OK. By 'a reject at V1' I mean taking the first action to reject the take-off at V1. In other words shouting stop, retarding the throttles, starting to brake if autobrake is not set, all at the instant the PNF calls V1.
The 50:50 stat comes from the idea of a normal distribution, where, if you take a large group of aircraft at identical weights and speeds, some stop very well, but only a few, some go miles off the end, but only a few, whereas most cluster around a mean. The Americans call it the 'bell-shaped curve'. Assuming the testing has been done correctly when you stop in the above circumstances the mean aircraft, or gross to use the proper term, will just stop in the EDA, by the end of the stopway. This is only the average aircraft, though. 50% of aircraft will lie to the right of the mean in a normal distribution and stop in a longer distance, 50% will stop in less.
In other words, there are no safety factors built into the stop case other than the improbability of a failure at VEF that requires a stop, which, from memory, is assessed at an improbability of 1:100,000 to 1:10,000,000. This is the principal reason why most take-off briefs have a niff naff and trivia cut off at 80 kts or thereabouts and will only require a stop at high speed but below V1 for killers e.g. engine failure, fire, structural failure and sometimes a config warning.