If the U.S. Senate Elections were held on 07-Nov-2006...

Expected breakdown: 49.6 Republican, 50.4 Democrat or Independent

Chance of Democratic Takeover: 53.4 percent

Notes for 11/17/06

Now that the dust has settled, I thought it would be a good time to see how well this method did. For a baseline, I used RealClearPolitics, which averaged together the most recent poll results for the 13 closest Senate races. Both methods called every race correctly, which is a testament to the quality of the polling data, on aggregate. The Kalman filter's prection of the final margin of victory was closer to the actual result in eight races, further in four races, and identical to the RCP prediction in one race. The mean error was 2.55 for the Kalman Filter and 2.9 for the RCP averages.

Some readers pointed out that undecided voters are thought to vote for a challenger more frequently than for an incumbent -- the rule of thumb is a ratio of two to one. That may be the case historically, but not in this election; assigning undecideds in this way increased the error for both methods. My standard approach, which assigns the undecideds 50/50 to each candidate, outperformed this variation in ten of the thirteen races. The mean error of the Kalman Filter with this variation increased to 3.62; for the RCP, it increased to 3.56.

You can find detailed results and check my math in this spreadsheet. (.csv)

Finally -- there's always more to do. All these results are based on the polls that were available on election day. It would be interesting to see how the methods compare when using the polls a week before the election, and a month before. Since polling data is sparser then, I'd like to think the Kalman filter would have an even greater advantage -- but that remains to be seen. I'd also like to see how accurate my estimates of polling house bias were, and whether including this bias in the model actually improved its performance.

Notes for 11/7/06

A few readers have noticed that the chance of a Democratic takeover is much higher today than over the past few days. A few polls came out very recently that showed big leads for Democratic candidates in Virginia, Missouri, and Montana, which other polls show as tied. For example, in the last ten polls in Virginia, neither candidate had more than a three point edge; but then SurveyUSA releases a poll showing an 8-point lead for the Jim Webb, the Democrat. The situation in Missouri is a little less confusing, since both Gallup and SurveyUSA now show subtantial leads for the Democrat, although a Rasmussen poll released the same day shows a tied race. It's surprising to me that polling numbers would diverge so significantly on the last day when they had been fairly consistent for the previous two weeks. At any rate, although I have a lot of faith in the method of combining polls that I'm presenting here, keep in mind that the rule of "garbage in, garbage out" still applies. The good news is that we won't have to wait long to find out which pollster was right.

Brief explanation

In these graphs, the dark line represents the estimated true level of support for each candidate, with red indicating the republican candidate, blue for the democrat, and green for the independent. The circles represent individual poll results, and the shaded areas represent confidence intervals. These estimates are computed using the Kalman Filter, a statistical technique that combines all previous observations, weighting recent observations more heavily. The chance of winning each seat is based on the estimated difference in support, and the confidence intervals around that estimate; again, this assumes that the election is being held today; future events will shape the actual election results, and predicting the future is not within the capabilities of this method.

More details can be found here.

Summary

Arizona

99.0 percent chance that the Republican is winning
  • Republican: 49.7 +- 3.4
  • Democrat: 41.3 +- 3.4
  • Last 10 polls

    RD RD RD DatePollster
    51.3 38.653.0 40.01.7 1.411/01SurveyUSA
    49.2 41.149.0 41.0-0.2 -0.111/01Mason
    49.9 44.550.0 46.00.1 1.510/31Polimetrix
    46.9 41.046.0 41.0-0.9 0.010/27Zimmerman
    50.4 39.652.0 44.01.6 4.410/25Zogby
    48.5 42.647.0 41.0-1.5 -1.610/20Arizona State U.
    48.4 42.451.0 42.02.6 -0.410/15Rasmussen
    46.3 41.648.0 43.01.7 1.410/15SurveyUSA
    48.7 35.149.0 33.00.3 -2.110/13Northern Arizona U.
    48.4 39.650.0 44.01.6 4.410/13Zogby
    CorrectedRawBias

    California

    0.0 percent chance that the Republican is winning
  • Republican: 30.5 +- 3.5
  • Democrat: 58.4 +- 3.5
  • Last 10 polls

    RD RD RD DatePollster
    30.4 58.931.0 60.00.6 1.111/03SurveyUSA
    28.2 60.229.0 61.00.8 0.810/31Polimetrix
    32.7 53.533.0 55.00.3 1.510/26Field Poll
    32.4 57.933.0 59.00.6 1.110/24SurveyUSA
    38.2 56.239.0 57.00.8 0.810/23Polimetrix
    25.7 53.223.0 53.0-2.7 -0.209/26Mason
    35.1 53.036.0 54.00.9 1.009/25LA Times
    34.4 53.935.0 55.00.6 1.109/25SurveyUSA
    28.7 55.529.0 57.00.3 1.509/19Field Poll
    36.6 50.438.0 49.01.4 -1.409/13Datamar
    CorrectedRawBias

    Connecticut

    0.0 percent chance that the Republican is winning
  • Republican: 7.6 +- 2.9
  • Independent: 48.4 +- 2.9
  • Democrat: 39.8 +- 2.9
  • Last 10 polls

    RID RID RID DatePollster
    8.4 47.7 38.99.0 49.0 38.00.6 1.3 -0.911/03SurveyUSA
    7.9 48.4 39.78.0 50.0 38.00.1 1.6 -1.711/02Quinnipiac U.
    5.8 48.2 42.75.0 48.0 44.0-0.8 -0.2 1.310/31Polimetrix
    7.2 50.3 39.27.0 51.0 39.0-0.2 0.7 -0.210/31Research 2000
    8.0 49.1 39.19.0 48.0 40.01.0 -1.1 0.910/28Rasmussen
    7.9 47.4 38.78.0 49.0 37.00.1 1.6 -1.710/27Quinnipiac U.
    8.8 49.1 36.98.0 49.0 37.0-0.8 -0.1 0.110/27Zogby
    8.0 49.1 39.19.0 48.0 40.01.0 -1.1 0.910/26Rasmussen
    6.8 47.1 42.96.0 47.0 43.0-0.8 -0.1 0.110/25Zogby
    9.0 49.8 36.59.0 49.0 37.0-0.0 -0.8 0.510/19ARG
    CorrectedRawBias

    Florida

    0.0 percent chance that the Republican is winning
  • Republican: 33.6 +- 3.1
  • Democrat: 59.3 +- 3.1
  • Last 10 polls

    RD RD RD DatePollster
    34.5 59.436.0 59.01.5 -0.411/03SurveyUSA
    29.5 60.931.0 60.01.5 -0.911/01Zogby
    34.4 58.534.0 58.0-0.4 -0.510/31Mason
    33.9 59.734.0 60.00.1 0.310/31Polimetrix
    38.5 54.940.0 54.01.5 -0.910/25Zogby
    32.1 61.229.0 64.0-3.1 2.810/20Quinnipiac U.
    31.4 57.531.0 57.0-0.4 -0.510/16Mason
    35.5 54.937.0 54.01.5 -0.910/13Zogby
    35.5 55.437.0 55.01.5 -0.410/08SurveyUSA
    36.1 58.233.0 61.0-3.1 2.810/05Quinnipiac U.
    CorrectedRawBias

    Maryland

    2.7 percent chance that the Republican is winning
  • Republican: 44.2 +- 2.6
  • Democrat: 49.6 +- 2.6
  • Last 10 polls

    RD RD RD DatePollster
    43.9 50.546.0 49.02.1 -1.511/04SurveyUSA
    44.0 48.144.0 47.00.0 -1.111/02Mason
    44.9 48.547.0 47.02.1 -1.511/01SurveyUSA
    44.8 49.845.0 50.00.2 0.211/01Rasmussen
    44.8 50.545.0 51.00.2 0.510/31Polimetrix
    43.7 48.843.0 49.0-0.7 0.210/29Potomac Inc.
    44.6 48.744.0 49.0-0.6 0.310/27Zogby
    41.8 48.842.0 49.00.2 0.210/26Rasmussen
    44.6 52.744.0 53.0-0.6 0.310/25Zogby
    43.2 52.943.0 54.0-0.2 1.110/24Washington Post
    CorrectedRawBias

    Michigan

    0.0 percent chance that the Republican is winning
  • Republican: 39.1 +- 3.0
  • Democrat: 52.3 +- 3.0
  • Last 10 polls

    RD RD RD DatePollster
    40.4 51.742.0 52.01.6 0.311/03SurveyUSA
    36.8 52.834.0 53.0-2.8 0.211/01Selzer
    37.6 52.837.0 53.0-0.6 0.211/01Mason
    39.7 54.140.0 55.00.3 0.910/31Polimetrix
    39.7 50.938.0 51.0-1.7 0.110/31EPIC
    39.7 51.938.0 52.0-1.7 0.110/28EPIC
    38.7 49.842.0 49.03.3 -0.810/25Zogby
    40.6 51.741.0 52.00.4 0.310/23Research 2000
    39.7 49.938.0 50.0-1.7 0.110/23EPIC
    42.4 50.744.0 51.01.6 0.310/23SurveyUSA
    CorrectedRawBias

    Minnesota

    0.0 percent chance that the Republican is winning
  • Republican: 37.9 +- 2.8
  • Democrat: 54.6 +- 2.8
  • Last 10 polls

    RD RD RD DatePollster
    38.1 55.840.0 56.01.9 0.211/04SurveyUSA
    37.1 52.834.0 54.0-3.1 1.211/01Star Tribune
    38.4 54.140.0 54.01.6 -0.111/01Rasmussen
    38.7 56.139.0 57.00.3 0.910/31Polimetrix
    34.3 54.633.0 55.0-1.3 0.410/25U. of Minnesota
    37.4 53.139.0 53.01.6 -0.110/25Rasmussen
    39.5 50.740.0 50.00.5 -0.710/25Mason
    40.2 50.843.0 51.02.8 0.210/25Zogby
    37.1 54.839.0 55.01.9 0.210/22SurveyUSA
    32.8 55.231.0 56.0-1.8 0.810/21St. Cloud U.
    CorrectedRawBias

    Missouri

    12.6 percent chance that the Republican is winning
  • Republican: 46.1 +- 2.1
  • Democrat: 48.7 +- 2.1
  • Last 10 polls

    RD RD RD DatePollster
    49.4 48.449.0 48.0-0.4 -0.411/05Rasmussen
    44.6 48.844.0 50.0-0.6 1.211/05SurveyUSA
    42.6 49.842.0 51.0-0.6 1.211/04SurveyUSA
    44.6 48.445.0 49.00.4 0.611/02Gallup
    48.4 49.448.0 49.0-0.4 -0.411/02Rasmussen
    46.1 46.845.0 46.0-1.1 -0.811/02Mason
    49.0 49.550.0 50.01.0 0.510/31Polimetrix
    47.4 48.447.0 48.0-0.4 -0.410/30Rasmussen
    46.6 47.846.0 49.0-0.6 1.210/29SurveyUSA
    48.2 48.549.0 49.00.8 0.510/27Opinion Research
    CorrectedRawBias

    Montana

    5.8 percent chance that the Republican is winning
  • Republican: 43.8 +- 2.8
  • Democrat: 48.4 +- 2.8
  • Last 10 polls

    RD RD RD DatePollster
    45.3 48.048.0 50.02.7 2.011/04Rasmussen
    41.9 49.241.0 50.0-0.9 0.811/02Gallup
    41.9 49.241.0 50.0-0.9 0.811/02Gallup
    43.3 48.046.0 50.02.7 2.011/01Rasmussen
    46.3 47.547.0 47.00.7 -0.511/01Mason
    45.2 47.546.0 47.00.8 -0.510/27Zogby
    44.3 49.047.0 51.02.7 2.010/26Rasmussen
    43.3 46.046.0 48.02.7 2.010/18Rasmussen
    42.3 46.543.0 46.00.7 -0.510/18Mason
    36.8 46.335.0 46.0-1.8 -0.310/12Montana State U.
    CorrectedRawBias

    Nevada

    99.9 percent chance that the Republican is winning
  • Republican: 53.9 +- 3.9
  • Democrat: 40.5 +- 3.9
  • Last 10 polls

    RD RD RD DatePollster
    53.3 41.553.0 42.0-0.3 0.510/31Polimetrix
    55.3 40.654.0 42.0-1.3 1.410/30Rasmussen
    52.0 39.554.0 37.02.0 -2.510/28Mason
    57.1 36.158.0 37.00.9 0.910/25Zogby
    54.0 41.555.0 41.01.0 -0.510/24Research 2000
    51.3 40.650.0 42.0-1.3 1.410/17Rasmussen
    51.1 42.152.0 43.00.9 0.910/13Zogby
    56.0 37.558.0 35.02.0 -2.509/20Mason
    51.3 39.650.0 41.0-1.3 1.409/06Rasmussen
    55.0 35.556.0 35.01.0 -0.509/06Research 2000
    CorrectedRawBias

    New Jersey

    0.5 percent chance that the Republican is winning
  • Republican: 41.7 +- 2.6
  • Democrat: 48.7 +- 2.6
  • Last 10 polls

    RD RD RD DatePollster
    40.3 49.140.0 50.0-0.3 0.911/02Gallup
    42.5 46.542.0 45.0-0.5 -1.511/02Monmouth U.
    41.2 48.241.0 48.0-0.2 -0.211/02Mason
    40.3 49.140.0 50.0-0.3 0.911/02Gallup
    41.7 51.342.0 50.00.3 -1.311/02Marist Coll.
    42.6 47.043.0 48.00.4 1.011/02Quinnipiac U.
    42.0 48.643.0 48.01.0 -0.611/01Rasmussen
    45.4 51.647.0 53.01.6 1.410/31Polimetrix
    42.4 46.042.0 46.0-0.4 0.010/30Rutgers
    43.0 49.644.0 49.01.0 -0.610/29Rasmussen
    CorrectedRawBias

    New Mexico

    0.0 percent chance that the Republican is winning
  • Republican: 34.4 +- 6.1
  • Democrat: 57.4 +- 6.1
  • Last 10 polls

    RD RD RD DatePollster
    36.1 56.138.0 58.01.9 1.910/25Zogby
    32.1 60.134.0 62.01.9 1.910/13Zogby
    21.9 63.119.0 65.0-2.9 1.909/26Research and Polling
    30.8 55.432.0 56.01.2 0.609/07Rasmussen
    31.1 57.133.0 59.01.9 1.909/01Zogby
    25.9 60.123.0 62.0-2.9 1.908/28Research and Polling
    30.1 52.132.0 54.01.9 1.907/15Zogby
    29.8 53.431.0 54.01.2 0.606/27Rasmussen
    34.1 53.136.0 55.01.9 1.906/15Zogby
    28.1 51.130.0 53.01.9 1.903/23Zogby
    CorrectedRawBias

    New York

    0.0 percent chance that the Republican is winning
  • Republican: 30.4 +- 3.8
  • Democrat: 63.6 +- 3.8
  • Last 10 polls

    RD RD RD DatePollster
    28.0 64.828.0 65.0-0.0 0.210/31Siena Coll.
    31.2 62.632.0 65.00.8 2.410/31Marist Coll.
    31.5 65.232.0 66.00.5 0.810/31Marist
    32.2 59.033.0 57.00.8 -2.010/25Zogby
    29.2 64.630.0 67.00.8 2.410/17Marist Coll.
    29.9 62.630.0 65.00.1 2.410/13Quinnipiac U.
    31.2 58.032.0 56.00.8 -2.010/13Zogby
    32.0 58.832.0 59.0-0.0 0.210/10Siena Coll.
    27.2 55.028.0 53.00.8 -2.010/07Zogby
    30.9 63.631.0 66.00.1 2.409/28Quinnipiac U.
    CorrectedRawBias

    Ohio

    0.0 percent chance that the Republican is winning
  • Republican: 41.9 +- 2.7
  • Democrat: 53.5 +- 2.7
  • Last 10 polls

    RD RD RD DatePollster
    42.5 51.342.0 54.0-0.5 2.711/04SurveyUSA
    41.9 54.044.0 56.02.1 2.011/03U. of Cincinnati
    42.9 51.944.0 50.01.1 -1.911/01Mason
    40.5 56.840.0 58.0-0.5 1.210/31Polimetrix
    39.0 60.238.0 62.0-1.0 1.810/29Columbus Dispatch
    42.7 54.443.0 54.00.3 -0.410/27Opinion Research
    42.1 49.542.0 49.0-0.1 -0.510/27Zogby
    47.1 49.547.0 49.0-0.1 -0.510/25Zogby
    43.6 50.844.0 51.00.4 0.210/24Opinion Consultants
    39.9 53.041.0 53.01.1 0.010/24Rasmussen
    CorrectedRawBias

    Pennsylvania

    0.0 percent chance that the Republican is winning
  • Republican: 40.2 +- 3.5
  • Democrat: 53.0 +- 3.5
  • Last 10 polls

    RD RD RD DatePollster
    39.0 52.339.0 52.0-0.0 -0.311/01Mason
    40.1 55.140.0 56.0-0.1 0.910/31Polimetrix
    42.1 52.443.0 51.00.9 -1.410/30Muhlenberg Coll.
    41.4 53.342.0 55.00.6 1.710/28Rasmussen
    37.2 54.438.0 53.00.8 -1.410/27Keystone Poll
    37.9 48.240.0 48.02.1 -0.210/27Zogby
    41.4 53.342.0 55.00.6 1.710/26Rasmussen
    42.0 51.542.0 52.0-0.0 0.510/26Quinnipiac U.
    41.9 53.244.0 53.02.1 -0.210/25Zogby
    39.3 50.739.0 50.0-0.3 -0.710/23West Chester U.
    CorrectedRawBias

    Rhode Island

    16.9 percent chance that the Republican is winning
  • Republican: 43.7 +- 3.2
  • Democrat: 46.9 +- 3.2
  • Last 10 polls

    RD RD RD DatePollster
    44.5 46.745.0 48.00.5 1.311/02Gallup
    44.5 46.745.0 48.00.5 1.311/02Gallup
    44.8 45.946.0 45.01.2 -0.911/01Mason
    39.1 51.839.0 53.0-0.1 1.210/27Zogby
    33.8 45.133.0 43.0-0.8 -2.110/24Rhode Island Coll.
    42.7 48.744.0 52.01.3 3.310/23Rasmussen
    41.8 48.943.0 48.01.2 -0.910/19Mason
    42.4 47.242.0 46.0-0.4 -1.210/12Fleming and Assocs.
    40.7 47.742.0 51.01.3 3.310/06Rasmussen
    37.8 42.137.0 40.0-0.8 -2.110/03Rhode Island Coll.
    CorrectedRawBias

    Tennessee

    99.2 percent chance that the Republican is winning
  • Republican: 50.4 +- 2.4
  • Democrat: 44.4 +- 2.4
  • Last 10 polls

    RD RD RD DatePollster
    50.5 46.051.0 47.00.5 1.011/04Rasmussen
    50.5 44.551.0 46.00.5 1.511/04SurveyUSA
    48.9 44.349.0 46.00.1 1.711/02Gallup
    52.5 44.053.0 45.00.5 1.011/02Rasmussen
    50.3 39.950.0 38.0-0.3 -1.911/02Mason
    50.8 45.551.0 46.00.2 0.510/31Polimetrix
    48.5 46.049.0 47.00.5 1.010/30Rasmussen
    51.4 44.252.0 44.00.6 -0.210/27Opinion Research
    52.4 42.553.0 43.00.6 0.510/27Zogby
    48.4 47.549.0 48.00.6 0.510/25Zogby
    CorrectedRawBias

    Texas

    100.0 percent chance that the Republican is winning
  • Republican: 61.0 +- 4.4
  • Democrat: 31.5 +- 4.4
  • Last 10 polls

    RD RD RD DatePollster
    63.7 29.865.0 29.01.3 -0.810/31Polimetrix
    55.4 35.055.0 36.0-0.4 1.010/25Zogby
    58.0 35.160.0 34.02.0 -1.110/23Rasmussen
    60.4 27.060.0 28.0-0.4 1.010/13Zogby
    48.4 38.048.0 39.0-0.4 1.009/01Zogby
    56.0 33.158.0 32.02.0 -1.108/31Rasmussen
    55.4 36.055.0 37.0-0.4 1.008/18Zogby
    59.0 32.161.0 31.02.0 -1.108/03Rasmussen
    52.4 36.052.0 37.0-0.4 1.007/15Zogby
    56.0 32.158.0 31.02.0 -1.107/13Rasmussen
    CorrectedRawBias

    Virginia

    20.1 percent chance that the Republican is winning
  • Republican: 46.4 +- 2.5
  • Democrat: 48.6 +- 2.5
  • Last 10 polls

    RD RD RD DatePollster
    43.0 51.544.0 52.01.0 0.511/04SurveyUSA
    48.0 46.449.0 46.01.0 -0.411/02Gallup
    48.0 49.249.0 49.01.0 -0.211/02Rasmussen
    46.1 47.945.0 46.0-1.1 -1.911/02Mason
    48.0 46.449.0 46.01.0 -0.411/02Gallup
    49.0 49.450.0 50.01.0 0.610/31Polimetrix
    45.0 48.246.0 48.01.0 -0.210/29Rasmussen
    46.0 49.146.0 50.0-0.0 0.910/27Opinion Research
    43.7 43.644.0 45.00.3 1.410/27Zogby
    45.4 43.545.0 42.0-0.4 -1.510/25Roanoke Coll.
    CorrectedRawBias

    Washington

    0.1 percent chance that the Republican is winning
  • Republican: 41.1 +- 3.6
  • Democrat: 53.5 +- 3.6
  • Last 10 polls

    RD RD RD DatePollster
    39.4 53.938.0 54.0-1.4 0.111/01Mason
    42.4 55.843.0 57.00.6 1.210/31Polimetrix
    42.3 50.343.0 51.00.7 0.710/28SurveyUSA
    41.1 52.741.0 53.0-0.1 0.310/28U. of Washington
    41.0 52.341.0 52.00.0 -0.310/26Rasmussen
    42.5 48.846.0 50.03.5 1.210/25Zogby
    38.4 51.937.0 52.0-1.4 0.110/18Mason
    38.0 53.338.0 53.00.0 -0.310/17Rasmussen
    42.3 50.343.0 51.00.7 0.710/14SurveyUSA
    41.5 50.845.0 52.03.5 1.210/13Zogby
    CorrectedRawBias

    Wisconsin

    0.0 percent chance that the Republican is winning
  • Republican: 26.3 +- 4.4
  • Democrat: 64.0 +- 4.4
  • Last 10 polls

    RD RD RD DatePollster
    24.8 67.324.0 69.0-0.8 1.710/31Polimetrix
    34.0 52.938.0 47.04.0 -5.910/25Zogby
    19.2 69.516.0 73.0-3.2 3.510/22U. of Wisconsin
    30.0 55.934.0 50.04.0 -5.910/13Zogby
    31.4 59.133.0 60.01.6 0.909/14Rasmussen
    31.0 55.935.0 50.04.0 -5.909/01Zogby
    29.4 58.131.0 59.01.6 0.908/18Rasmussen
    29.0 56.933.0 51.04.0 -5.908/18Zogby
    25.4 59.127.0 60.01.6 0.907/12Rasmussen
    15.5 62.314.0 63.0-1.5 0.706/27Diversified Research
    CorrectedRawBias