The hot-hand 'fallacy' is a mistaken belief that if an individual successfully achieves an objective randomly, this causes a greater chance of additional success in the given activity for the short term future. The phenomenon has been studied in greatest detail through the lens of sport, in particular basketball, and is often cited by behavioural economists as an example of how individuals make cognitive ‘errors’, making up stories to explain apparent patterns or rationalising what has gone before them in a narrative.
Originally applied to a sporting context by Thomas Gilovich and Amos Tversky in the mid 1980's, the majority of the literature on the issue suggests that sports stars going through ‘hot’ or ‘cold’ streaks, in terms of performance, is an illusion (contrary to what fans and coaches so often think!). Simply put, basketball players are not more likely to make their next shot given that they have made their previous two or three shots in a row.
However a recent study that accesses panel data from Major League Baseball finds evidence to support the existence of the 'hot-hand'. The author’s claim to overcome several problems not given due attention by previous studies such as controlling for strategic interactions within a tie and conclude that the (10!) statistical tests conducted by them actually all show evidence in favour of the hot-hand.
The authors attribute the presence of this to differences between baseball and basketball suggesting that basketball presents “sufficient opportunity for defensive responses to equate shooting probabilities across players whereas baseball does not. As such, much prior evidence on the absence of a hot hand despite widespread belief in its
presence should not be interpreted as a cognitive mistake as it typically is in the literature, but rather, as an efficient equilibrium adjustment.”
From my reading of things, the authors are simply pointing out that in basketball 'hot' players can be targeted more intensively by defensives but such luxuries don't exist in baseball.