I downloaded match results for ~167,000 One For All games and came up with some stats... because why not?
Win Rates
Let's start with win rates. Trundle and Wukong are the only champions with a WR > 80%. Darius and Voli are only a couple percent behind. These are popular champs with high confidence on their win rate.
By far the worst popular champions are Bard, Thresh and Zoe, at 11%, 15% and 19%. The other bad picks are comparatively rare, and Bard has the single worst win rate of all champions. I guess they must be really fun to play if they are picked so often despite the win rate!
Popularity
Yasuo and Lux are the most popular champs, which is entirely unsurprising. Zoe stands out as a very popular pick with a very bad win rate. Conversely, Shyvana and Kayle are some of the least picked yet extremely strong champions in One For All. I can certainly think of less fun champions to pick than Shyvana; her low pick rate feels undeserved.
Unfair matchups
Analysing matchups is a little tricky with only 167k matches. Most matchups occur only a small number of times in this data set, with more than half of all possible matchups seen 8 times or fewer. Rito why you have to rate limit so much? :`(
So, limited to matchups popular enough to have enough data, which matchups are already decided at the loading screen when you see the champs?
Bard is the leader, of course, with his 10% overall WR. He is essentially guaranteed to lose to at least 10 different champions. Illaoi beats Katarina, Shaco and Thresh, guaranteed. Darius destroys Blitz, Galio and Zac. Malphite stomps Zed. Heimerdinger and Swain stomp Thresh.
Now, "guaranteed" is a little hard to assert due to the sample size, but in the above cases, there's a 95% confidence that the win rate is at least 90-95%. In fact for many of the above, there is not a single loss in my data set, out of 30-70 matches each!
Which champions are the most reliable stompers? Taking only matchups with enough data to ascertain at least a 65% win rate, and averaging an 80% win rate, Darius stomps a whopping 59 distinct champions, Illaoi 55, Wukong 53 and Volibear 45. These numbers are very rough though, as many stompy matchups are filtered out due to insufficient data.
Fair matchups
Fair matchups are maximally close to a 50% win rate at the loading screen – excluding the most fair of all matchups, the mirror matchup, for obvious reasons.
I'm going to declare Lux vs Darius as the most fair matchup, as Jhin vs Rengar doesn't really have enough matches for a good confidence range on the win rate. The "top fairest matchups" statistic is very heavily affected by the small sample size so... this is more of a guesstimate. In any case, here are some more:
Hard counters to strong champs
Trundle: with an 82% overall win rate, who is it that Trundle can't beat? As far as I can tell, only Rakan hard-counters Trundle, winning 5 out of 7 games on record.
Wukong is twice as popular, also with an 82% win rate. His biggest weakness is definitely Illaoi, winning 35 out of 37 games against Wukong – that's 95%. He also struggles against Cho'Gath, Dr. Mundo and possibly Shyvana, with a sub-33% win rate against these.
Darius is twice as popular still, with a 78% win rate. He doesn't have 100% counters like Wukong vs Illaoi, but he's extremely weak against Vel'Koz, winning only 25% of 69 games on record. Kog'Maw and Kayle also fare well, winning more than 2/3 of games against Darius.
Volibear's win rate is 78% and he's mostly weak against the other top champions in this list, namely Darius, Trundle and Illaoi. Vel'Koz also wins 2/3 of his games against Voli.
Illaoi's biggest weakness is that she's well-countered by at least 10 different champions; she's not in the same league as the above four and her win rate suffers (71%). Vel'Koz dominates Illaoi with an 87% win rate, with 13 other champions winning 70-80% of their games.
It is interesting to note that Vel'Koz hard-counters three of these champions, and he's also reasonably strong against Trundle at 52% win rate. Wukong doesn't care though, winning 87% of the games against Vel.
Bans
Suppose you are a premade of 5 and want to play Trundle. You should ban Darius, Vel'Koz, Brand, Heimer and Ekko, and and your win rate goes up from 82% to over 85%. This calculation takes into account the popularity of the champions the enemy team might pick.
Some champions are not impacted much by bans. If you pick Zoe or Thresh, you will lose no matter what you ban, with a ~1.5% change in win rate even with 5 optimal bans. Similarly, Yasuo's 62% WR is not highly affected by your bans (2.5% change). That is, unless you ban Yasuo himself. Which you should, because there's just Too Much Yasuo.
There are quite a few champions who benefit a lot from 5 optimal bans, with Illaoi and Nasus improving by almost 6%. I'm discounting Shyvana due to a small sample size.
If it's just you, your single ban is most impactful if you ban Yasuo and play Ornn (2% improvement), though of course there is no guarantee you will get Ornn, and he's still only a 51% win rate with your ban.
The spreadsheet
If you are so inclined, the spreadsheet with all of the above as well as the raw stats is here.
Updates
2 April: updated based on 167,000 matches, up from the previous 55,000. Shyvana is not as OP as she looked at first glance, her updated win rate estimate is 70% - just outside the original 95% confidence interval of 71%-87%. All other figures have been updated. As expected, the rankings of matchups were the least accurate piece of information and remain rough guesses.
Ekko is the only other champion whose revised win rate is outside of the original 95% confidence range. Overall, 5%, or 7 champions, are expected to have their true win rate outside the confidence interval).
Technical Notes
From the statistical rigour perspective, apart from win rate confidence intervals many of the above results are likely not very trustworthy, especially when it comes rankings. Honestly, if it wasn't League and instead something serious, I wouldn't publish half of the above due to trustworthiness concerns.
Whenever I mention an "overall" win rate for a champion, it's their win rate at the champ select screen, with no knowledge about who they are up against. This is an accurate predictor of the outcome of the match that is about to occur, as it takes into account the popularity of the champions that the enemy team might pick. I do believe this is the more interesting statistic to consider than win rates adjusted to compensate for champion popularity.
Confidence intervals were calculated using the Wilson score interval.
When calculating the win rate of a champion, mirror matchups are counted as 50% win rate games where appropriate.