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OK, this one’s for you math nerds out there.

On Saturday night, my colleague Nanea Kalani looked at voters’ rejection of Honolulu Hale’s leaders, and said the fates of former Mayor Mufi Hannemann were tied to those of Acting Mayor Kirk Caldwell.

On Sunday, Aloha Vote pollsters told Civil Beat editor John Temple that polling data suggests Hannemann’s negative campaign tactics hurt both candidates.

Do the final — as of this moment, anyway — election results back up those theories? It’s hard to say for sure, as the contents of each ballot are confidential. But at least one metric — a statistical model called a correlation coefficient — supports the Hannemann-Caldwell connection and reveals other interesting relationships as well.

Let’s cut to the chase first, and then we’ll explain what the numbers mean.

Here are the relationships between the three leading gubernatorial candidates and three leading mayoral candidates, sorted from strongest relationship to weakest — regardless of whether it’s a positive or negative one:

Source: Civil Beat analysis

The numbers tell us that while the positive relationship between support for Hannemann and Caldwell was a strong one, it was slightly less strong than the negative relationship between rail proponent Hannemann and the rabid anti-rail Panos Prevedouros. Conversely, Republican gubernatorial nominee James “Duke” Aiona and Prevedouros shared support, while Aiona and Caldwell had a negative mathematical relationship.

Another fun note: There was almost zero mathematical relationship between the areas where the winning gubernatorial candidate, Neil Abercrombie, was successful and where the winning mayoral candidate, Peter Carlisle, was successful. Instead, support for the left-leaning Abercrombie had a strong positive relationship with support for the conservative Prevedouros, meaning the latter tended to do relatively well where the former did.

What is a correlation coefficient, you ask? The Pearson product-moment correlation coefficient is a measure of the linear dependence between two variables and can be determined by using this formula:

Source: Screen capture of

Don’t worry, it’s all Greek to us, too. Luckily, Microsoft Excel has a handy PEARSON function that lets us quickly input two arrays of data — for example, the district-by-district results for a gubernatorial candidate and a mayoral candidate.

The formula’s output is a number somewhere between 1.0 (for perfect correlation, when the data go up and down in tandem) and negative 1.0 (for when they mirror each other perfectly, with one going up when the other goes down). A result of zero means the two sets of data are mathematically independent of each other.

To be clear, the above table only means that where Hannemann performed relatively well, Caldwell was somewhat likely to do the same. Just because the coefficient representing their relationship was .770 does not mean that Caldwell got 77 percent of the votes that Hannemann did, and doesn’t mean the likelihood of Caldwell winning a district was 77 percent if Hannemann won it.

It’s impossible to draw a straight line between candidates in different races. The correlation coefficient is not about causality, and to attribute a causal relationship between two candidates from this data would be a bridge too far.

It’s up to us humans to interpret the data and figure out why things went the way they did. The relationships we’re describing are in no way personal but entirely mathematical, like love between two robots.

Civil Beat used the formula to investigate the relationships between the relative successes and failures of candidates in different races across Hawaii’s 51 House districts. Like you saw above, some of the findings pretty much support conventional thinking, and some are counterintuitive.

Here are the relationships between the leading candidates for governor and lieutenant governor based on their percent take of the ballot in each of their respective parties in all 51 House districts statewide. They’re sorted from strongest relationship to weakest.

Source: Civil Beat analysis

You’ll notice that the Abercrombie and Hannemann coefficients for each LG candidate are essentially mirror images of one another. That’s because every vote for Abercrombie was one taken away from Hannemann, and vice versa, in the Democratic Party primary. The general election tickets of Abercrombie-Brian Schatz and Aiona-Lynn Finnegan scored nearly evenly by this metric.

Here are the relationships between the leading mayoral candidates and prosecutor candidates based on their percent take of votes cast in Oahu’s 35 House districts. They’re sorted from strongest relationship to weakest.

Source: Civil Beat analysis

Not surprisingly, vote percentages for Carlisle and Franklin “Don” Pacarro, Jr. — who worked together in the prosecutor’s office for years before Carlisle resigned to run for mayor — had a positive relationship. But it’s somewhat surprising that Keith Kaneshiro managed to win the race despite the fact that his support had a strong negative relationship with the support for both Carlisle and Prevedouros. Caldwell-friendly districts couldn’t make Caldwell mayor, but they were able to make Kaneshiro prosecutor.

And here are the relationships between the leading gubernatorial and mayoral candidates and voter turnout for each House district.

Source: Civil Beat analysis

Positive numbers mean that higher overall turnout helped a candidate. Negative numbers mean that lower overall turnout helped a candidate. Numbers closer to zero mean it didn’t particularly matter what the turnout was in determining a candidate’s chances of success.

The takeaway: Aiona probably needs a low overall turnout in November if he’s going to become the second consecutive Republican governor.

We don’t claim to have a monopoly on mathematical acumen. (In fact, yours truly — Mike, not Randy — failed Calculus III two different times freshman year of college, foreshadowing an eventual transition from Material Science Engineering to Journalism.) If you see any errors or other trends in the you’d like explored, please let us know.