Sen. J.D. Vance’s recent op-ed in the New York Times, “The Math on Ukraine Doesn’t Add Up,” is a classic case of muddled thinking. The junior senator from Ohio would be well advised to do some homework before expressing his opinions on a topic he obviously doesn’t fully understand.

Vance starts by asserting that victory or defeat in war is exclusively a question of numbers: “Ukraine’s challenge is not the G.O.P.; it’s math. Ukraine needs more soldiers than it can field, even with draconian conscription policies. And it needs more matériel than the United States can provide.”

To be sure, Russia has outnumbered and will continue to outnumber Ukraine in just about any category, from population size to number of missiles to number of soldiers. That’s not new or insightful. Or correct, as wars also turn on other things, such as morale, courage, perseverance, leadership and strategy — as the Persian Empire learned when they twice invaded ancient Greece and as the U.S. learned in Vietnam, Iraq and Afghanistan.

Vance commits a far more egregious error by ignoring the other side of the equation and failing to give any consideration to Russia’s internal conditions. But they surely matter in any assessment of Ukraine’s chances of winning or losing. The fact is that Vladimir Putin is under attack from Russian elites; most Russians are tired of the war; the Russian economy is spiraling downward; and the Russian military is suffering staggering losses. Such a state of affairs is no recipe for victory, as Russian opposition scholars, who just may know their country better than American policymakers, insist.

Vance then writes the following: “Mr. Biden has failed to articulate even basic facts about what Ukraine needs and how this aid will change the reality on the........

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