The Top 10 Greatest Generals of All-Time - According to Mathematics

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First, where is all this information coming from? Although an imperfect source, Arsht complied Wikipedia data from 3,580 battles and 6,619 generals. He then compiled lists of key commanders, total forces, and of course, the outcome. The general's forces were categorized and his numerical advantage or disadvantage weighted to reflect tactical ability. The real power is ranking the general's WAR score, the aforementioned Wins Above Replacement.

For each battle, the general receives a weighted WAR score, a negative score for a loss. For example, at the Battle of Borodino that pitted Napoleon against Russian General Mikhail Kutuzov, the French had a slight numerical advantage against the Russians. So, the model devised by Arsht gave Bonaparte a WAR score of .49, which means a replacement general had a 50 percent chance of still winning the battle. Kutuzov gets a -.49 for Borodino, meaning a replacement for him had a 51 percent chance of losing anyway.

The more battles a commander fights and wins, the more opportunities to raise their scores. Fighting fewer battles doesn't help, either. There were some surprises in the model, like the apparent failures of generals like Robert E. Lee and more modern generals. For the more modern generals like Patton, that can be attributed to the relatively small number of battles commanded.

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10. Alexander the Great

As previously mentioned, Alexander was a great strategist, but since his life was cut short and he had only nine battles from which to draw data, it leaves the model very little to work with. Still, the conqueror of the known world is ranked much higher than other leaders with similar numbers, including the Japanese Shogun Tokugawa, German Field Marshal Erwin Rommel, and Confederate General J.E.B. Stuart.

It should be noted that Alexander's per-battle WAR average is higher than anyone else's on the list.

9. Georgy Zhukov

Zhukov has only one more battle than Alexander and his overall score barely squeaks by the Macedonian. Interestingly enough, his score is far, far above that of Gen. Douglas MacArthur and Confederate Generals Jubal Early and John Bell Hood. That's what overcoming the odds does for your WAR score.

8. Frederick the Great

Ruling for more than 40 years and commanding troops in some 14 battles across Europe earned the enlightened Prussian ruler the number 8 spot on this list. His per-battle average was also lower than Alexander's but, on the whole, he was just a better tactician.

7. Ulysses S. Grant

Grant's performance commanding Union troops in 16 battles earned him the seventh spot on the list – and the U.S. presidency. Although his performance on the battlefield is clearly much better than those of his contemporaries, it should be noted that his Civil War arch-rival, Robert E. Lee, is so far below him on the list that he actually has a negative score.

6. Hannibal Barca

Hannibal, once captured by Scipio Africanus, is believed to have given his own ranking system to Scipio, once the two started talking. His personal assessment wasn't far off from the truth. He listed Alexander the Great and himself. Both of whom are in the top ten, even centuries later.

5. Khalid Ibn al-Walid

Khalid was a companion of the Prophet Mohammed, and one of the Islamic Empire's most capable military leaders. In 14 battles, he remained undefeated against the Byzantine Empire, the Sassanid Persians, and helped spread Islam to the greater Middle East. Compared to others who fought similar numbers of battles, his score eclipses even Frederick the Great.

4. Takeda Shingen

Being one of the best military minds in feudal Japan is a really big deal, because almost everyone seemed to be a military mind and being better than someone else might mean you get challenged to a duel. After 18 battles, the Tiger of Kai reigned supreme – in Japan, anyway.

3. Arthur Wellesley, 1st Duke of Wellington

It's a pretty big deal to be the guy who delivered a solid defeat to the man they called "Master of Europe." Napoleon's old nemesis, the Duke of Wellington, also saw command of 18 battles, but his WAR score is considerably higher than that of Takeda Shingen, his nearest challenger.

2. Julius Caesar

Caesar didn't have command in as many battles as Shingen or the Duke of Wellington, but his WAR score reflects a lot more risk and shrewdness in his battlefield tactics. But Caesar also couldn't top Alexander's per-battle WAR average.

1. Napoleon Bonaparte

Yes, you might have guessed by now, but the number one spot belongs to l'Empereur. Napoleon is so far ahead of the normal distribution curve created by the data for these 6,000-plus generals, it's not even close. After 43 battles, he has a WAR score of more than 16, which blows the competition away. There can be no question: Napoleon is the greatest tactical general of all time, and the math proves it.

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