We investigate the origin and the validity of common beliefs regarding “the hot hand ” and “streak shooting ” in the game of basketball. Basketball players and fans alike tend to believe that a player’s chance of hitting a shot are greater following a hit than following a miss on the previous shot. However, detailed analyses of the shooting records of the Philadelphia 76ers provided no evidence for a positive correlation between the outcomes of successive shots. The same conclusions emerged from free-throw records of the Boston Celtics, and from a controlled shooting experiment with the men and women of Cornell’s varsity teams. The outcomes of previous shots influenced Cornell players ’ predictions but not their performance. The belief in the hot hand and the “detection ” of streaks in random sequences is attributed to a general misconception of chance according to which even short random sequences are thought to be highly rep-resentative of their generating process. G 1985 Academic Press. Inc. In describing an outstanding performance by a basketball player, re-porters and spectators commonly use expressions such as “Larry Bird has the hot hand ” or “Andrew Toney is a streak shooter. ” These phrases express a belief that the performance of a player during a particular period

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We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high-speed photography are reported. For natural flips, the chance of coming up as started is about.51.

Evolutionary theory is awash with probabilities. For example, natural selection is said to occur when there is variation in fitness, and fitness is standardly decomposed into two components, viability and fertility, each of which is understood probabilistically. With respect to viability, a fertilized egg is said to have a certain chance of surviving to reproductive age; with respect to fertility, an adult is said to have an expected number of offspring. There is more to evolutionary theory than the theory of natural selection, and here too one finds probabilistic concepts aplenty. When there is no selection, the theory of neutral evolution says that a gene’s chance of eventually reaching fixation is 1/(2N), where N is the number of organisms in the generation of the diploid population to which the gene belongs. The evolutionary consequences of mutation are likewise conceptualized in terms of the probability per unit time a gene has of changing from one state to another. The examples just mentioned are all “forwarddirected” probabilities; they describe the probability of later events, conditional on earlier events. However, evolutionary theory also uses “backwards probabilities ” that describe the probability of a cause conditional on its effects; for example, coalescence theory allows one to calculate the expected number of generations in the past that the genes in the present generation find their most recent common

there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a

Does evolutionary theory have implications about the existence of supernatural entities? This question concerns the logical relationships that hold between the theory of evolution and different bits of metaphysics. There is a distinct question that I also want to address; it is epistemological in character. Does the evidence we have for evolutionary theory also provide evidence concerning the existence of supernatural entities? An affirmative answer to the logical question would entail an affirmative answer to the epistemological question if the principle in confirmation theory that Hempel (1965, p. 31) called the special consequence condition were true: The special consequence condition: If an observation report confirms a hypothesis H, then it also confirms every consequence of H. According to this principle, if evolutionary theory has metaphysical implications, then whatever confirms evolutionary theory also must confirm those metaphysical implications. But the special consequence is false. Here‟s a simple example that illustrates why. You are playing poker and would dearly like to know whether the card you are about to be dealt will be the Jack of Hearts. The dealer is a bit careless and so you catch a glimpse of the card on top of the deck before it is dealt to you. You see that it is red. The fact that it is red confirms the hypothesis that the card is the Jack of Hearts, and the hypothesis that it is the Jack of Hearts entails that the card will be a Jack. However, the fact that the card is red does not confirm the hypothesis that the card will be a Jack. 2 Bayesians gloss these facts by understanding confirmation in terms of probability raising: The Bayesian theory of confirmation: O confirms H if and only if Pr(H│O)> Pr(H). The general reason why Bayesianism is incompatible with the special consequence

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Abstract. We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of coming up this way depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high-speed photography are reported. For natural flips, the chance of coming up as started is about.51. Key words. Berry phase, randomness, precession, image analysis