BOXING metaphors are hard to duck when the contestants are as pugnacious as Barack Obama and Mitt Romney were at Hofstra University. If their first meeting was a one-sided pummeling by Mr. Romney, and the Joe Biden-Paul Ryan debate offered a classic boxer-vs.-puncher matchup, this one was one long, grueling bout of infighting, not pretty, not artful, just intended to do damage.

Of course the president performed better than in the first debate in Denver. He could only have performed worse had he entered the auditorium with a zombie gait and bitten Candy Crowley. He attacked Mr. Romney's business record, his primary-campaign rhetoric, and his honesty. The former Massachusetts governor, abandoning the good-humored confidence and well-timed potshots that served him well in the first debate, accepted the toe-to-toe challenge, vociferously painting Mr. Obama's first term as an abject failure. A plurality of viewers thought that the president "won" on points, an opinion we share.

But the real value of these debates isn't in the entertainment they deliver line by line or exchange by exchange. It's in what they reveal about larger matters--not always obvious as sharp words fly and adrenaline rushes. Tuesday's debate revealed at least two major weaknesses, one per candidate:

1. Mr. Romney's plan to cut tax rates, boost military spending by $2 trillion, and balance the budget, without doing any harm to such middle-class boons as the mortgage deduction, makes sense--if you throw into the kettle wool of bat, adder's fork, and howlet's wing, and know the right magic words to suspend the laws of budgetary mathematics. Mr. Romney's fanciful formula, indeed, reminds us of the promise of Mr. Obama in 2008 that he would expand entitlements like crazy and cut the debt. We all know how that worked.

2. Mr. Obama was unable to successfully defend his domestic record--his signature achievement, health care reform, he hardly mentioned--or to say how the next four years would be different if he were re-elected. The excuse of Republican obstructionism hardly washes. Mr. Obama enjoyed a Democratic Senate and House during his first two years, and he made no use of the mass media, à la Ronald Reagan, to exhort the American public to lean on obstinate Congress members.