First, lets be clear that ‘average’ means exactly what it says. It is not the representation of any given game, but a collective assessment over a wide range of games. The actual experience in any given game of that average is virtually always going to be different from ‘the average’- apart from that fluky game where a player shoots his exact average!

In that context, I think that what ‘hot hand’ means is that in this particular game, a player’s scoring mechanics are most finely aligned (tendons and ligments, mental game, e.t.c) while in a ’slump’ they are most off. So in game 2, for some reason, Ray’s shooting mechanics were about as sharp as they can be, while in game 3, they were as off as they can be. In game 4, they are more likely to return to an intermediate state, in which the actual manifestation is more in line with what has been seen before (5/7, 3/8, 2/5 shooting nights, that kind of thing).

The issue I see with statistical statements that say a certain sequence is bound to happen even randomly is that it obscures what is going in the mind and body of a player, which is not entirely random at the point of experience. Rather I believe what should actually be indicated is that for any given good basketball player, there is a very high likelihood that playing mechanics will be so finely tuned that an exceptional game will result at some point, and that we should not be surprised if that happens.

The surprise comes if that exceptional occurence happens for so long that it appears to be a performance even beyond the rare exceptional performance expected from good players. At this point, we could maybe call it the 'miraculous hand' and make a much bigger deal out of it :) Thus to my mind, it is entirely okay to believe in the 'hot hand' and note those performances, as long as hot hand means the rare occasions when a players entire playing tools (mind and body) are entirely in sync. Perhaps Neil you could do a spread analysis on the Ray's shooting percentages so we can see the most exceptional shooting games (or streaks of games?) he's had (good and bad) and we can term his experience in those games 'hot hand/streak' or 'slump'.

Game 2, Ray goes for 8 for 11 from 3.
Game 3, Ray goes for 0 for 8 from 3.

8 for 19 = 42.1%

His playoff average? 41.6%

http://tinyurl.com/38spklr

Detecting the Hot Hand: An Alternative Model
Yanlong Sun (Yanlong.Sun@uth.tmc.edu)

Abstract
The belief in the hot hand was suggested to be a “cognitive
illusion” since no significant evidence was found in the
basketball-shooting data to reject the simple binomial model
(Gilovich, Vallone & Tversky, 1985). The present study
argues that in order to evaluate the validity of human
perception and cognition such as the hot hand belief, a datadriven
approach is needed to compare multiple alternative
models. A hot hand model with nonstationary shooting
accuracy was tested and showed significantly better
approximation to the data than the binomial model, indicating
that the simple binomial model may not be accurate enough to
serve as a normative model. This finding suggests that the hot
hand might indeed have existed, and weakens the argument
that the hot hand belief might be “seeing patterns out of
randomness.”

Athletes can increase their vertical leap on any given jump at any given time due to VARIOUS factors, of which some are mental above physical. This has been documented multiple times in sports analysis and is and echoed by pro-ball players often.

Jesus,Ray (no pun intended), way to play the ultimate turnaround.

An opposite extreme is the playground basketball skirmish where everyone is his own 'team'. Jim gets hot and goes a couple of baskets ahead; the game (for everyone else) becomes "stop Jim".

If Jim is hot enough, he'll win on shots beyond his normal range. If it's random luck, he'll be shut down quickly.

Nick Anderson, a 70% FT shooter, went 0-4 at the end of a Finals game. This will happen one time in 80. Then he went on to shoot 40% for a whole season. Then 64%. Without defense.