One thing is that you shouldn't focus on stats other than long term placing too much, because they can be misleading. Something like play in rate doesn't tell you the value of hands you play into and the situation. If you're in a big lead and you play into a cheap hand from someone who's not the dealer, that's usually a good thing. On the other hand, if you play into an avoidable big hand chasing a low value hand, that's usually bad. So two different players could theoretically play in a similar amount, but one tends to play in in situations where it's good and ends up placing well because of it, while one tends to play in in the wrong situations and fares poorly. Other things might vary by play style. For a while I thought I had to call more to do better because my call rate seemed really low compared to the tenhou averages. But, I ended up making 7th dan with a call rate of .276 (for comparison, the average 7th dan player's call rate is .358). Now, I think this low call style is viable on tenhou, and calling at a .35 rate isn't necessary to doing well.
Maybe the hardest part to getting better at mahjong is being able to determine if you are making good decisions, because you can't judge by the result. Sometimes you can make good decisions and get really unlucky, and you can make bad decisions and get really lucky, and anywhere inbetween. Sometimes your play might be a bit below the average for your current rank but you just get dealt a lot of winning hands. Sometimes your play might be as good as the next rank up but you just get dealt unlucky situations or can't draw winning hands. In terms of long term rank, you can play a lot of games and if your skill level isn't changing, eventually you should find the rank that suits you, but that would require a lot of games to determine through outcome alone, and your skill level might vary too. What makes it really hard is that you want to analyze your decisions, and that analysis is going to be based on probabilities that you can't really determine through long term averages. Let's say after 6 discards from each player, someone riichis on 2p. What is the chance that 1p is dangerous? Here are some data you might examine:
- All riichi's on 2p
- All riichi's after 6 discards
- All riichi's on 2p after 6 discards
- All riichi's on 2p after 6 discards where the riichi player's discards are identical
- All riichi's on 2p after 6 discards where the riichi player's discards are in identical order including discarded on draw vs from hand
- All riichi's on 2p with the same visible tiles (tiles in discards or in your hand), and/or same discarded tiles per player, discarded order, etc
- All riichi's on 2p with a player with the same play style, and/or same visible tiles and discards
- All riichi's on 2p with the same player, same discards for every player, and your hand is the same
Obviously, when you get to the more specific cases, you won't have sufficient data for regression to the mean to come into effect. How often can you say you've been dealt an identical hand while observing identical discards from every other player while playing against the same players? However, those specific details might hold important information. Maybe it's important that it was 6 discards, or maybe it's important what the specific discards were, or maybe it's important the player played with a specific style, and so on. So, the only way to beat out the lack of repeatable data is through good reasoning. In this specific example, exactly 6 discards probably isn't important, and the amount the hand progressed and what middle tiles the player discarded in order to hold 2p are probably more important. Visible tiles are probably less important unless something notable is visible (multiple tiles near the area of concern or a wall of tiles). Style info such as how quickly does a player discard extra pairs, and how often a player declares riichi on hands that can win without riichi, is important. So, to answer the original question, you have to take all the important information you know and use that to narrow down the situation and come up with a rough guess that doesn't really depend on what was actually true in that one situation.
I guess you could say everything in mahjong is just betting on probabilities, but many of the probabilities are virtually impossible to calculate or generate enough data to determine. Tile efficiency is something you can calculate, but even that has some challenges. The discards other players make tell you something about their hand, for example if someone discards a 1, they're more likely to have a 4 in their hand, so you now have to take into account that someone is more likely to have that 4 in their hand, as well as information for all the other players. The perfect statistics would go from the choice you make to the odds of you ending up 1st/2nd/3rd/4th as a result. You can't calculate that, so you have to break it up into something like: if I declare riichi here and win this hand, what are the chances I get each place? Now, if I riichi here, what are the chances I actually win the hand? Or, if I play in here, what are the chances I get each place, and then what are the chances I play in on this discard?
That's my thoughts on the theory, but in terms of making actual decisions, the two things you should do are probably: 1) think about how your decision will affect your end result (if I discard this dangerous tile here, what are the odds I play in or win or get tenpai, and based on those, what are the odds I get each place?) and 2) try to find and learn from the most important information in every situation. You could say, "Once I discarded a middle tile after 8 discards and played into a damaten mangan, so I don't think it's safe to discard middle tiles after 8 discards." But there's more information to it. Maybe you notice, say, the player had been discarding other middle tiles and then switched out a certain tile from their hand, and you can improve your rule to not discarding middle tiles that haven't been previously discarded and aren't near a player's most recent discard from the hand when their hand looks good. And luck comes into play too. Sometimes you can take a good bet and truly get unlucky, and you have to use your reasoning to be able to say it was luck and not a poor decision. The other side is true too, sometimes you'll take a bad bet, and it won't pay off and you have to realize that it was a bad bet, and not just bad luck. Being able to find that balance, not just calling everything bad luck but not just assuming everything that doesn't work is a bad play either, is really difficult. The same is true on the positive side, not just assuming you're winning because of skill and good decisions but not just writing off your good decisions as good luck either.
I don't know if my thoughts followed your intended topic, but those are my thoughts.