Both liberal and realist international theories argue that naval arms races occur largely in reaction to foreign threats. There are several rival explanations describing how this competition unfolds. However, the empirical case for all of them is weak. One of the most common models, whether asserted informally or formally, as in Organski’s Power Transition Theory or the misnamed “Thucydides Trap,” is that a rising power initiates an arms race, thereby challenging the leader. The leader responds, creating tit-for-tat mutual escalation. The end of this vicious circle is probably war. I examine all major naval powers’ capital ship construction during the period 1858-1940 to show that most accelerations of naval arms races, whether measured quantitatively or qualitatively, were initiated by the dominant leader, rather than by any aspirant to greater power. For most of this period that leader was Britain, until the massive US Two-Ocean Navy Bill of 1940, the end of this study, catapulted the US into thalassocracy ever since. Major inflection points of battleship construction, whether upwards or downwards, occur more because of business interest in countercyclical public spending, leading to building booms, or credit tightening by leading bankers, leading to retrenchment. These changes follow business cycle rhythms more closely than any logic of inter-state competition. The conclusion suggests that something similar occurs today, when the only superpower, the US, accelerates or retrenches military spending more for domestic business and political reasons rather than as a proportionate response to any actual foreign threat.