Is the Geller curse real?

His Amazingness James Randi--who incidentally will be back at the reins of Swift next week--points us to an interesting article by the Sun. It talks about what apparently is the curse of that cutlery mangler Uri Geller. Sports fan "John [Atkinson] found Uri more often than not scuppered the chances of sportsmen and teams he was trying to help." Nothing new really. Swift has been keeping us informed of Geller's forays and granstanding in the field of sports, and his dismal performance at it.

Among his various flops:

Geller asked televiewers to touch an orange spot on their tv sets to help England win the Euro '96 Football Championship. England was knocked out of the competition by Germany.

In 2001 Geller predicted David Coulthard would win the British Grand Prix. Coulthard crashed during the first lap and was out of the race by lap 3.

In the same year Geller used his "powers" to make Tim Henman win the Wimbledon Championship. Goran Ivanisevic beat Henman during the semi-finals.

Earlier this year Geller "helped" the Scottish Falkirk soccer team. Inverness Caledonian Thistle won instead.

The examples provided by the Sun do seem to indicate that Geller has a malus touch, that being favored and helped by Geller means disaster. However, by themselves these failures don't tell us whether there's any relationship between Geller's intervention (prediction of a win or paranormal assistance) and a team/player's performance.

The problem with the data (as those in the Sun and in Swift) is that they're insufficient for us to arrive at a conclusion about the relationship between the two variables. Specifically, we don't have the outcomes of the competitions entered into by the same players/teams when Geller made no intervention. We need these data in order to know whether there is a relationship, whether there is a correlation. Merely looking at the partial data curently available to us we can easily end up with an illusory negative correlation which leads us to believe there's some sort of a Geller curse.

The following 2 x 2 table summarizes the information required for computing the correlation.

		Geller intervened, i.e., predicted a win or assisted in a paranormal way (Variable 1)
		Yes	No
Outcome (Variable 2)	Won	a	b
	Lost	c	d

The data that we lack are those for cells b and d.

Before proceeding, it is important to keep in mind a couple of pitfalls in looking for and presenting evidence: selective attention and confirmation bias (or in this case we can perhaps call it disconfirmation bias). We usually will look for and zero in on examples and evidence that confirm our position (in this case Geller's failures). Not infrequently we present these and only these as evidence. An example would be psychics and marketing people who are unscrupulous or ignorant enough to cherry pick only hits and successes, hoodwinking the naive into buying into their products and services. But such selectiveness can hide the true picture. The Sun article may have been aware of this in that it does, in fairness, cite one instance when the purported assistance by Geller was followed by a positive result (boxer Peter McDonagh won). Of course whether or not this is the only time Geller scored a hit we don't know.

From my reading of the two sources above I gather there have been at least 8 unambiguous instances when Geller bombed out. And as the Sun article says there is at least one time when fate was kind to Geller. Plugging those numbers into our table we have:

		Geller intervened?
		Yes	No
Team or Player	Won	1	-
	Lost	8	-

As can be clearly seen half the table is empty. Let's now toy around with various hypothetical numbers for cells b and d to see how they affect the correlation.

1. Let's say we find out that Tim Henman had played in Wimbledon in two other years and never made it to the semis either. Let's suppose as well that the other teams and players also lost in events very similar to the ones they played for which Geller made predictions and did his psychic hocus pocus. All in all let's say we uncover 100 events and all were losses.

		Geller Intervened?
		Yes	No
Team or Player	Won	1	0
	Loss	8	100

Computing for the correlation we obtain +0.32 (see endnote for equation). What this means is that rather than a curse there is in fact a weak positive correlation between Geller's intervention and sports performance. Certainly no Geller curse to speak of when the correlation is positive.

2. Now what if out of those 100 events there were 11 wins and 89 losses? The correlation would be, for all practical purposes, zero, meaning there is no relationship whatsoever between the two variables. There is neither a curse nor a Midas touch.

3. Let's increase the number of wins even further and bloat it to say 80. As you probably can guess the correlation has swung over to the negative.

		Geller Intervened?
		Yes	No
Team or Player	Won	1	80
	Loss	8	20

Give the above data the correlation coefficient is now -0.43. There is now a moderately strong negative relationship between the two variables. And as we increase the value in cell b relative to cell d the correlation becomes stronger such that when cell b = 100 and cell d = 0 the correlation becomes -0.94. With such a high correlation there would be reason to consider talk of a Geller curse. And there certainly would be very good reason to put all your money on the other team.


In summary, as long as we don't have information for all the cells we can't conclude anything about the relationship between the two variables and thus the so-called curse may be illusory, just as it would've been had it been the other way around--that more teams and players won than lost when Geller intervened. Belief in a Geller curse is just like belief that walking under a ladder brings bad luck. It is a superstition. And it is insufficient information and lack of proper analysis that lead to erroneous conclusions about the relationship between two events--a purported cause and an (observed) effect.


---

Correlation for two variables in a 2 x 2 table is obtained by computing for the phi coefficient of association:

            ad - bc
r = -------------------------
 [(a+b)(c+d)(a+c)(b+d)]0.5 

Note: the denominator is raised to the power of 0.5, i.e., we take its square root.

---

Reference:

Vyse, Stuart A. 1997. Believing in Magic: The Psychology of Superstition. New York: Oxford University Press. p. 114-119.