Thoughts from a cut rate mathematician and an even worse gamer.
TL;DR: interactions with the RNG in LOL and TFT are fundamentally different, hence should be regarded and analyzed differently by players and developers; the dominant LOL RNG interaction is with the matchmaker, and these issues probably need to be addressed directly, because the Central Limit Theorem does not seem to apply; the dominant TFT RNG interaction is with the champion and item rolls, but since the CLT seems to apply, the question of whether a particular player should gain or lose rank/Elo for their performance in a particular match is well addressed by awarding points to the top 3 or 4 and detracting from the bottom 3 or 4 (and maybe not changing the rank/Elo of the placement 4 and/or 5 players); however, because the CLT seems to apply, opportunities for strategically interacting with the RNG and other players should occur earlier and more often than is presently the case.
There is a lot of talk--in game, on streams; everywhere--about random number generation and application in TFT. Something occurred to me when the discussion crescendoed on bam's twitch channel that seemed like it might have implications for both players and developers: thought I should share, but this is my first (and probably only) post, so be gentle!
The two most common and, unfortunately, most dangerous errors in probabilistic reasoning are 1) confusing inductive (heuristic) and deductive (mathematical) probabilities, and 2) misapplying the central limit theorem. For the uninitiated, the central limit theorem says that, when you combine enough, well behaved, mathematically random events, the result is very nearly that of a single, very well behaved, mathematically random variable. Heuristic probabilities often arise in describing the future behaviors of humanoids: "I would probably lie if a police officer asked me how fast I was going," is an example of a statement that cannot be made reliably quantitative using statistics, because the speaker can choose to render the statement true or false when the situation arises. Maybe some of you who made it this far will have noticed the similarity between that statement, and "I would probably play more conservatively if my teammates get tilted," or even "I will go for the spatula if it drops on my quadrant of the carousel;" all three are evidently different than "assuming this is a fair coin, the chance of it flipping two consecutive heads is 25%."
Regarding RNG in LOL. I do believe it is safe to say that, between ten players of about the same skill, the principal driver of early game scenarios is the team compositions rolled by the match maker. Now, on the one hand, there are so many aspects of this that if we think of each aspect for each player as a mathematically random variable, we might think that the central limit theorem applies, and so we can just think of this roll as one from a normal distribution. But this is wrong on two counts: 1) even though there are aspects which are indeed mathematical, like "on how many champions in each role does the player maintain a win rate of >=50%," there is no way to quantify how these aspects interact with the nonmathematical ones, like "will this player get tilted this game (think about this carefully: players on both teams can tilt each other and even [read: especially] themselves!);" and 2) in order for the central limit theorem to apply, no only do all material events need to be mathematical, but they all need to be well behaved, and there is just no reason to think this is the case... of course your rank and Elo are in some sense representative of your skill, but even if we could quantify skill as a mathematical variable, there is just no reason to think that expected skill in a given game--that is, expected elo performance; "is this player going to perform like a D2 jg or a D4 jg?"--will be a well behaved variable. So how do elo or rank work, if this is the case? Simple: "is this player going to perform more like a D1 jg or an S5 jg?" is well behaved enough that, over the course of enough games, you can sort out the diamonds from the slivers. But sorting diamonds among themselves? If this were actually possible, there would be no need for commentary in pro games--when the skill level of all players is close enough, the unlimited variance ("is this player D2 or D4?") and downright nonmathematical ("will this player tilt?") aspects dominate any attempt at calculation, which is why we talk about them inductively, rather than analyze them deductively. The math only works when the quantitatively estimable aspects of players differ enough that they dominate the interactions.
How best to deal with this? It seems sensible that if the nonmathematical aspects are dominant, directly working to minimize them is a good strategy. This would mean, for instance, working to eliminate potential sources of tilt, like auto fill, even if it lengthened wait times (and it I imagine that, once people got tired of waiting, they would switch to secondary support and try to find ways to carry); perhaps the sensible middle ground is, allow players to order all five roles, and work harder to avoid giving them their bottom roles--this way the match maker is not making any guarantees, which inflate wait times, but players have bought into the process, and will know they don't need to dodge because two teammates got their "middle ordered" role. That's a point worth making explicitly: the current system might minimize wait times for game offers but it might not minimize wait times for game loads because of the number of dodges.
On the other hand, there is something to be said for speculating how the mathy and nonmathy aspects interact, and working harder on the mathy ones if only to indirectly lever the nonmathy. This would mean, for instance, allowing more bans (maybe 2 per person, or even just 1 or 2 for the highest elo player on each team in addition to and after the first normal round of bans), since there is a tenancy for players to ban things they do not want to see in lane, rather than the things in most desperate need of balance overall, perhaps in trying to manage their own tilt, or perhaps just because their knowledge of their role is higher. Something like this would dynamically insulate players from some tilt sources between balance patches.
Now then, regarding RNG in TFT. The game is much less dynamic and much more discrete than LOL, which suggests that applications of the CLT may be more appropriate, which is wonderful from the analysis and development perspectives. Indeed, the developers seemed to have gotten the right answer for the wrong reasons: one of the most statistically dubious questions is also one of the most obvious; "will this player exhibit placement 1 skill, or placement 3 skill, this match?" The developer comments seem to suggest that, because of the consistent and obvious role of the RNG in matches, that the definition of winning has been expanded to include the top three, and sometimes 4, placements. Since the CLT is more likely to apply to things like "will I have the opportunity to buy 6 vaynes without rerolling before level 6?" there is certainly less reason to worry about such things impacting placements than the actual player matchups themselves. However, because TFT placements afford 8 rather than 2 slots, as in LOL, the flexibility in the definition of winning wonderfully accomodates the nonmathy aspects of deciding which player executed with a rank D3 placement 1 and which a rank D4 placement 2 skill level.
Furthermore, in thinking that applications to the CLT may be appropriate to the question, "should this player gain or lose rank/Elo this match?", players and developers are free to focus on that question, and expect that the answer is, in some sense, normally distributed. Players may focus on making choices that they forecast will increase their expectation of a favorable outcome, with less fear that unlimited variance or nonmathematical aspects will render those choices pointless (indeed, the real fear seems only to be that you will unjustly place 5 instead of 4, which seems much less likely than your team unjustly placing 2 instead of 1 in a LOL game). Developers may focus on making choices that they forecast will increase or decrease the variance in outcomes so that more prudent players executing high expected placement strategies win more often, but still lose an appropriate number of times to less prudent players executing high risk placement strategies. (Note that more skilled players executing better placement strategies should lose with some nontrivial frequency, since we are thinking the CLT applies to outcomes, so that we may think of them as a single, very well behaved, but still mathematically random, variable).
As with LOL, though, there is a problem to be mentioned and potential solution offered. Success in LOL, in the moment that a match is made so that everyone is purportedly of similar skill, is very much about managing the unlimited variance and nonmathematical aspects of the game: hitting a particular skillshot in a particular fight that turns the tide of the game, for instance, has numerous mathematically intractable aspects. Success in TFT, on the other hand, is very much about directly and profitably interacting with the RNG. Certainly, the nonmathematical battle of wits that is champion placement and composition substitution plays a role, but it seems reasonable to expect that the expanded win definition will subsume much of these aspects. What this means is that, if the purpose was to separate players who should gain rank/Elo from those who should not in a given match, opportunities for RNG interaction should start early and happen often. In particular, there is absolutely no calculus that factors into the very first round of combat: it is just raw RNG--who gets what, if any, items? Although it is less so for the second and third PVE rounds as well, they are still not interactive enough. Krugs provide a much more sensible interaction: you actually have the option to try and barely win or barely lose, to start/continue a streak, with preserving a loss streak costing health and potentially items. With this in mind, you might consider consolidating the early PVE rounds of combat into something more meaningful: punish players taking a level 1 champion with a great item that they do not even benefit from at the carousel, or from the other prospective allow for the beginnings of a loss streak, by making the first PVE fight loseable.
Futhermore, if after 1 consolidated round of PVE, PVP immediately commenced, you also increase the importance of the part of the "outcome" question which turns on issues like hero placement and comp substitutions, which for most people is probably the most fun aspect of the game--just barely winning a fight to preserve a streak, due to an ult going off right before a champ died, due to it being placed off center before the fight, feels awesome; losing by exactly 1 unit, to preserve a streak but preserve health, likewise feelsOkMan; these aspects are integral to the game and should be fostered, so long as they are not made to dominate the CLT aspects regarding the central question of whether a particular player should gain or lose rank/Elo in a given match.
A second issue, and a final caveat. I will be brief, since the dev comments suggests they are very aware of the issue: when you mix random variables, if you are mixing things which contribute unevenly in terms of expectation or variance to the end result, it can result in the CLT--where remember the "L" stands for limit--taking too long to converge upon the single, very well behaved, mathematically random variable you had anticipated. Right now in the game, the RNG for item generation, especially for big camps like the 2nd and 3rd minion, the Krugs, and the Raptors, seems to dominate the mid game, and since the mid game is very much determinant of whether you are in the top or bottom half of placements by the end game, these 4 collections of rolls are likely overpowering the many dozens of champion and match up and other rolls, hence leading for games where players--especially ones on long win or lose streaks--who gets great item rolls to feel like they are coin flips, rather than strategic--err, tactical-- affairs. In other words, because the games where players have great item rolls are decided soon after, the CLT does not have time to kick in. I do believe this is the issue that the poster, linked below, was getting at, since the implication is that lose streaking affords quicker item completion. The narrative around the issue is a rather bit clouded in that thread, though, which is why I made this post in the first place.
A potential solution, which seems both to address the tilting issue of that post but that does not require serious dev time, might be the following: let everyone approach the carousel at the same time, but adjust the win and lose streak amounts and scaling to compensate. If this is done in conjunction with the present efforts of balancing items and item drops, there might be a more immediately positive response from the players who feel "frustrated at/by the RNG" but who cannot quite put their finger on what exactly is so tilting.
Here is a link to a post which is representative of the sort of conversations others are having on the topic. My replies there provide much more targeted responses to the specific issues people tend to be raising--many of them valid, but some of them not.
Likewise, here is another post which affords a thoughtful solution to the "dominant item rolls" problem. Being able to swap items for gold, hence for champs and levels, would go a long way to normalize things presently, and insulate things from imbalance in the future.