Cheers,
The Gaffer

Statistics is emphatically not about “trivia” like X player has gone 7 for 17 against Y pitcher. The premise of statistics is that any small sample size will be so gummed up by random variation that it holds virtually no testable significance. This is true in sports, economics, politics, advertising and countless other areas. The goal should be to offer data sets large enough to test whether the prevailing theories actually bear out.

If teams really do behave in a certain way following certain results, then there ought to be evidence for it.

It's important to note that this is a DIFFERENT project than the one that you have engaged in with this particular match. That is a historical analysis, which attempts to tell the story of that particular event. Your story may very well be perfectly accurate. But no story of that event should have anything but the smallest bearing on the statistical project of attempting to explain and predict the general patterns of football.

Obviously, psychology can and does have a tremendous effect. But I have a hard time believing it has anything close to the predictive value that it's given. Rather, once an event occurs, it's very easy to construct a story about why it *had* to happen that way – a story which could have been told completely opposite if things had gone differently.

Malcolm Gladwell has a book out right now that focuses on this phenomenon. One conclusion many people have drawn is that we (humans, that is) tend to assume that results necessarily follow from personal characteristics. Successful people are assumed to be that way because of their intelligence, determination, character, heart, etc. We have a very difficult time recognizing that out of many, many people who work really hard only one can end up on top. And while there's plenty of reason to believe that the winners contributed to their success in a general sense, there's actually almost no evidence to support the ideas that the winners are particularly any better than the 2nd, 3rd, and 4th place folks.

Surely people have looked into this for football. People discuss the “form table” as if it has tremendous value. Why? Is there any evidence that how a side has done in the past six matches correlates to how they will do in the upcoming one any better than their overall season record?

Is there any evidence that a striker who scored in his previous match is more likely (as compared to his overall record) to score in his next one? It seems obvious that there should be, and yet it seems equally obvious that a hitter in baseball will be in “the zone” and thus more likely to hit well in an upcoming game. The evidence of our eyes tells us this must be so, because we all have seen guys get “hot” and it seems like everything is golden. However, studies have shown that such examples are rare. Not impossible – of course – but far less common than we would believe from theorizing.

The general conclusion is that most examples of “hot” and “cold” are statistical noise – the outliers at the ends of a fairly natural bell curve.

I think you are on to something important, but that you are being perhaps too pessimistic.

I do think you are right that it is something we “see.” We are employing whatever our theory of mind (in the technical, cognitive faculty sense) turns out to be in order to interpret others. I do not have a lot of confidence in this, however, as there is no decision procedure for resolving conflict.

Yet, there are certainly grounds for statistical analysis on the matter. A lot of the advanced work in baseball is done by studies of correlation – by determining how strongly some statistic correlates with another (for example, whether OBP or BA correlates better with winning to take a simple case). You could study teams which started after their rivals, and see if there was any difference. You could establish more stringent conditions on cases in which the earlier game was favorable or unfavorable to the second team, etc. Now, this would only establish correlation, and not causation – but a robust correlation would at least provide evidence in favor of the hypothesis.

If, on the other hand, despite the fact that we “see” it, there is no correlation, then this would falsify the hypothesis. So these sorts of methods could at least determine if the hypothesis was viable, even if (and you are right), actual psychological motivations are too difficult to give a complete account of.

Based on the baseball comparison, I'm guessing you're an American like myself. One thing I learned quickly about football, and European sports in general, is that they aren't nearly as statistical as what we have here in America (this pitcher throws 95% fastballs on Wednesdays after 7:00pm, etc.). Also, I don't see how it's possible to quantify these psychological effects, especially considering there's no way to see what would happen if matches were played simultaneously.

I referenced the United – Everton match because on that day you could really SEE in their play how badly they wanted it, knowing that just an hour earlier the title became clearer. In support of the Gaffer, I can't see a single way to “prove” it, especially with statistics. This is just one of those things you'll need to see for yourself.