The developing conventional wisdom is that Democrats’ chances of taking back the Senate in 2016 hinge on their ability to claim a third term in the White House. But is this true? Like most conventional wisdom, there is some truth here, but it probably overstates the case.

To address this question, I decided to revisit a Senate election model I developed early in 2014. I won’t completely rehash the details of the model here (you can read them at the above links), but the basic theory is simple: Our federal elections have become so polarized that you can now predict Senate races accurately knowing just three variables: The president’s job approval rating, whether there is an incumbent in a race, and whether one party or the other nominates a badly damaged, controversial candidate (think Christine O’Donnell).

The data are collected from 2004, 2006, 2010 and 2012. I’ve updated the model to include data from 2014 as well. The 2008 results are not included because at a certain point, presidential job approval stops mattering; a president with a 25 percent job approval (which George W. Bush had in late 2008) does little more harm than a president with a 35 percent job approval, because that difference largely occurs with partisan Republicans who are likely to vote for a Republican regardless (more on this later). For the same reason, I do not go back to 1998-2002. In years where the job approval question did not appear at the state level in the exit polls, job approval is estimated from the national job approval in the exit polling, modified by the state’s partisan voter index.

The model generally performs well. For starters, in early 2014, it indicated that if Barack Obama’s job approval on Election Day were 44 percent, then Republicans should gain nine seats. That is where the exit polls had his job approval, and Republicans gained nine seats. It predicted the Democrats’ vote shares pretty accurately as well, including coming within one point of the results in hard-to-predict races like North Carolina and Colorado (there were misses in excess of four points in South Dakota, where Larry Pressler depressed the Democratic vote, and in Oregon, where Monica Wehby’s campaign imploded). Across all years, the median error is one point, as is the mode.

When modeling, it can be useful to go back after the fact and check to see if your model did indeed predict things well. For example, if we run the model using only the data from 2006 and 2010-2014 to try and predict 2004, it suggest that Republicans should have picked up four seats that year, which they did. Utilizing this approach for other years in the sample results in a prediction of Democrats picking up six seats in 2006 (they indeed picked up six), losing five seats in 2010 (they lost six), and losing one seat in 2012 (they picked up two). Incidentally, it performs terribly in 2008, predicting Democratic gains of 13 seats. Republicans over-perform the predictions by about seven points on average. This seems to validate the assumption that 2008 is too dissimilar to include.

So what does this model predict for 2016? Well, we’re faced with two problems. First, we don’t know what President Obama’s job approval will be. There are a few ways to deal with this, but I ultimately utilized the same approach as I did in 2014: by generating random numbers following a normal distribution around various means (I’ll explain more on this below).

More importantly, we don’t know where problem candidates will surface, so I assigned probabilities. I gave Republicans a 10 percent chance of nominating a problem candidate in Nevada (where Sharron Angle is considering another bid), 30 percent in Florida, 10 percent in Illinois, 10 percent in New Hampshire, 10 percent in Alaska, 20 percent in Arizona, and 30 percent in Indiana. I also marked Wisconsin as a state with a problematic incumbent, given Ron Johnson’s steeper-than-usual learning curve. One could make a case for including Mark Kirk in Illinois as well, but I ultimately opted not to consider him problematic (mostly because I had made a judgment call in the opposite direction with Johnson).

I then ran the model with some different assumptions about where Obama’s job approval would likely be this fall. For example, let’s assume that the most likely outcome is that the president’s job approval will stay more or less around 45 percent, but acknowledge that it could be higher or lower. If we run 10,000 simulated races within these parameters, then the median outcome is no net change in the makeup of the Senate. Democrats win control of the Senate only about 5 percent of the time in this scenario.

On the other hand, if we see the president’s job approval increase to 50 percent (with allowances on either side) then the median likely outcome is a Democratic pickup of two seats, with Democrats winning the Senate 26 percent of the time.

If we see a substantial increase in the president’s job approval, to around 55 percent, Democrats win the Senate around 67 percent of the time, and pick up five seats. At 60 percent job approval, Democrats pick up eight seats, and control the Senate 94 percent of the time (this is different from what I found in 2014 because the model’s parameters have been re-estimated, there have been fewer Republican retirements than I anticipated, and problematic challengers, at least for now, haven’t really emerged).

Finally, we can run the model directly on a variety of job approval ratings, and estimate Democratic gains. This estimates that the president would have to improve his job approval to 46 percent for a Democratic takeover to be realistic, and to 53 percent for it to be more likely than not.

As always, there are caveats. First, there are probably too many states included. I included states classified as anything other than “Safe” by the Cook Political Report. In this instance, it includes California. In a normal electoral system, with a quality GOP candidate, you can see scenarios where Republicans win this seat at Obama’s current job approval. But neither is the case in California, and it is hard to see a Republican winning there (unless two Republicans sneak into the top-two primary). Likewise, the GOP’s recruiting failure in Colorado probably makes it much less likely to flip than the model suggests. Usually these cancel each other out (in other words, there are similar categorizations that help Democrats), but this cycle I can envision the Democratic long shots (Arizona, Georgia, Indiana and Missouri) flipping much more easily than I can Colorado or California.

In addition, the model does have some significant misses, which reminds us that candidates really do matter, even beyond the “damaged candidate” category I utilize. For example, the model cannot figure out how Kelly Ayotte won by 25 points in 2010, or how Lincoln Chafee managed to keep it relatively close in 2006. It rarely sees Heidi Heitkamp winning. So an unusually good recruiting season could push things toward Democrats; Maggie Hassan (pictured, with Hillary Clinton) probably has a better chance of winning in New Hampshire than “generic Democrat.”

We might also wonder whether open presidential seats work in the same fashion as seats where we have an incumbent running. Open elections still seem to be referenda on the incumbent, so it is probably the better assumption that Senate elections will function in the same manner. But it is nevertheless an assumption.

Finally, we have to take seriously the possibility that a candidate like Donald Trump or Ted Cruz could damage Republican down-ticket candidates. While I believe that these candidates’ chances in the general election are probably understated by most pundits, they could turn this election into a real “choice” election, rather than the traditional referendum.

Overall, I do think this model probably overstates Republican chances somewhat. But I thought the same thing in 2014, and it proved to be spot on. But for now, the fact that Republicans have relatively few retirements in vulnerable seats provides them with a bit of a bulwark against a narrow Democratic win. But it isn’t a significant one, and an upsurge in Democratic fortunes could make it very difficult for Republicans to hold the Senate.