mon will be more likely to have 50% win rate if it has high usage, so the #8 most used mon in NU might be closer to 50% win rate only because it's used more than the #8 most used mon in UU. The comparison is not fair when done like that. We need to look at win rate as a function of usage in order to make a proper assessment. What berto did with his screenshots is present win rate as a function of usage rankings and that method is very flawed.

I do want to ignore the reality where someone discusses statistics while refusing to acknowledge basics math or to even open a spreadsheet. "The 50% effect only applies to the top usage mons, because that's a statistical reality. A reality that doesn't apply in reverse." The reverse of "the 50% effect only applies to the top usage mon" is "the 50% effect doesn't apply to low usage mon". Did you think I said that low usage mon would necessarily tend to not be around 50%? You can look back at my posts; I never once said that. Giving you the benefit of the doubt here, but since you apparently blocked me while still quoting me, I'm not sure what to really expect from this conversation.

? It's well established that mons with high usage will automatically be close to 50% win rate because of mirror matches. Mons with low usage do not see as many mirror matches and therefore will not necessarily be close to 50% win rate. Since you are actively denying that, I will assume the rest of your post is probably of the same quality and not worth getting into.

If higher usage implies a win rate closer to 50%, it also means mons with low usage will be more likely to have a win rate further away to 50%. When the top 10 mons in NU have an average usage of 19.92% and the top 10 mons in UU have an average usage of 17.44%, is it really surprising to see supposedly higher win rate for the UU mons? We're not looking at problematic usage here. People insist that the stats show there is a problem in UU. If that's the case, please do something. Don't just post a screenshot and say the numbers speak for themselves and magically confirm your statements. This is a pokemon game where we need to manage our odds of winning when battling all the time, but no one is willing to process the data we have. I truly did not believe what I was reading from Bertolfoso. For me, his conclusions did not lineup at all with the reasoning he presented, so I just thought it was another disguised Lucario rant. @Bertolfoso, I apologize for making an assumption on what your intentions were. I respect you trying to make an objective analysis. It's more than many here are doing with their emotional pleas. In my eyes, your analysis is categorically wrong, flawed and shows some fundamental contradictions. I hope you can see those issues now. If you don't, that's fine. I will remain baffled that people will pretend like your reasoning is coherent with your conclusion, simply because they want something banned.

Aside from the personal jab, why would my vision of what makes something uncompetitive being different than yours have anything to do with UU? Can you point out what about that post you did not understand? Uber bans and Unhealthy bans have always been treated differently. Idk what's shocking about that post. It's also the reason why in early pokemmo years, unhealthy bans were always followed with a suspect test period to ensure the meta was actually healthier where as uber ban were pretty much final.

I don't need you to paraphrase in a distorted manner what I have said before. My stances were: Wobbuffet was untiered without Tickle and most likely would still be. Dugtrio was fine imo until it wasn't anymore (Endeavor). Tyranitar is not broken, it's just significantly better than Diglett at being uncompetitive.

Apparently, if I don't reply to every single sentence you wrote, you will be unhappy. I don't know what you want me to add that wasn't already mentionned already. Do we need to go in circles non stop? If I don't comment on something it's simply because I either don't find your statement interesting, relevant or that I just agree. I said I agree with your statements, but not the conclusions. I'm under no obligation to go into more details than that. And honestly, you're not putting me in a comfortable position here. I'm not a teacher and I have no interest of educating you or anyone else, especially since there is no way where I will not be extremely condescending when doing so. But hey, I'll give it a try since you are asking so nicely. What you said about mons with higher usage being naturally closer to 50% win rate than mons with lower usage. That was never disputed. We both agree on this. I never took the time to say "Yes, I agree" because what you said is honestly as basic as saying "1+1=2". It's undeniable period. Nothing to comment on the matter. However, you concluded something completly wrong from that statement: "The general frustrations that have been directed towards UU can now more easily be explained. For the past months (multiple), the most used Pokemon have had very high Win % even though their success rate is diminished by the mirror matchup phenomenon. This also means that these top Pokemon win way more against teams that are not using them. If you still do not believe this (which is pure maths, so uhh go to school?), it's undeniable that the other singles tiers are not in a similar situation." First of all, you said the general frustrations towards UU is linked to your statement. That's a purely subjective statement. It's easy to disagree with this. It's the equivalent of saying "1+1=2" and therefore "I'm hungry". It's not because the first statement is true that the second one is linked to it. The general frustration with UU is simply that lower tier players are a bunch of cry babies. They are mentally weak and fragile. I'm sorry, but it really comes down to that. You may believe players are frustrated because 1+1=2, that's fine. I believe they are frustrated because they are just a bunch of uguus that will always complain no matter what. Then you said that the most used mon in UU had high win rate. "High" is also a subjective statement. I explained to you that we have seen mons with higher usage with similar or higher win rate. So you already know why I disagree here. And then you ended your conclusion by saying that mon with higher win rate win more against teams that are no using them. That's a completly valid statement, but just like "1+1=2" it's a statement that doesn't back up what you said in any way. Your post did not require such a detailed answer because most of your mute points had no relevance to the claim you made. If every time you post, I need to explain that correlation doesn't imply causation, we'll get nowhere. Since I need to reply to every single sentence you post. Please find in spoilers below the answer I already provided to why your conclusion based on statistics is wrong: First off, you directly refered to the Lucario thread as an inspiration for your post. So you know what's up, let's not kid ourselves here. You're not posting about rainbows and butterflies, your agenda is very clear. I stated already why I don't give you the benefit of the doubt in these discussions. The point you are trying to make here is pure and utter stupidity. I'm sorry, but I can't say this in a nicer way. I either have to take you at your word and conclude that you're an idiot or I consider your real agenda. Explanation as to why your point is moronic: If we look at all the most used pokemon in the tiers, why would they not have a positive win rate? They are used for a reason. People don't play to lose. If I play something that doesn't work, I'm not going to spam it the exact same way expecting other results. People play to win! It's not problematic to see positive win rates for the most used mons. If you're trying to argue that those win rates are also "high", they really are not that high at all. Nothing crazy that I am seeing here looks crazy. If and only if UU really had more high usage mons with positive win rates, it would only mean that UU players are "better" at UU than the players of other tiers are at playing that other tier PROPORTIONALLY when all other variables are equal. You litteraly insisted usage and win rate need to be looked at together, but you did not even do that! You looked at the top 10 most used mons in each tier, but the top 6 in usage in UU doesn't have the equivalent usage to the top 6 in OU or NU. The following table from February's usage shows why that is: If mirror matches make it harder for a pokemon with high usage to go significantly above 50%, then you need to take that into consideration when claiming there is centralization because we see high win rate with the most used mons. You either chose to ignore your own statement in order to draw a flawed conclusion or you want to make up problems when there are none, at least non statistically speaking. And yes, my table compares the function of usage and win rate for mons with non equivalent usage. This is absolutely wrong, but it's what you did and I'm only presenting the results of what you were trying to do. I may have misunderstood your first post. But cmon, how could I possibly anticipate that you were trying to say simulatenously that usage matters when looking at win rate while disregarding usage entirely when looking at win rate. I simply could not consider such backward logical fallacy. If you truly thought your point made sense, I apologize for my harsh words. But I'm pretty sure you're just throwing shit at the wall to see if it sticks and gets the ban you want.