The association between any two events can be measured statistically in terms of a correlation. For events over time, it's a regression. Any events can be correlated, but may or may not truly related. In scientific studies, one hopes to develop correlated events into events in which one causes the other by removing error, but that concept is somewhat slippery.
For example, we know that increases in global temperature are associated with increased CO2 in the atmosphere, but we can't show a clear causal relationship. The correlation between these events is far above zero (pure chance), but less than a true causal relationship (100% positive association). In other words, the correlation between the events is increasing, the regression over years is positive. If we compare the calculated correlation with chance, it reaches a point where we must reject chance as an explanation. The slope of a regression line is clearly rising. We say that CO2 is forcing increases in temperature--but not causing the increase.
IMO, that statistical language captures what you are saying about synchronicities: the likelihood of the association between the events is too strong to be reasonably explained by chance. The strength of the association is the square of the correlation coefficient. In practical terms, that means an association with 25% strength is interesting, and over 50% may be forcing.
I think that's a better way of saying it than an odds ratio.