What comes closest is some studies on extreme forms of Buddhist meditation. One of the interesting discoveries is that during normal meditation, the parasympathetic system (homeostasis, breathing, etc.) is very dominant, but during the peak enlighentment experiences of the advanced meditators, the sympathetic system (fight-or-flight) system associated with athletic performance also runs at very high levels. Normally, the sympathetic & parasympathetic systems are in opposition, when the sympathetic system is active, parasympathetic is suppressed, and vice-versa. The other situation where both systems activate is during sex (arousal needs paracympathetic, orgasm sympathetic). The interesting connection I made is that I'd noticed these intense flow states sometimes occurring in the most intense times, where everything in my mind was absolute calm - I called it "fast meditation", as in meditating at 85mph. I know others also experience this. I conjecture that this is some of the same phenomenon seen in advanced meditation, just form the opposite end (here, maxing out the sympathetic system and the parasympathetic maybe kicks in, but I have no measurements other than my mental state).
There's also some research on the "flow state" related to accelerated perception, where people feel that they can see insane levels of detail and time slows down, as in accidents. They were trying to recreate it to understand it, and I found the efforts entirely lame and a waste of time. I can tell all kinds of stories about seeing very clearly both important and trivial things at high speed, and having entire trains of thought which I can verify happened in fractions of a second by noting the beginning and end points of the chain of thought and calculating in the distance and speed. These studies catch none of it, and I can say that even with years of training and effort, it is still extremely elusive (which is why I can't really fault the researchers, I don't yet have any great ideas on how to capture it).
I wish I could point you to specific references, but these were all readings from a while back.
BTW, ML and sports training seems like a potentially very fruitful area! I'd love to hear more about it. I found that much of the most interesting areas are at the intersections of different fields, so I wish you good luck in your pursuit!
I discovered I could trigger the state reliably without risk during high-level matched competitive video-game play. (Smash Bros) I had nearly 10 years of low-skilled competitive practice but with infinite online matched games I found I could reach a flow-like state on a nightly basis, so long as I played long enough. (I played for approximately 4 hours per night over a two-year period). I was also able to achieve a flow-like state with near certainty using a very simple piano tile tapping game, given long enough sessions. I had simply been using the game to train my thumbs for speed.
Eventually I left my career in software to pursue flow in Skydiving, which I now consider to be a mistake. After studying meditation and Yoga, it has become clear to me that the state is not triggered by external factors at all, and that it is itself a skill.
Admittedly far fewer of these states stand out as truly peak, quasi-religious experiences. I suspect there is a continuum and the binary classification is a judgement we place on the experience "retroactively". It comes from having enough space in your attention to notice the contrasting state of the body and the mind, the level of current performance, and then to notice the noticing itself. The rush of pleasure and excitement is not pre-existing, it is the result of a positive judgement you place on the situation. Despite its appeal this is undesirable, and tends toward interrupting flow in the precisely the same way as one loses control of a lucid dream after just having reached it. IMHO focusing on the subjective threshold for isolated study is misguided.
My current work focuses on creating an abstract framework which adapts to the athlete in order to create the external conditions which allow the athlete to most easily find the flow state. Rather than teach them how directly I hope to trigger it unexpectedly and allow for it to be sustained indefinitely during training. Of course, I'm not foolish enough to admit this to my benefactors.
Do you suppose I might be able to get a grant for this sort of work?
I totally agree about the continuum - for the most part it is so strange from ordinary experience that it seems like a binary shift, but yes, I think it is important to see it as a continuum (perhaps a bit stepped/quantized, but not sure).
Fascinating that you managed to get there with the tapping game doing speed drills. I often had ideas but it was before common MRIs and other technology that we had for examining brain functions at high resolution. That is something you could get into an MRI, and/or an intense electrode-sensor grid and measure! So, yes, I'd think some funding might be possible. I know academic funding is it's own labrynthine nightmare, so probably best to be in a program supported by an experienced professor/primary researcher who knows the ropes. OTOH, if you can get to show some results that improve performance, perhaps approaching some top pro sports team owners for funding? (I know if I were a billionaire with a team, I'd be interested in something that could give us an edge!) The question is whether you can generate useful results soon, and in what sport. You seem to have made a lot of progress in eSports, there might be some money there... Let me know if you're interested in chatting offline (is there a DM function here to exchange contact info w/o publishing?)