Former Sen. Eugene J. McCarthy (D-Minn.) tells a story about the late Sen. Carl Hayden (D-Ariz.).

Hayden was the patriarch of Arizona politics, and he served as chairman of the Senate Appropriations Committee into his nineties. According to McCarthy's tale, the last couple times Hayden ran for reelection, there was only one issue: his age and health. And each time, Hayden disposed of it very simply.

Shortly after the session of Congress ended and before Hayden was scheduled to go home to campaign, McCarthy says, the senator would enter Bethesda Naval Hospital. Rumors would sweep the state that he was in critical condition and perhaps even at death's door.

Hayden would let the rumors build for a few days, and then his press secretary would arrange for an Associated Press photographer to take a picture of the senator in his hospital bed. "Hayden would lift his hand off the sheet," McCarthy says, "and the campaign was over."

For some reason, I was reminded of this story while watching Sunday night's debate here between President Reagan and Walter F. Mondale.

When the age question, raised by Reagan's inept performance in Louisville, came up a half-hour into this debate, and Reagan disposed of it by his quip that he certainly wasn't going to exploit "my opponent's youth and inexperience," it was the equivalent of that Hayden hand-lift.

An awful lot of voters just wanted to know that Reagan had not lost his faculties -- including his sense of humor -- before they followed their inclination to give him another term.

By almost any kind of detached and rational analysis, Mondale won the Sunday debate. He was more precise, more coherent and, for the most part, more competent-sounding than the incumbent. If this were a debate between equals, between two men seeking the presidency for the first time, the Democrats would have every reason to be jubilant. But this debate occurred 45 months after Reagan became president and two weeks before the election -- and it was hardly a contest of equals.

The majority of the voters watching the debate were predisposed by the events of the past 45 months to grant Reagan a second term -- unless he did something that made them distinctly uncomfortable doing so.

My guess is that he did not provide the degree of discomfiture that would dissuade them from following that inclination. He did, however, say some remarkable and almost bizarre things.

He invented a CIA station chief in Nicaragua and quickly decided he better move him elsewhere -- lest he confirm the widespread suspicions that the CIA really is directing the contras effort to overthrow the Sandinista government.

He started talking about the relevance to today's nuclear world of the Biblical vision of Armageddon in a way that -- according to a nearby spectator -- brought gasps of, "Oh, no" from First Lady Nancy Reagan.

He made the shah of Iran sound like a humanitarian developer of low-cost housing for his people. And he turned his closing statement into a rambling anecdote about time capsules, California coastlines and today's younger generation that was cut off in mid- sentence by moderator Edwin Newman before it got to its point -- if any.

But all of this may well be rationalized by those voters who want to give Reagan another four years. So long as he did not disgrace himself -- and he did not -- what the Russians would call "objective conditions" are working powerfully in his favor.

Inflation is down. Real income is up. The nation is at peace. Those things count -- more heavily than a debate, unless the debate discredits one candidate.

Allan J. Lichtman, an American University history professor whose work has been quoted here before, has identified 13 "keys" to election outcomes. When the incumbent party has had less than five keys against it, it has won. When it has had six or more keys against it, it has lost.

Going into the debate, Lichtman said, only two of those keys had turned against Reagan: He lagged on the annual mean per capita growth in real gross national product; and he lacked a major foreign policy or military success.

Lichtman thought before the debate that two more keys were in jeopardy -- Reagan's reputation as a charismatic leader and the belief that the administration had avoided any major setback in foreign policy. My view is that neither of these keys turned against Reagan Sunday night.

That should, by historical standards, make him a strong favorite, if not a shoo-in, for victory. Lichtman hedges his bet a bit by pointing out that the Geraldine Ferraro nomination is a "wild card," untested by historical precedent.

But the points on his checklist remind us of objective reality: A popular vote of more than 51 percent in the previous election; a president running for reelection; a major change in national policy initiated by the incumbent; no serious contest for the incumbent party nomination; no major third-party activity; no election-year recession; no major social unrest; no major scandal.

That -- plus the Carl Hayden precedent -- should get Reagan through.