That is from the new and interesting Only the Dead: The Persistence of War in the Modern Age, by Bear F. Braumoeller, which is largely a critique of Pinker on trends toward peacefulness (Pinker gives only the more optimistic data on Europe). And from the text:
…there is variation in the rate of conflict and war initiation over time, and it’s pretty substantial. Leaving aside the two jumps during the World Wars, the median rate of conflict initiation quadruples in the period between 1815 and the end of the Cold War, after which it abruptly drops by more than half.
The “falling rate of conflict” is thus not entirely reassuring.
How about the deadliness of occurring conflicts?:
Analyzing the two most commonly used measures of the deadliness of war, I find no significant change in war’s lethality. If anything, the data indicate a very modest increase in lethality, but that increase could very easily be due to chance…Worse still, the data are consistent with a process by which only random chance prevents small wars from escalating into very, very big ones.
Overall, the arguments in this book are strong, and the discussion of data issues is subtle throughout. You can buy the book here, its arguments seem fundamentally correct to me.