The weather I have this morning is cold and wet and dreary, so here’s a post to match that mood.

Let’s pick, pretty much at random, four of this year’s crop of truly lunatic Republican Senate candidates. And let’s look at how likely they are to be making a complete fool of themselves on Capitol Hill for the next six years. (Full disclosure of working assumption: for each of them, the probability of making a complete fool of themselves on Capitol Hill, conditional on being elected, is assumed to be 100%.)

Here, in alphabetical order, is the starting four: Sharron Angle (Nevada), Ken Buck (Colorado), Joe Miller (Alaska), Rand Paul (Kentucky).

Nate Silver had this assessment of Sharron Angle’s prospects yesterday:

In Nevada, two of three polls released this week show the Democrat, Harry Reid, with a slight lead over the Republican, Sharron Angle. The model still regards Ms. Angle as an incremental favorite — but it now sees the race as closer to 50-50 after having assigned her a two-in-three chance of winning last week.

“Closer to 50-50″ actually means a 56% probability that Angle wins.

Last week, Public Policy Polling had Ken Buck locked in a neck-and-neck contest that seems to be a lesser-of-the-two-evils race:

PPP’s newest Colorado poll finds (Michael Bennet) holding onto a 46-45 lead over Ken Buck.
[...]
Bennet continues to be, as we’ve found in all of our polling for the whole cycle, an unpopular Senator. His approval rating is just 35% and 49% of voters disapprove of the job he’s doing. If a moderate Republican had been nominated against him this race might be over. But Buck’s unpopular too at a 41/46 favorability spread and that’s keeping this race close.

Nate Silver — who is well known to walk on water — is, once again, not too impressed with the Democrat’s chances, though:

One survey, from Public Policy Polling, in fact gives Mr. Bennet a single-point lead (Mr. Bennet’s internal polling, not used by the model, also puts him slightly ahead). But the bulk of the evidence still suggests an advantage for the Republican, Ken Buck; the model has him as the 73 percent favorite, down from 79 percent last week.

That 73% was last week; Silver now has that probability at 68%.

In the three-way Alaska race, a Public Policy Polling poll for Daily Kos this week shows Joe Miller at 35%, with renegade write-in candidate Lisa Murkowski at 33% and Democrat Scott McAdams at 26%.

This is Nate Silver’s two-week-old assessment, based on complex adjustments to account for the fact that “polls evaluating Senator Lisa Murkowski’s chances as a write-in may be unreliable”:

Right now, it is not clear if Ms. Murkowski or Mr. Miller would be favored if she were named on the ballot — the polls, in addition to other issues, are of mixed opinion on this question. But if the penalty that Ms. Murkowski suffers for being a write-in is at all substantial, that would make Mr. Miller a reasonably clear favorite — and our model thus gives him an 85 percent chance of winning, versus 12 percent for Ms. Murkowski and 3 percent for Mr. McAdams.

He currently assigns a 74% probability to Miller winning.

A recent independent poll has Rand Paul leading Jack Conway by four points:

Ophthalmologist Rand Paul (R) is running virtually even with state Attorney General Jack Conway (D) in the Kentucky Senate race, according to a new independent poll.

The survey shows Paul taking 43.4 percent to Conway’s 39.5 percent among likely voters. Seventeen percent were undecided in the survey, which had a margin of error of 3.5 percentage points.

Nate Silver doesn’t seem to have a recent post assessing the Kentucky Senate race (not that I could find, anyway), but the probability he assigns to Rand Paul winning the race is currently 86%.

Time to step back, and heave a deep sigh. Not one of these crazies is a clear underdog by the polls. Not one of them has less than a 56% probability of winning, according to Nate Silver.

We can go ahead and have a little more fun with these very unfunny numbers. Let’s assume Nate Silver’s probability estimates are independent. That is to say, the estimation errors in his probability estimates are independent. (Of course, that can’t be strictly true, to the extent that there are common assumptions in the forecast models for these four states. But it’s the only way to do combined number-crunching with the estimates.)

The probability that at least one of these crazies will be elected to the Senate is a sobering 99%. The probability that all of them will be elected is an extremely uncomfortable 24%.