One of the weaknesses of our Senate forecasting model is that, for all the precision we apply to the general election forecasts, we only eyeball the primaries, making estimates about the likelihood of each potential matchup on the basis of the polling and other factors. Nevertheless, we try to be pretty careful. For instance, we had assigned a 25 percent likelihood that Joe Miller would defeat the Republican incumbent, Lisa Murkowski, in Alaska, as happened. We had also assigned small likelihoods to a number of other outcomes that did not come to fruition, like J.D. Hayworth ousting John McCain in Arizona (Mr. McCain won by 24 points) or Chet D. Traylor unseating David Vitter in Louisiana (Mr. Vitter won by 81).

But in the case of Christine O’Donnell, who defeated Michael N. Castle in the Republican Senate primary in Delaware last night, it hadn’t even occurred to me to add that possibility to the model until a few weeks ago. Mr. Castle had been elected statewide 12 times — twice as governor, once as lieutenant governor and nine times as Delaware’s at-large United States representative. Ms. O’Donnell had run for Senate twice before — in the Republican primary in 2006 and in the general election in 2008 — and lost badly both times.

I’m not saying that we would have carefully considered Ms. O’Donnell’s case and assigned it zero probability. Rather, it wasn’t something I had thought about at all — in the same way that one doesn’t think about a strong earthquake occurring unless one lives in California.

In fairness, primary elections can have a self-fulfilling quality to them, and until Mr. Miller beat Ms. Murkowski in Alaska three weeks ago, Ms. O’Donnell probably wasn’t on the minds of a lot of voters either. Ms. O’Donnell’s major endorsements, like that from Sarah Palin, came late in the race; before that, some key conservative groups like FreedomWorks had deliberately declined to endorse her, fearing that she wasn’t electable.

Nevetheless, Ms. O’Donnell’s victory — like Scott Brown’s in Massachusetts this year, or Hillary Rodham Clinton’s in the New Hampshire primary two years ago — was an emphatic reminder that voters write the script. The rest of us self-proclaimed political professionals — journalists and pollsters, activists and bundlers, lobbyists and party-leaders, presidents and senators — are just the stagehands.

So what does this mean as we head into November — and beyond?

There are some fairly tangible conclusions. For instance, Ms. O’Donnell’s win almost certainly reduces the possibility of a Republican takeover of the Senate. She could still defeat the Democrat in the race, Chris Coons — as Mr. Castle could have lost to him. But on the basis of the polling (and here we are, thankfully, again on solid empirical ground) the Republicans went from being extremely likely to win the race to extremely likely to lose it. They may now need to bring another state like Connecticut or West Virginia into play to have a decent chance of taking the Senate; indeed, I would expect to hear a lot of chatter about opportunities like these, as the Republican establishment seems ready to concede Delaware.

Another conclusion, of course, is that the Tea Party is a mixed blessing for the Republicans. Undoubtedly, in my view, they have done the party more good than harm over the past year and a half, bringing it back from what pundits assumed was the brink of irrelevance (but may instead just have been the nadir of a political cycle), to a position where they are poised to make electoral gains that could rival or exceed 1994.

But in order to achieve those gains — not a fairly ordinary gain of 20, 30 or even 40 House seats, but the earth-shattering, upside results that Republicans are dreaming about — they will need for three basic things to happen. First, they will need a solid majority of independent voters to select their candidates. Second, they will need the Democratic base to be uninterested in the election. And third, they will need their own base to be enthused.

For a number of reasons — but foremost the condition of the economy and the Democrats’ seeming inability to craft a winning message around it — the first factor seems almost certain to be in place for Republicans, and it is probably too late for Democrats to do much to change it. And this shows up plenty well in the polling; President Obama’s approval rating among independents is under 40 percent in many polls, for instance.

The second factor — Democratic disinterest — is the most uncertain of the three, and has probably been taken somewhat too much for granted by analysts. One should keep in mind that, even in an ordinary midterm election year, this factor tends to cut against the Democrats, since some key groups in their constituency, like young voters and Hispanics, traditionally vote in lower numbers in these elections. But whether Democratic participation will be merely average for a midterm year, or quite a bit worse than that, is unclear. Late in a political cycle, it tends to be easier to motivate a voter than to persuade him, and the Democrats do have some rallying points with their base like the health care bill (even if they are hush-hush about some of the same points when independents are in the room). They also have, as a consequence of the huge reach of President Obama’s campaign in 2008, good voter lists and databases. There is actually some evidence that Democrats closed their enthusiasm gap late in the 2009 races for governor in New Jersey and the Senate in Massachusetts, even if they ultimately lost them. And the Democrats have won a couple of elections with strong base support, like the special election in May in Pennsylvania’s 12th Congressional District. Still, the pluralistic nature of the Democratic base tends to make it harder to rally, and much of the party’s work — even if it were eventually to succeed — remains to be done.

The final factor — Republican engagement — also seems like something of a foregone conclusion. There is little doubt that many on the right view November’s election as one of historic importance. But, after last night, this factor may need to be read with a bit more nuance. What conservative voters seem to be most engaged by is their distaste for the establishment. But they seem to be somewhat equal-opportunity in this respect, disliking the Republican establishment nearly as much as the Democratic one. So even though in Florida, Republicans have nominated a fresh and compelling face in Marco Rubio, what happens in Ohio, where they have nominated a familiar and establishment candidate in Rob Portman? Or in Illinois, where they have nominated Mark Kirk, who is both establishment and quite moderate? Will Republican voters have the same gusto — and turn out in the same numbers — for these candidates? In Mr. Portman’s case, it might not matter — he is doing well enough with independents that he’s liable to win, even with mediocre base participation. But for someone like a Mr. Kirk, or a Dino Rossi in Washington, Republicans could find that their “enthusiasm gap” isn’t as large as they were expecting.

To some extent, the Republicans’ problem is nothing new. Parties often face a trade-off between nominating more extreme candidates, who may have more appeal to the party base, and more moderate ones who may have greater appeal to independents. Arguably, it is a decent problem to have; at least the Republicans know their voters are fired up about something (it’s just a question of whether it might be harnessed in quite the right way), which is less certain for the Democrats.

Still, there’s the possibility that Republicans end up with a lot of half-loaves: independent voters get them almost close enough in some states and districts, base voters in some others, but they come up a few points short in a lot of key races and wind up winning “only” 30 House seats and 4 or 5 Senate seats. Or just the opposite could be true. Independent voters rally them to surprising wins in some blue-leaning states, while base voters shore up the home front and allow them to roll back the gains Democrat made in 2006 and 2008.

But some analysts are making forecasts that seem imprudent, especially after last night. For instance, the Republican pollster Steve Lombardo suggested without qualification yesterday that “Republicans will win the House,” and the Weekly Standard’s Jay Cost set an over-under line of a gain of 57 House seats.

Indeed, it’s considerably more likely than not that Republicans will win the House (we place the odds at about 2 to 1 in their favor), and the achievement of a 57-seat (or larger) gain is quite distinctly possible. Both Mr. Lombardo and Mr. Cost are smart observers, and neither tend to be cheerleaders.

But the degree of certainty that their claims imply is not warranted by history — including very recent history.