Since this is my initial forecast, I’ll just try to develop a reasonable prior. Here’s what I think; why I think it follows:

- Republican retain control of Congress with 51+ Congressional seats: 0.42
- Democrats seize control of Congress with 51+ Congressional seats: 0.24
- Republicans and Democrats each have 50 Congressional seats: 0.34

Here are the basic facts (which you can skip if you’re already in-the-know): There are 34 seats are up for re-election. 24 are currently held by Republicans, and 10 are held by Democrats. Since there are 54 Republicans in the Senate now, that means that the Republicans can count on a bare minimum of 30 seats after the election, and the Democrats can count on a bare minimum of 36 seats. (I’m counting the 2 independents who caucus with the Democrats *as* Democrats for now, but I’ll revisit this point later.) 17 of the seats up for election are functionally out of play. 10 of these are held by Republicans, so they can really count on 40 seats after the election. The other 7 are held by Democrats, so their floor is really 43 seats. Of the 17 seats that are competitive to one degree or another, 14 of these competitive seats are currently held by Republicans and 3 are held by Democrats.

So much for the basic facts. It would be nice to have some sense of how likely it is that a Democrat or a Republican will win each of these 17 competitive elections. And Wikipedia (of all places!) provides some raw useful information to this end[a]:

The final four columns of this table list estimates of how likely each of these Senatorial seats is to go to either a Republican or a Democrat. The estimates come from the Cook Report, the University of Virginia Center for Politics, Roll Call, and the Daily Kos. Since these are *qualitative* assessments, and we need *quantitative* assessments, I (somewhat arbitrarily) came up with the following cypher:

- Safe D = 0.90 probability of D victory
- Likely D = 0.75 probability of D victory
- Lean D/Tilt D = 0.60 probability of D victory
- Tossup = just what it sounds like, 0.50 probability of D victory

And, of course, I did the same for Republicans. I’m certainly open to better translation of the qualitative assessments into quantitative assessments, but this seems like a reasonable place to start.

My next step was to average the four quantitative assessments. While I didn’t weight any of the sources of these assessments, I was tempted to give the Cook Report added weight because of its reputation for accuracy[b]. Again, I’m open to better approaches. Next, I determined the mean, median, and standard deviation of the average assessments. Here’s what that looks like:

Hence, for any given competitive Senate seat, the expected value to the Republicans is 0.61, and the expected value to the Democrats is 0.39. And the most likely outcome is that Republican end up with 50.5 Senate seats, while Democrats get 49.5. Of course, there’s a small problem here – namely, that actual Senate seats come in discrete quantities along the lines of the positive integers. No one is going to end up with 0.583774 of a Senate seat any time soon!

But the magic of numbers[c] comes to the rescue again. We know that in order to retain their majority in the Senate, Republicans will need to win 11 of the 17 seats up for grabs in these competitive races, since they have a floor of 40 seats. And 11/17 = 0.65, rounding up a bit. Furthermore, we know that the standard deviation for the data series I mentioned is 0.20[d], which you can take my word for if you don’t want to do your own calculation. Given this data, there’s a 0.4207 (call it 0.42) probability that the Republicans will retain 51 or more Senate seats in this election cycle. Contrariwise, Democrats need 8 of the 17 Senate seats, since they have a floor of 43 seats. And 8/17 is about 0.47. Given all of the data we have, we can estimate a 0.242 probability of that happening.

But here’s the thing. Eagle-eyed readers will surely have noted that 0.4207 (the probability of Republicans retaining control of the Senate) + 0.242 (the probability of the Democrats seizing control of the Senate) does *not* equal 1. That’s because there’s a rather remarkable 0.3373 probability that we’ll see 50 Republicans and 50 Democrats in the Senate, according to the (admittedly overly) simple model I’ve pieced together! That’s a big surprise to me.

Here are 2 take aways from this fact: To start with, GJ needs to step up and tell us how they mean to score this event if there’s a 50/50 split in the Senate. For practical purposes, of course, control will rest in the hands of the party that has the tie-breaking vote, and that will be whichever party wins the presidential election. If that’s what GJ has in mind, I hope they’ll say so soon (and I apologize if they’ve already done so, but I’ve missed it). Furthermore, if the importance of the presidential election didn’t seem clear enough to me before, it certainly does now. The outcome of the presidential election has a more than 1-in-3 chance of determining which party has control of the Senate. That’s *huge*. The upshot for the time being: I’m going to assign each party half of the value of 0.3373, but that’s just a temporary fix.

Four more points need to be made: First, the two independents in the Senate are Angus King (ME) and Bernie Sanders (VT). Both Sen. King and Sen. Sanders caucus as Democrats. Hell, Sen. Sanders is running to be the Democratic nominee for president in 2016. So it’s *pretty* safe to think of them as Democrats, though it would be very nice to have confirmation from the GJ judges on this point. By the way, neither Sen. King nor Sen. Sanders is up for reelection this year, as they are both Class 1 Senators.

Second, I haven’t tried to use any historical data to help guide my forecasting, and that worries me. I *believe* that there’s a rough-and-ready tendency for the party who has a two-term president completing his time in office to lose Senate seats[e]. But I need to do more homework on this before I try to upgrade my little toy of a model.

Third, I’ve treated the Senate elections as if they were independent variables. That’s something of a fiction. Senate elections are likely to be deeply influenced by the presidential election, and there’s long been speculation that a Trump candidacy could be a disaster for Republicans in Congress[f]. But this election cycle has been pretty damn hard to predict. (The good news: It’s not *boring*. The bad news: It’s *not* boring.) So I’m going to put a pin in this until there’s enough solid empirical data to use. (And, for Pete’s sake, please tell me if there is, and I’m not in the loop.)

Fourth and finally, all of this bean counting gets scrambled if a Senator dies or has to leave office. “The U.S. Constitution grants the state legislatures the power to determine how U.S. Senators are to be replaced, including empowering the chief executive (the governor) do make these appointments”[g]. Since Republican governors outnumber Democratic governors more than 3-to-2[h], and Republicans control a little more than twice as many State legislatures as Democrats[i]. So Republicans have a huge advantage – an advantage I don’t yet have a way of incorporating into my forecast.

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[a] https://en.wikipedia.org/wiki/United_States_Senate_elections,_2016

[b] http://www.acsu.buffalo.edu/~jcampbel/documents/CookAccuracySummary.pdf

[c] http://jwilson.coe.uga.edu/EMAT6680Fa06/Hobgood/Pythagoras.html

[d] Our old friend Andrey Kolmogorov reminds us that all probability values fall between 0 and 1, inclusive[c]. So we need to be a bit careful about using the standard deviation here. If we has a perfectly normal distribution, then 0.025 of the data would sit north of 1.0, while about 0.0011 would be south of 0. I’ll just fix that on the fly.

[e] http://www.senate.gov/history/partydiv.htm

[f] For example, http://www.rollcall.com/news/how-donald-trump-could-swing-the-senate-opinion/

[g] http://uspolitics.about.com/od/thecongress/a/senate_vacancy.htm

[h] http://www.politico.com/story/2015/11/republican-governors-association-winning-streak-216000

[i] https://www.washingtonpost.com/news/the-fix/wp/2015/03/04/the-remarkable-republican-takeover-of-state-legislatures-in-1-chart/