As excerpted from "The Reader's Companion to Military History" article "War Games" by Thomas B. Allen:
"Fletcher Pratt's Naval War Game became popular in the United States in the late 1930's, introducing a pastime that would become widespread by the 1960's. To determine whether a ship would be sunk, Pratt, a military writer, used a complex formula involving the thickness of a ship's armor, its speed, and the caliber and number of guns on each of the ships in an engagement. As proof of his formula, Pratt used the real-world fate of the Admiral Graf Spee, the German 'pocket battleship' fatally damaged in 1939 during a running battle with three Royal Navy cruisers. 'Rated on gun-power and armor,' Pratt wrote, the Graf Spee 'should have been more than a match for the three British cruisers, but by the formula . . . they should have beaten her. They did.'"
See this Binkov You tube video an analysis a naval war game the adversaries the World War Two battleships USS Iowa and the IJN Yamato. Who would win? Describes quite well the variables that must be taken into consideration when modeling such an encounter. As to the eventual outcome of such a duel, you have to go see the entire video.
Those of you devoted readers to the blog further interested in the topic of war gaming and naval war gaming in particular as it was done in the Fletcher Pratt mode go see the War Times Journal "QUICKFIRE PRE-DREADNOUGHT ERA FAST-PLAY RULES"
Have fun and good luck. I recommend highly without reservation or qualification. And YES, luck and the throw of the die favorable or otherwise does play a role.