Kahneman and Tversky are the scientists behind the theories of thinking fast versus slow, intuitive versus rational. Even football commentators proved them right, once more!
In their fast thinking mode all the commentators and other "experts" came to the conclusion that Liverpool, after their draw with Crystal Palace last night, have really squandered their chances for this year's Premier League championship. Those of us, no experts nor commentators, who think more slowly, wonder about the commotion "right now". Indeed, not much has changed because of this tie.
There is no doubt that Liverpool's chances to win the title race have diminished after forgetting to secure a ("normal") win at Crystal Palace. By how much? Because there is no useful statistic on this kind of problem, it is hard to exactly quantify it. Indeed, if one discards the possibility that Liverpool could have overcome its goal difference deficit (requiring it to win its last to games with a surplus of at least 10 goals!), then the difference between before and after "the Palace debacle" is that they now (=after) require Manchester City to lose (at least) one game, as opposed to need them, before, not to win the last two games.
More succinctly put: the decrease in probability that they become champions, all other things being equal, is reduced to the difference in probability that City loses one of its upcoming games versus that they tie one of those games. Of course, it is more likely that Manchester City wins its two remaining games than that it loses one of them. And it is presumably more likely that they draw one of those games than that they lose one.
If beating Wigan (second division club) in the quarterfinals of the FA Cup was a virtual certainty a couple of months ago, they proved then and there that loosing is a distinct possibility, for they lost. at home indeed. Assuming that their chances of winning that game were nine out of ten, then the chance that they would have drawn the game instead of losing it, is negligible, as both outcomes were "ex ante" very improbable.
Therfore, the debacle at Crystal Palace has diminished Liverpool's chances of winning the title by a similar and small amount, and - thinking fast here!! - the next two opponents of City are, intuitively and statistically speaking, stronger than Wigan a few months ago!
Therefor the new situation has changed little for Liverpool but they better win their next game which, of course, is a virtual certitude, as was the Crystal Palace fixture!!
Grimbergen, May 6th 2014