May - might
Notice that there is a difference between may and might when they are used to express doubt in past circumstances.
- May (and most particularly, in this area, the past form may have) means that there is a possibility (now, in the present moment, at the time of writing) that something exists, or has been done, and the writer is not sure about it - whether it does exist, or has been done. "There may be fairies at the bottom of my garden - but I have never seen them"; "my son's football team may have won their match this morning - but I won't know until I see him this evening"; "there may be intelligent life on Mars, but I have no proof of it". The past tense of 'may' in this sense is 'might'. In the sense of possibility, the most usual past tense is might have.
- 'Might have' means that there was a possibility, but that possibility has now disappeared - the 'window of opportunity' has now closed. "He was a good runner - he might have won the gold medal. But he was injured the week before the Olympics." Here is a more academic example. We can say "Hitler may have thought that he could win the war" [= it is possible that that is what he thought at the time]. We cannot say "Hitler may have won the war". This means that there is still a possibility, now, that the Nazis were the winners in 1945. This did not happen. The possibility has gone. We can say "Hitler might have won the war" ("if he had not attacked Russia", let us say, or "if Japan had not attacked the USA"). This means that there was a possibility then that things would have turned out differently, if - .
Sports reporters - amongst others - in daily papers often make mistakes in this area. If a reporter says "Beckham may have scored" it suggests (if we read it grammatically) that the writer is a bad reporter: s/he does not know whether there was a goal or not. What s/he usually means is "Beckham might have scored" - but something stopped him. There was a possibility, during the game - but it ceased to exist. The moment passed, and Beckham did not, in fact, score. The writer now knows that it did not happen. There is now no chance that Beckham scored, in that particular part of that game.
A subheading in a newspaper reads "Operation Orc may never have happened had it not been for crucial work by a UK detective constable." The report is wrong. There is no doubt now that Operation Orc happened. It might never have happened if the constable had not done his work - there was a possibility then - but happen it most certainly did.