This is an incredibly difficult task for several reasons. First of all, there are over 500,000 elected offices in the country (not all of which are partisan) so there is an enormous amount of data to track. Second, you have to make some sort of value judgement about the relative value of each office (how much more valuable is it to win a senate seat than a house seat? for example). And third, these offices don't exist in a vacuum so we have to consider how they interact. Normally people would value a senate seat over a house seat, but what if the senate seat increases the party total from a minority 43 to a minority 44, but the house seat is the one that gives your party control of the house?
Despite this, I've taken a stab at it, but I've incredibly simplified it in several ways.
1. I only considered the President, Senators, Representatives, Governors and who control each legislature. I have ignored Nebraska's legislature because it is non-partisan and figuring out which party is actually in control is not easy, especially in the past. I realize that other elected offices wield great power and can even determine the outcome of federal races (see: Florida 2000), but this has to be kept manageable.
2. I only went back to 1/1/2000. I probably could have gone back a few more years, but by the mid-90's tracking down state legislature data becomes difficult.
3. The hardest part was assigning points (and I'd love it if someone had some thoughts on it). I started by making the total of all state governments equal to the federal government. And then making the executive equal in power to its legislature. But then I decided that the President was more powerful than Congress because there is much he can do on his own (regulations, executive orders) or with little oversight (appointments) but the only thing Congress can do on its own is investigations. I had hoped that economists had already taken a stab at this, but the only analysis I could find (S. Brams) compared the President to Congress for purpose of legislation, and the President (and Senators) have more power than just that. In the end I set the President as 20% more powerful than Congress.
The base unit, 1 point, is equal to 1 Representative. For the minority party, the score is equal to the number of members. For the majority it is 500 points, plus 1 for every extra house member. If a party had all the house seats that would give them 717 points
Each Senator is equal to 5 points and for the minority party the score is simply the number of Senators times 5. Having a simple majority in the Senate is worth less than in the House because of the filibuster so that is equal to 325 plus 5 for each additional Senator. Having a filibuster-proof, super majority is equal to 550 points plus 5 for each additional Senator. Because the Senate weakened the filibuster rule in December of 2013, I increased the value for a simple majority to 330 (since it only involves votes on appointments and not Supreme Court justices) following that point. If a party had control of all Senate seats that would be worth 750 points.
Each Governor is worth 20 points. Each state legislature is worth 10. Trying to getting a more nuanced count for each state legislature was too daunting, so I made it binomial. That makes all states combined worth 1980 (no Nebraska legislature).
The President is worth 1200 points. More than control of both houses.
This is probably very very wrong, and I'm open to criticism of it.
4. I did not count non-voting delegates or the local government of the District of Columbia.
Here is what the graphs of each political parties power looks like since 2000. [The Reform Party had a Governor and, briefly, a Senator, in the early years]
This isn't too surprising. When a party controls the presidency, they are in the driver's seat. There are four big swings - when Republicans take the White House in 2001, when Democrats take the House and Senate in 2007, when Democrats take the White House in 2009 and when Republicans take the House in 2011.
The peak power that either party reached during this period is from November 3, 2009 to December 22, 2009 when Democrats controlled the White House, had a super majority in the Senate, and controlled the House, 28 governors and 61 of 98 legislatures. Specifically this period started when John Garamendi (D-CA) and Bill Owens (D-NY) won special elections to the House and ended when Rep. Parker Griffin of Alabama switched parties to the Republicans.
The Republican peak was from December 9, 2003 to January 20th, 2004 (except for January 12th). They controlled the White House, the Senate and the House along with 28 governors and 53 of 98 legislatures. This peak started when Ernie Fletcher became Governor of Kentucky and resigned his House seat and ended when Bill Janklow (R-SD) resigned from the House following a felony conviction related to a traffic crash. There was a brief interruption in the peak because Democrats took the Louisiana governor's mansion on January 12th, but then the Republicans took Mississippi's the following day.
The nadir of power for either party was on January 20, 2009, the day Barack Obama was sworn in, when Republicans power was cut by more than 50%. But, on the same day, Democrat Janet Napolitano resigned as Governor of Arizona to become Secretary of Homeland Security and so the next day, Republican Jan Brewer was sworn in as the new Governor of Arizona pulling the party back up - if only a little bit.
The low point for Democrats was from November 25, 2002 to November 30, 2002. On Nov 25th, Jim Talent (R-MO) took the seat Jean Carnahan (D-MO) had been temporarily filling in the Senate, technically giving control to the Republicans (50-50 tie with Vice-President Cheney as the tie-breaker). But the Senate didn't go in session again, so it never reorganized. 5 days later, Ed Case (D-HI) was seated in the House to fill the term of Patsy Mink who was elected posthumously, pulling Democrats up by 1 point.
Another thing we can see is who won each year. By the end of January or in early February everyone who won a race in a year has been seated and there is usually a lull in change. So using that, we can determine who won year by year and by how much. Won meaning increased their power.
2000 - Republicans (1175 points)
2001 - Democrats (80 points)
2002 - Republicans (60 points)
2003 - Republicans (38.5 points)
2004 - Tie (Both -5 points due to split of the Montana state house)
2005 - Democrats (Republicans lost 0.5 points when Duke Cunningham resigned)
2006 - Democrats (619 points)
2007 - Democrats (20.5 points)
2008 - Democrats (1299.5 points)
2009 - Republicans (50 points)
2010 - Republicans (696.5 points)
2011 - Republicans (10.5 points)
2012 - Democrats (19.5 points)
2013 - Democrats (40 points)
It might surprise people to find out that Democrats won 2013 with all the attention paid to Obamacare problems, but the year was mostly a status quo year in which none of the special elections resulted in party changes but the Democrats picked up points in three places.
1. Governor Lincoln Chafee of Rhode Island, who was elected as an Independent, became a Democrat
2. Democrats won the governor's race in Virginia and took that from Republicans
3. Democrats changed the filibuster rules in the Senate making their simple majority slightly more powerful.
Anyway, much of this model changes if you change the assumptions, but it sort of jibes with what has happened on the ground.