Why does the phone always ring when you're in the shower? Why are there always more subways or buses going in the opposite direction? Was God helping Tim Tebow?
Answers: It doesn't, there aren't, and no. We are subject to "confirmation biases:" our experience, memory, and interpretation of events are frequently influenced not only by objective reality, but also by our expectations and motivations.
- Some events are "one-sided," in the sense that people only really notice one of two outcomes. For example, you notice when the phone rings when you're in the shower: it's salient and annoying. When it doesn't ring, though, that's a "non-event" that doesn't register at all. ("Hey, did you hear that? The phone didn't ring just now. Hey, it did it again!") You develop a biased store of memories and believe in a false connection, because of noticing events that confirm it but not the non-events that disconfirm it.
- Some events are "two-sided," such that you do notice either outcome--like a win or a loss in gambling. In those cases, though, people often explain away losses as "near wins," and feel even more sure they are right. ("I should have won that time, but XYZ happened! I'll get it next time.") People explain away unwanted data but unquestioningly accept desired data, allowing them again to confirm what they expect or want to see.
- Sometimes, we have ambiguous facts, and we often interpret them to confirm what we expect or want to see. For example, consider the saying, "bad things happen in threes." There is no definition of "bad things" set ahead of time, and no endpoint specified in time. (If the stock market slumps a few points, does that count as bad? If three bad things happen over a year, does that count?) It is very, very easy to stretch the facts to fit an ambiguous story, if you have not specified clear criteria in advance as to what counts and what does not count as an event.
These biases show up frequently in religious thought. People cite miracles performed by rabbis, like curing someone through prayers. However, failures to cure are never reported--making them non-events that never receive attention and are not remembered. In the unlikely event that someone does hear of a failure, it is likely to be explained away as a "near-success" that failed for any number of reasons. (You can also imagine applying these points to alleged "personal miracles.")
Meanwhile, Tim Tebow's favorite bible verse--John 3:16--seemed to be appearing everywhere in his games. In one game, Tebow had 316 yards passing, averaged 31.6 yards, and the final quarter-hour television ratings for the game was 31.6 million! Aside from comedian Jamie Kilstein's response, is there anything else we can say?
As you may notice, there are no definitions here of what counts as a meaningful event. Should we only accept 3.16 as a sign from God, or does 316 count? What about other combinations of these numbers? Would his second-favorite verse count, or his fourth? Meanwhile, there are thousands of statistics you could examine for signs: viewers in the first quarter-hour, viewers in the second quarter-hour, the number of yards the Broncos collectively ran, yards passed in the first half-hour, etc. Without specifying in advance what counts, it is easy to find something that works, and then convince yourself it's what you were looking for all along.
This is why science a) defines its terms ahead of time, and is clear about what counts or does not count as evidence, b) insists on replicability of findings--by third parties, in particular--and c) uses formal statistical procedures to evaluate whether or not something happened due to chance. Because, that is, our intuitions and memory are subject to biases.