In order to accept these abilities, it is only necessary to redefine statistical probability:
We had to mark on our paper which shape [the primary school teacher] was thinking about. I scored far, far higher than the odds of even a "lucky" guesser.
So we can ignore the Bell Curve, statisical range and single trial tests. I could toss a coin 100 times and get all heads. It wouldn't imply psychic powers, only probability in operation in the real world. Now, if every time I tossed a coin 100 times I got heads I would be more suspicious of psychic powers (or a weighted coin). I bet a few of the students also scored far worse than the odds of even a "hopeless" guesser. The significant word here is, of course, "guesser".
There are fakes out there, I can spot 'em in a heartbeat. Usually, they are the ones performing in nightclubs and they are right 98 to 100% of the time. Anybody who gets everything right is doing research and running a scam, not using psychic abilities. The real psychics, and yes, we know each other when we meet, have a lot higher success rate than simple guessing, but not perfect.
This is the Alison-Dubois-Argument: "I'm the only real psychic! Those others are just pretenders to the throne! Don't listen to them! Buy my book!" There are apparently two reasons for this less than ideal hit rate:
How clearly the messages come through depends a lot on how clear the "transmissions" are, whether or not there is any interference and how good the receiver is.
Is it cloudy? Is it sunny? Is Mars in Venus? Is the wind blowing in the wrong direction? Are the spirits calling on a dodgy ethereal line? So many excuses, so little information.
The other factor is the reason why predicting the future is not, nor ever will be 100% accurate, no matter how good the psychic doing the prediction. Our lives are not predestined. The future is not cast in stone...
EoR pauses a moment for some deep thinking, and in order to clear his head. If a psychic is accurate, that is proof that they are a fake but if they're only randomly correct (EoR uses the term "randomly" advisedly) in a general sort of sense, then they're the real McCoy. Now I understand. Oh, and anything a psychic predicts might come true, or it might not. But the psychic is really and truly channelling ESP powers. Honest.
Nothing is ever definite. Anything can happen. The future can turn on a dime.
People might also believe this self-serving mental masturbation. Sadly.
Meanwhile, the only future predictions that EoR has found which are 100% accurate are at www.crazyhoroscopes.com. EoR never goes out the front door without checking what the day holds for him.