In the race for the Democratic nomination for the office of President, one thing is clear: Pretty much anybody could win.

Well, not really, but this time in previous elections, over several years, it has been uncommon for the leading candidate to stay the leading candidate, and it has been difficult to predict which of the candidates might eventually take the nomination. That prediction will be something one can make on Super Hangover Wednesday, I suspect (the day after Super Tuesday) in this particular year, or maybe a couple of weeks later.

However, that does not mean that an examination of the polling data is without merit or interest. Or, at least, interest.

Here, I look only at the three candidates that have been consistently in the double digit range for months: Biden, Warren, and Sanders. There are three simple and very interesting observations to make.

1) Sanders is to the polls like a nuclear power plant is to the electric grid supply. Baseload steady. People remark now and then that his numbers are up, or down, or whatever. But as the analysis below shows, Sanders’ position in the polls have been uncannily steady for months.

2) Biden has undergone a steady decline, starting with a stronger decline owing to simple stabilizing of numbers (with no real meaning, I think) followed by a long period of slow decline, and ending over the last few weeks with some real drops in the polling. Statistically speaking, using the i-statistic (“I can see this without even calculating any numbers) Biden is still probably in the number one slot, but we are observing a transition, which leads us to…

3) Warren has gone from a highly variable third/fourth place position to a strong second place position, and is moving on first place like a Marine.

In this analysis, numbers from only the three candidates are considered, and recalculated in relation to each other. This removes effects of other candidates moving into the race, out of the race, or around the race in relation to each other.

The usual most statistically reliable and widely understandable way of tracking a sequence of numbers (where you have an x and y axis or similar) is as simple regression analysis, where a single line is constructed that minimizes the total difference between the line and each data point. However, if the data points have some sort of oscillation or cycling, one must instead use entirely different techniques (like Fourier Analysis). In this case, the data have the potential of shifting orientation over time, so for a while the numbers are going up, or going down, or staying flat, then changing, but at a time and in a way you can’t know a priori.

The most accurate way to describe time series data, especially when it is kinda fudgably true that each point is from a different point in time (maybe by averaging all the polls released on a given day) is to make an equation that has one term for each and every point. However, that would be absurd. A lesser and more useful way to describe the data is to use a polynomial equation with just a couple of terms. that allows for the line the equation traces to track changes in direction as long as they aren’t too abrupt.

For this analysis I used a second order polynomial with an extension out in the future of 30 days, just for fun, and with no argument being made by me of the statistical significance of stability of such a line.

What we see here is a remarkably straight line, even though the line is allowed to curve if it wants to, representing Sanders. Look at that line. Flat.

We also see the double drop of Biden, with the second part of that drop much less clear and quite possibly not at all real. And, the two part upward sweep of Warren, with her early move into second/third placesness, and her later move int something challenging first place.

In particular note the small cluster of four red markers for Warren handing out up there with the Biden markers, near the end of the series.

If Warren’s rise to possible first place is real, most of the next half dozen polls, over the next few days, will be up there with these. We’ll see.

Here’s the graph: