By setting the threshold at 7.2%, you are arbitrarily excluding Reagan. You could set it at any point, really, depending on what conclusion you want to draw. We could set it at 9% and say, 2 times out of 3 candidates with over 9% unemployment won. So if Obama can only maintain the rate over 9% he's golden! You really need to stop underestimating the intelligence of the people you debate here.
Yet even if we take your self-serving 7.2% threshold, only those cases where the condition is met are relevant here. There are exactly six cases where an incumbent ran with over 7.2% unemployment in your entire chart. Twice for FDR, who had, by far, the highest unemployment rate of the bunch (along with Hoover). Once Hoover, once Ford, once Carter and once GHWB. 4 times out of 6 your observation holds. Yeah, that's way too small a sample size for predictive accuracy. I've never heard of anything being considered scientific with a sample size that small.
There are also numerous factors that impacted those particular elections outside the unemployment rate. For example, GHWB ran against a candidate who was a much stronger campaigner than him, was hurt badly by his "read my lips" pledge, and supposedly (so say conservatives), a third party candidate sucked away more of his votes than his opponent's. None of those things had anything to do with the unemployment rate, did they?
- wolf