A couple of Israeli researchers have some evidence to suggest that goal keepers save more goals when they stay still, instead of jumping to the right or left. Their analysis of 286 penalty kicks taken in elite matches around the world showed that keepers saved 33.3 per cent of penalties when they stayed in the centre, compared with just 12.6 per cent of kicks when they jumped right and 14.2 per cent when they jumped left.
The researchers believe the anomaly may be a reversed manifestation of what is known in economic psychology as the inaction effect or the omission bias. That is, people tend to suffer more regret after a negative outcome follows something they've done, compared with something they haven't done. In the case of keepers, the researchers surmised, they feel greater regret at letting a goal in after standing still in the centre, compared with jumping. If the ball ends up in the back of the net after they've jumped, at least it will have felt as though they had made a decent attempt to save it.
There is an article on the same subject by Tim Harford, World Cup Game Theory, in which he argues that, "Game theory, applied to the problem of penalties, says that if the striker and the keeper are behaving optimally, neither will have a predictable strategy... Professionals such as the French superstar Zinédine Zidane and Italy's goalkeeper Gianluigi Buffon are apparently superb economists: Their strategies are absolutely unpredictable, and, as the theory demands, they are equally successful no matter what they do, indicating that they have found the perfect balance among the different options."