The Lotto Effect: Towards a Technology of the Paranormal. - book reviews

The Lotto Effect: Towards a Technology of the Paranormal by Damien Broderick. Hawthorn: Hudson, 1992. Pp. 279. Paper. ISBN 0-949873-41-1.

When is a psi experiment not a psi experiment? When it's lotto. Okay, not exactly a classic riddle, I admit, but it is the underlying theme of Broderick's book. Let me explain. To play lotto, you are typically required to attempt to predict which numbers will be chosen from a larger pool of numbers by a mechanical draw machine at the end of the week (or, alternatively, on a Wednesday evening if it is a midweek draw). Although the size of the number pool can vary, one common variation is that you choose six numbers from the range 1-45. When it is time for the draw, the draw machine makes a random choice of six numbers, usually by mixing up 45 numbered balls and allowing just six to be released (a supplementary "bonus" number is also often selected). If your six chosen numbers match the six numbers chosen by the draw machine, then you are a jackpot winner, which means you share the jackpot prize--which could be in the region of a million dollars--with anybody else who chose the same six numbers. Fortunately, as there are over 8 million different possible combinations of six numbers from a pool of 49, you are not likely to be sharing the prize with that many other people. Unfortunately, it is just as unlikely that your six numbers will match the six winning numbers in the first place; that is, the odds are you will not be a jackpot winner. However, do not despair. If you match five, four, or just three numbers, you will also qualify for a prize, although the size of the prize decreases drastically as fewer numbers are matched.

Lotto, it would therefore appear, shares a number of characteristics with many psi experiments. Performance in both is measured in terms of how well one is able to accurately predict the output of a random number generator. Furthermore, one might argue that lotto is a particularly good place to look for evidence of psi, because lotto players are clearly motivated to perform well and, with hundreds of thousands of players taking part each week, the resulting databaseshould be sufficiently large to detect even the smallest of psi effects.

This is the line of reasoning taken by Broderick. He analyzed 20 draws' worth of data from the Australian Tattslotto game (eleven Saturday draws and nine midweek draws, which comprised over 700 million guesses made during February and April 1991) to test the notion that psi may sometimes influence lotto players' attempts to guess the winning sets of numbers. In essence, Broderick did this by examining each of the 45 numbers' popularity with the thousands of lotto players in each draw; he then compared this measure of each number's popularity when it was a winning number with its popularity when it was not a winning number.

Are players, on average, therefore more likely to choose numbers when they turn out to be a winning number than when they turn out to be one of the losing numbers? Getting at the answer to this question required Broderick to transform his raw data in two ways. First, the data were normalized to allow fair comparisons between draws where the absolute numbers of entries varied somewhat. Thus, each number's "vote" was translated into a percentage of the mean vote received per number for that draw. Second, in order to take account of temporal drifts in popularity for certain numbers, Broderick took each number (from 1 to 45) and plotted a line of regression through the normalized scores it received for each draw (Saturday and midweek draws were analyzed separately). This allowed him to calculate a set of residuals-to-be (i.e., the deviations of the actual percentage vote received from the percentage vote "predicted" by the regression line). These two transformations resulted in data that would be more sensitive than a list of simple mean averages.

If psi was to be seen operating in some reliable way in this vast database, Broderick argued, we should expect the mean deviation of the 66 winning numbers in the eleven Saturday draws and the mean deviation of the 54 winning numbers in the nine midweek draws to be significantly greater than what would be expected by chance. Alas, this was not found; the residuals for winning numbers in both sets of draws were well within chance expectation, providing no evidence for psi in this set of lotto data. The difficulty, of course, as Broderick notes, is that any psi effect is likely to be extremely small and is therefore likely to be masked by the random noise inherent in these kind of data; there are sometimes great variations in the numbers of players who choose a particular number even when it does not turn out to be a winner.

However, in what appears to be a last-ditch attempt to find evidence for the Lotto Effect, Broderick does present a finding that might support the psi hypothesis. He took the top one percent of positive residuals (i.e., the numbers whose percentage vote deviated most in a positive direction from the regression-predicted vote) in each of the two sets of draws (four from the 405 midweek numbers--of which 54 were winners--and five from the 495 Saturday numbers--of which 66 were winners--and found something unusual. Now, by chance alone, we would expect 39 nontargets to every 6 targets in any arbitrarily selected grouping such as this one. In fact, when we segregate out the one percent of "largest positive residuals," 3 of the top 4 in midweek draws correctly identified winning numbers, as did 4 of the top 5 in the Saturday draws. These anomalous figures are extremely surprising, if we expect (as skeptics must) that nothing is going on here other than blind random chance (p. 223).

Could these anomalous figures be the footprints of psi in the lotto database? Possibly. It may be that a small precognitive psi effect across the many thousands of players does increase our chances of identifying winning numbers by focusing our attention on those numbers associated with the greatest deviation of votes over and above what would typically be expected. This, then, might be the Lotto Effect. However, before we get too excited and start playing lotto in the belief that if we just concentrate hard enough then our numbers will eventually come tumbling out of the draw machine, Broderick has a few words of caution. First, the finding may simply be a statistical anomaly: the author himself notes that this analysis of the largest residuals was not his first and only analysis of the data, and so the anomaly may be a spurious product of multiple analyses. To assess this possibility it is necessary to conduct the same analysis on a fresh (and, ideally, much larger) set of data. Easier said than done when lotto companies are notoriously secretive about such figures. Second, any attempt to use the Lotto Effect, if it is real, to help an individual increase his or her chances of winning would require access to the lotto company's database because the votes were counted during the week before the draw. Again, not a likely prospect and bad news for wishful lotto players.

However, all is not lost. It is likely that readers of the Journal will find this book of interest for several reasons, first of all because it represents an attempt to examine psi in a "naturally occurring" setting. Much of the book is also devoted to applications of majority vote and repeated guessing methods in studying psi (indeed, for the review of this area of research alone the book is well worth a read); the author even suggests ways of applying such techniques to playing lotto. Finally, Broderick's flamboyant writing style (he has written a number of science-fiction novels) serves to lift the book away from the tedious discussion of statistics it could have become. My only criticism is that a fuller set of references might have been included, rather than the less than comprehensive bibliography.

In short, this book is recommended for those who are interested in applications of psi. Indeed, its success in motivating parapsychologists to continue the hunt for psi among lotto data might be measured in terms of the number of lotto companies who happily allow such researchers to retrospectively wade through their masses of data in search for the Lotto Effect.

MATTHEW D. SMITH
Centre for Applied Psychology
Liverpool John Moores University
Trueman Building
15-21 Webster St.
Liverpool L3 2ET
England

M.D.Smith@livjm.ac.uk

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