Contrary to current discussions, all statistical pictures thus obtained show that 1) the risk of violent conflict has not been decreasing, but is rather underestimated by techniques relying on naive year-on-year changes in the mean, or using sample mean as an estimator of the true mean of an extremely fat-tailed phenomenon; 2) armed conflicts have memoryless inter-arrival times, thus incompatible with the idea of a time trend. Our analysis uses 1) raw data, as recorded and estimated by historians; 2) a naive transformation, used by certain historians and sociologists, which rescales past conflicts and casualties with respect to the actual population; 3) more importantly, a log transformation to account for the fact that the number of casualties in a conflict cannot be larger than the world population.