sat, 29-oct-2016, 21:14
Equinox Marathon Relay leg 2, 2016

Equinox Marathon Relay leg 2, 2016


A couple years ago I compared racing data between two races (Gold Discovery and Equinox, Santa Claus and Equinox) in the same season for all runners that ran in both events. The result was an estimate of how fast I might run the Equinox Marathon based on my times for Gold Discovery and the Santa Claus Half Marathon.

Several years have passed and I've run more races and collected more racing data for all the major Fairbanks races and wanted to run the same analysis for all combinations of races.


The data comes from a database I’ve built of race times for all competitors, mostly coming from the results available from Chronotrack, but including some race results from SportAlaska.

We started by loading the required R packages and reading in all the racing data, a small subset of which looks like this.

race year name finish_time birth_year sex
Beat Beethoven 2015 thomas mcclelland 00:21:49 1995 M
Equinox Marathon 2015 jennifer paniati 06:24:14 1989 F
Equinox Marathon 2014 kris starkey 06:35:55 1972 F
Midnight Sun Run 2014 kathy toohey 01:10:42 1960 F
Midnight Sun Run 2016 steven rast 01:59:41 1960 M
Equinox Marathon 2013 elizabeth smith 09:18:53 1987 F
... ... ... ... ... ...

Next we loaded in the names and distances of the races and combined this with the individual racing data. The data from Chronotrack doesn’t include the mileage and we will need that to calculate pace (minutes per mile).

My database doesn’t have complete information about all the racers that competed, and in some cases the information for a runner in one race conflicts with the information for the same runner in a different race. In order to resolve this, we generated a list of runners, grouped by their name, and threw out racers where their name matches but their gender was reported differently from one race to the next. Please understand we’re not doing this to exclude those who have changed their gender identity along the way, but to eliminate possible bias from data entry mistakes.

Finally, we combined the racers with the individual racing data, substituting our corrected runner information for what appeared in the individual race’s data. We also calculated minutes per mile (pace) and the age of the runner during the year of the race (age). Because we’re assigning a birth year to the minimum reported year from all races, our age variable won’t change during the running season, which is closer to the way age categories are calculated in Europe. Finally, we removed results where pace was greater than 20 minutes per mile for races longer than ten miles, and greater than 16 minute miles for races less than ten miles. These are likely to be outliers, or competitors not running the race.

name birth_year gender race_str year miles minutes pace age
aaron austin 1983 M midnight_sun_run 2014 6.2 50.60 8.16 31
aaron bravo 1999 M midnight_sun_run 2013 6.2 45.26 7.30 14
aaron bravo 1999 M midnight_sun_run 2014 6.2 40.08 6.46 15
aaron bravo 1999 M midnight_sun_run 2015 6.2 36.65 5.91 16
aaron bravo 1999 M midnight_sun_run 2016 6.2 36.31 5.85 17
aaron bravo 1999 M spruce_tree_classic 2014 6.0 42.17 7.03 15
... ... ... ... ... ... ... ... ...

We combined all available results for each runner in all years they participated such that the resulting rows are grouped by runner and year and columns are the races themselves. The values in each cell represent the pace for the runner × year × race combination.

For example, here’s the first six rows for runners that completed Beat Beethoven and the Chena River Run in the years I have data. I also included the column for the Midnight Sun Run in the table, but the actual data has a column for all the major Fairbanks races. You’ll see that two of the six runners listed ran BB and CRR but didn’t run MSR in that year.

name gender age year beat_beethoven chena_river_run midnight_sun_run
aaron schooley M 36 2016 8.19 8.15 8.88
abby fett F 33 2014 10.68 10.34 11.59
abby fett F 35 2016 11.97 12.58 NA
abigail haas F 11 2015 9.34 8.29 NA
abigail haas F 12 2016 8.48 7.90 11.40
aimee hughes F 43 2015 11.32 9.50 10.69
... ... ... ... ... ... ...

With this data, we build a whole series of linear models, one for each race combination. We created a series of formula strings and objects for all the combinations, then executed them using map(). We combined the start and predicted race names with the linear models, and used glance() and tidy() from the broom package to turn the models into statistics and coefficients.

All of the models between races were highly significant, but many of them contain coefficients that aren’t significantly different than zero. That means that including that term (age, gender or first race pace) isn’t adding anything useful to the model. We used the significance of each term to reduce our models so they only contained coefficients that were significant and regenerated the statistics and coefficients for these reduced models.

The full R code appears at the bottom of this post.


Here’s the statistics from the ten best performing models (based on ).

start_race predicted_race n p-value
run_of_the_valkyries golden_heart_trail_run 40 0.956 0
golden_heart_trail_run equinox_marathon 36 0.908 0
santa_claus_half_marathon golden_heart_trail_run 34 0.896 0
midnight_sun_run gold_discovery_run 139 0.887 0
beat_beethoven golden_heart_trail_run 32 0.886 0
run_of_the_valkyries gold_discovery_run 44 0.877 0
midnight_sun_run golden_heart_trail_run 52 0.877 0
gold_discovery_run santa_claus_half_marathon 111 0.876 0
chena_river_run golden_heart_trail_run 44 0.873 0
run_of_the_valkyries santa_claus_half_marathon 91 0.851 0

It’s interesting how many times the Golden Heart Trail Run appears on this list since that run is something of an outlier in the Usibelli running series because it’s the only race entirely on trails. Maybe it’s because it’s distance (5K) is comparable with a lot of the earlier races in the season, but because it’s on trails it matches well with the later races that are at least partially on trails like Gold Discovery or Equinox.

Here are the ten worst models.

start_race predicted_race n p-value
midnight_sun_run equinox_marathon 431 0.525 0
beat_beethoven hoodoo_half_marathon 87 0.533 0
beat_beethoven midnight_sun_run 818 0.570 0
chena_river_run equinox_marathon 196 0.572 0
equinox_marathon hoodoo_half_marathon 90 0.584 0
beat_beethoven equinox_marathon 265 0.585 0
gold_discovery_run hoodoo_half_marathon 41 0.599 0
beat_beethoven santa_claus_half_marathon 163 0.612 0
run_of_the_valkyries equinox_marathon 125 0.642 0
midnight_sun_run hoodoo_half_marathon 118 0.657 0

Most of these models are shorter races like Beat Beethoven or the Chena River Run predicting longer races like Equinox or one of the half marathons. Even so, each model explains more than half the variation in the data, which isn’t terrible.


Now that we have all our models and their coefficients, we used these models to make predictions of future performance. I’ve written an online calculator based on the reduced models that let you predict your race results as you go through the running season. The calculator is here: Fairbanks Running Race Converter.

For example, I ran a 7:41 pace for Run of the Valkyries this year. Entering that, plus my age and gender into the converter predicts an 8:57 pace for the first running of the HooDoo Half Marathon. The for this model was a respectable 0.71 even though only 23 runners ran both races this year (including me). My actual pace for HooDoo was 8:18, so I came in quite a bit faster than this. No wonder my knee and hip hurt after the race! Using my time from the Golden Heart Trail Run, the converter predicts a HooDoo Half pace of 8:16.2, less than a minute off my 1:48:11 finish.

Appendix: R code


races_db <- src_postgres(host="localhost", dbname="races")

combined_races <- tbl(races_db, build_sql(
    "SELECT race, year, lower(name) AS name, finish_time,
        year - age AS birth_year, sex
     FROM chronotrack
     SELECT race, year, lower(name) AS name, finish_time,
        CASE WHEN age_class ~ 'M' THEN 'M' ELSE 'F' END AS sex
     FROM sportalaska
     SELECT race, year, lower(name) AS name, finish_time,
        NULL AS birth_year, NULL AS sex
     FROM other"))

races <- tbl(races_db, build_sql(
    "SELECT race,
        lower(regexp_replace(race, '[ ’]', '_', 'g')) AS race_str,
        date_part('year', date) AS year,
     FROM races"))

racing_data <- combined_races %>%
    inner_join(races) %>%

racers <- racing_data %>%
    group_by(name) %>%
                                   FALSE, TRUE),
                            'M', 'F')) %>%
    ungroup() %>%
    filter(gender_filter) %>%

racing_data_filled <- racing_data %>%
    inner_join(racers, by="name") %>%
    mutate(birth_year=birth_year.y) %>%
    select(name, birth_year, gender, race_str, year, miles, finish_time) %>%
    group_by(name, race_str, year) %>%
    mutate(n=n()) %>%
    filter(!, n==1) %>%
    ungroup() %>%
    collect() %>%
    mutate(fixed=ifelse(grepl('[0-9]+:[0-9]+:[0-9.]+', finish_time),
                        paste0('00:', finish_time)),
           group=paste0(gender, age_class),
           gender=as.factor(gender)) %>%
    filter((miles<10 & pace<16) | (miles>=10 & pace<20)) %>%
    select(-fixed, -finish_time, -n)

speeds_combined <- racing_data_filled %>%
    select(name, gender, age, age_class, group, race_str, year, pace) %>%
    spread(race_str, pace)

main_races <- c('beat_beethoven', 'chena_river_run', 'midnight_sun_run',
                'run_of_the_valkyries', 'gold_discovery_run',
                'santa_claus_half_marathon', 'golden_heart_trail_run',
                'equinox_marathon', 'hoodoo_half_marathon')

race_formula_str <-
    lapply(seq(1, length(main_races)-1),
               lapply(seq(i+1, length(main_races)),
                      function(j) paste(main_races[[j]], '~',
                                        '+ gender', '+ age'))) %>%

race_formulas <- lapply(race_formula_str, function(i) as.formula(i)) %>%

lm_models <- map(race_formulas, ~ lm(.x, data=speeds_combined))

models <- tibble(start_race=factor(gsub('.* ~ ([^ ]+).*',
                 predicted_race=factor(gsub('([^ ]+).*',
                 lm_models=lm_models) %>%
    arrange(start_race, predicted_race)

model_stats <- glance(models %>% rowwise(), lm_models)
model_coefficients <- tidy(models %>% rowwise(), lm_models)

reduced_formula_str <- model_coefficients %>%
    ungroup() %>%
    filter(p.value<0.05, term!='(Intercept)') %>%
    mutate(term=gsub('genderM', 'gender', term)) %>%
    group_by(predicted_race, start_race) %>%
    summarize(independent_vars=paste(term, collapse=" + ")) %>%
    ungroup() %>%
    transmute(reduced_formulas=paste(predicted_race, independent_vars, sep=' ~ '))

reduced_formula_str <- reduced_formula_str$reduced_formulas

reduced_race_formulas <- lapply(reduced_formula_str,
                                function(i) as.formula(i)) %>% unlist()

reduced_lm_models <- map(reduced_race_formulas, ~ lm(.x, data=speeds_combined))

n_from_lm <- function(model) {
    summary_object <- summary(model)

    summary_object$df[1] + summary_object$df[2]

reduced_models <- tibble(start_race=factor(gsub('.* ~ ([^ ]+).*', '\\1', reduced_formula_str),
                         predicted_race=factor(gsub('([^ ]+).*', '\\1', reduced_formula_str),
                         lm_models=reduced_lm_models) %>%
    arrange(start_race, predicted_race) %>%
    rowwise() %>%

reduced_model_stats <- glance(reduced_models %>% rowwise(), lm_models)
reduced_model_coefficients <- tidy(reduced_models %>% rowwise(), lm_models) %>%

coefficients_and_stats <- reduced_model_stats %>%
               by=c("start_race", "predicted_race", "n")) %>%
    select(start_race, predicted_race, n, r.squared, term, estimate)


make_scatterplot <- function(start_race, predicted_race) {
   age_limits <- speeds_combined %>%
      filter_(paste("!", start_race, ")"),
               paste("!", predicted_race, ")")) %>%
      summarize(min=min(age), max=max(age)) %>%

   q <- ggplot(data=speeds_combined,
               aes_string(x=start_race, y=predicted_race)) +
            # plasma works better with a grey background
            # theme_bw() +
            geom_abline(slope=1, color="darkred", alpha=0.5) +
            geom_smooth(method="lm", se=FALSE) +
            geom_point(aes(shape=gender, color=age)) +
                              limits=age_limits) +
            scale_x_continuous(breaks=pretty_breaks(n=10)) +

   svg_filename <- paste0(paste(start_race, predicted_race, sep="-"), ".svg")

   height <- 9
   width <- 16
   resize <- 0.75

   svg(svg_filename, height=height*resize, width=width*resize)

lapply(seq(1, length(main_races)-1),
            lapply(seq(i+1, length(main_races)),
                        make_scatterplot(main_races[[i]], main_races[[j]])
tue, 13-sep-2016, 18:31


Andrea and I are running the Equinox Marathon relay this Saturday with Norwegian dog musher Halvor Hoveid. He’s running the first leg, I’m running the second, and Andrea finishes the race. I ran the second leg as a training run a couple weeks ago and feel good about my physical conditioning, but the weather is always a concern this late in the fall, especially up on top of Ester Dome, where it can be dramatically different than the valley floor where the race starts and ends.

Andrea ran the full marathon in 2009—2012 and the relay in 2008 and 2013—2015. I ran the full marathon in 2013. There was snow on the trail when I ran it, making the out and back section slippery and treacherous, and the cold temperatures at the start meant my feet were frozen until I got off of the single-track, nine or ten miles into the course. In other years, rain turned the powerline section to sloppy mud, or cold temperatures and freezing rain up on the Dome made it unpleasant for runners and supporters.

In this post we will examine the available weather data, looking at the range of conditions we could experience this weekend. The current forecast from the National Weather Service is calling for mostly cloudy skies with highs in the 50s. Low temperatures the night before are predicted to be in the 40s, with rain in the forecast between now and then.


There is no long term climate data for Ester Dome, but there are several valley-level stations with data going back to the start of the race in 1963. The best data comes from the Fairbanks Airport station and includes daily temperature, precipitation, and snowfall for all years, and wind speed and direction since 1984. I also looked at the data from the College Observatory station (FAOA2) behind the GI on campus and the University Experimental Farm, also on campus, but neither of these stations have a complete record. The daily data is part of the Global Historical Climatology Network - Daily dataset.

I also have hourly data from 2008—2013 for both the Fairbanks Airport and a station located on Ester Dome that is no longer operational. We’ll use this to get a sense of what the possible temperatures on Ester Dome might have been based on the Fairbanks Airport data. Hourly data comes from the Meterological Assimilation Data Ingest System (MADIS).

The R code used for this post appears at the bottom, and all the data used is available from here.


Ester Dome temperatures

Since there isn’t a long-running weather station on Ester Dome (at least not one that’s publicly available), we’ll use the September data from an hourly Ester Dome station that was operational until 2014. If we join the Fairbanks Airport station data with this data wherever the observations are within 30 minutes of each other, we can see the relationship between Ester Dome temperature and temperature at the Fairbanks Airport.

Here’s what that relationship looks like, including a linear regression line between the two. The shaded area in the lower left corner shows the region where the temperatures on Ester Dome are below freezing.

Ester Dome and Fairbanks Airport temperatures

And the regression:

## Call:
## lm(formula = ester_dome_temp_f ~ pafa_temp_f, data = pafa_fbsa)
## Residuals:
##    Min     1Q Median     3Q    Max
## -9.649 -3.618 -1.224  2.486 22.138
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.69737    0.77993  -3.458 0.000572 ***
## pafa_temp_f  0.94268    0.01696  55.567  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 5.048 on 803 degrees of freedom
## Multiple R-squared:  0.7936, Adjusted R-squared:  0.7934
## F-statistic:  3088 on 1 and 803 DF,  p-value: < 2.2e-16

The regression model is highly significant, as are both coefficients, and the relationship explains almost 80% of the variation in the data. According to the model, in the month of September, Ester Dome average temperature is almost three degrees colder than at the airport. And whenever temperature at the airport drops below 37 degrees, it’s probably below freezing on the Dome.

Race day weather

Temperatures at the airport on race day ranged from 19.9 °F in 1972 to 68 °F in 1969, and the range of average temperatures is 34.2 and 53 °F. Using our model of Ester Dome temperatures, we get an average range of 29.5 and 47 °F and an overall min / max of 16.1 / 61.4 °F. Generally speaking, in most years it will be below freezing on Ester Dome, but possibly before most of the runners get up there.

Precipitation (rain, sleet, or snow) has fallen on 15 out of 53 race days, or 28% of the time, and measurable snowfall has been recorded on four of those fifteen. The highest amount fell in 2014 with 0.36 inches of liquid precipitation (no snow was recorded and the temperatures were between 45 and 51 °F so it was almost certainly all rain, even on Ester Dome). More than a quarter of an inch of precipitation fell in three of the fifteen years (1990, 1992, and 2014), but most rainfall totals are much smaller.

Measurable snow fell at the airport in four years, or seven percent of the time: 4.1 inches in 1993, 2.1 inches in 1985, 1.2 inches in 1996 and 0.4 inches in 1992. But that’s at the airport station. Four of the 15 years where measurable precipitation fell at the airport, but no snow fell, had possible minimum temperatures on Ester Dome that were below freezing. It’s likely that some of the precipitation recorded at the airport in those years was coming down as snow up on Ester Dome. If so, that means snow may have fallen on eight race days, bringing the percentage up to fifteen percent.

Wind data from the airport has only been recorded since 1984, but from those years the average wind speed at the airport on race day is 4.9 miles per hour. Peak 2-minute winds during Equinox race day was 21 miles per hour in 2003. Unfortunately, no wind data is available for Ester Dome, but it’s likely to be higher than what is recorded at the airport. We do have wind speed data from the hourly Ester Dome station from 2008 through 2013, but the linear relationship between Ester Dome winds and winds at the Fairbanks airport only explain about a quarter of the variation in the data, and a look at the plot doesn’t give me much confidence in the relationship shown (see below).

Ester Dome and Fairbanks Airport wind speeds

Weather from the week prior

It’s also useful to look at the weather from the week before the race, since excessive pre-race rain or snow can make conditions on race day very different, even if the race day weather is pleasant. The year I ran the full marathon (2013), it had snowed the week before and much of the trail in the woods before the water stop near Henderson and all of the out and back were covered in snow.

The most dramatic example of this was 1992 where 23 inches of snow fell at the airport in the week prior to the race, with much higher totals up on the summit of Ester Dome. Measurable snow has been recorded at the airport in the week prior to six races, but all the weekly totals are under an inch except for the snow year of 1992.

Precipitation has fallen in 42 of 53 pre-race weeks (79% of the time). Three years have had more than an inch of precipitation prior to the race: 1.49 inches in 2015, 1.26 inches in 1992 (which fell as snow), and 1.05 inches in 2007. On average, just over two tenths of an inch of precipitation falls in the week before the race.


The following stacked plots shows the weather for all 53 runnings of the Equinox marathon. The top panel shows the range of temperatures on race day from the airport station (wide bars) and estimated on Ester Dome (thin lines below bars). The shaded area at the bottom shows where temperatures are below freezing. Dashed orange horizonal lines represent the average high and low temperature at the airport on race day; solid orange horizonal lines indicate estimated average high and low temperature on Ester Dome.

The middle panel shows race day liquid precipitation (rain, melted snow). Bars marked with an asterisk indicate years where snow was also recorded at the airport, but remember that four of the other years with liquid precipitation probably experienced snow on Ester Dome (1977, 1986, 1991, and 1994) because the temperatures were likely to be below freezing at elevation.

The bottom panel shows precipitation totals from the week prior to the race. Bars marked with an asterisk indicate weeks where snow was also recorded at the airport.

Equinox Marathon Weather

Here’s a table with most of the data from the analysis. Record values for each variable are in bold.

  Fairbanks Airport Station Ester Dome (estimated)
  Race Day Previous Week Race Day
Date min t max t wind prcp snow prcp snow min t max t
1963‑09‑21 32.0 54.0   0.00 0.0 0.01 0.0 27.5 48.2
1964‑09‑19 34.0 57.9   0.00 0.0 0.03 0.0 29.4 51.9
1965‑09‑25 37.9 60.1   0.00 0.0 0.80 0.0 33.0 54.0
1966‑09‑24 36.0 62.1   0.00 0.0 0.01 0.0 31.2 55.8
1967‑09‑23 35.1 57.9   0.00 0.0 0.00 0.0 30.4 51.9
1968‑09‑21 23.0 44.1   0.00 0.0 0.04 0.0 19.0 38.9
1969‑09‑20 35.1 68.0   0.00 0.0 0.00 0.0 30.4 61.4
1970‑09‑19 24.1 39.9   0.00 0.0 0.42 0.0 20.0 34.9
1971‑09‑18 35.1 55.9   0.00 0.0 0.14 0.0 30.4 50.0
1972‑09‑23 19.9 42.1   0.00 0.0 0.01 0.2 16.1 38.0
1973‑09‑22 30.0 44.1   0.00 0.0 0.05 0.0 25.6 38.9
1974‑09‑21 48.0 60.1   0.08 0.0 0.00 0.0 42.6 54.0
1975‑09‑20 37.9 55.9   0.02 0.0 0.02 0.0 33.0 50.0
1976‑09‑18 34.0 59.0   0.00 0.0 0.54 0.0 29.4 52.9
1977‑09‑24 36.0 48.9   0.06 0.0 0.20 0.0 31.2 43.4
1978‑09‑23 30.0 42.1   0.00 0.0 0.10 0.3 25.6 37.0
1979‑09‑22 35.1 62.1   0.00 0.0 0.17 0.0 30.4 55.8
1980‑09‑20 30.9 43.0   0.00 0.0 0.35 0.0 26.4 37.8
1981‑09‑19 37.0 43.0   0.15 0.0 0.04 0.0 32.2 37.8
1982‑09‑18 42.1 61.0   0.02 0.0 0.22 0.0 37.0 54.8
1983‑09‑17 39.9 46.9   0.00 0.0 0.05 0.0 34.9 41.5
1984‑09‑22 28.9 60.1 5.8 0.00 0.0 0.08 0.0 24.5 54.0
1985‑09‑21 30.9 42.1 6.5 0.14 2.1 0.57 0.0 26.4 37.0
1986‑09‑20 36.0 52.0 8.3 0.07 0.0 0.21 0.0 31.2 46.3
1987‑09‑19 37.9 61.0 6.3 0.00 0.0 0.00 0.0 33.0 54.8
1988‑09‑24 37.0 45.0 4.0 0.00 0.0 0.11 0.0 32.2 39.7
1989‑09‑23 36.0 61.0 8.5 0.00 0.0 0.07 0.5 31.2 54.8
1990‑09‑22 37.9 50.0 7.8 0.26 0.0 0.00 0.0 33.0 44.4
1991‑09‑21 36.0 57.0 4.5 0.04 0.0 0.03 0.0 31.2 51.0
1992‑09‑19 24.1 33.1 6.7 0.01 0.4 1.26 23.0 20.0 28.5
1993‑09‑18 28.0 37.0 4.9 0.29 4.1 0.37 0.3 23.7 32.2
1994‑09‑24 27.0 51.1 6.0 0.02 0.0 0.08 0.0 22.8 45.5
1995‑09‑23 43.0 66.9 4.0 0.00 0.0 0.00 0.0 37.8 60.4
1996‑09‑21 28.9 37.9 6.9 0.06 1.2 0.26 0.0 24.5 33.0
1997‑09‑20 27.0 55.0 3.8 0.00 0.0 0.03 0.0 22.8 49.2
1998‑09‑19 42.1 60.1 4.9 0.00 0.0 0.37 0.0 37.0 54.0
1999‑09‑18 39.0 64.9 3.8 0.00 0.0 0.26 0.0 34.1 58.5
2000‑09‑16 28.9 50.0 5.6 0.00 0.0 0.30 0.0 24.5 44.4
2001‑09‑22 33.1 57.0 1.6 0.00 0.0 0.00 0.0 28.5 51.0
2002‑09‑21 33.1 48.9 3.8 0.00 0.0 0.03 0.0 28.5 43.4
2003‑09‑20 26.1 46.0 9.6 0.00 0.0 0.00 0.0 21.9 40.7
2004‑09‑18 26.1 48.0 4.3 0.00 0.0 0.25 0.0 21.9 42.6
2005‑09‑17 37.0 63.0 0.9 0.00 0.0 0.09 0.0 32.2 56.7
2006‑09‑16 46.0 64.0 4.3 0.00 0.0 0.00 0.0 40.7 57.6
2007‑09‑22 25.0 45.0 4.7 0.00 0.0 1.05 0.0 20.9 39.7
2008‑09‑20 34.0 51.1 4.5 0.00 0.0 0.08 0.0 29.4 45.5
2009‑09‑19 39.0 50.0 5.8 0.00 0.0 0.25 0.0 34.1 44.4
2010‑09‑18 35.1 64.9 2.5 0.00 0.0 0.00 0.0 30.4 58.5
2011‑09‑17 39.9 57.9 1.3 0.00 0.0 0.44 0.0 34.9 51.9
2012‑09‑22 46.9 66.9 6.0 0.00 0.0 0.33 0.0 41.5 60.4
2013‑09‑21 24.3 44.1 5.1 0.00 0.0 0.13 0.6 20.2 38.9
2014‑09‑20 45.0 51.1 1.6 0.36 0.0 0.00 0.0 39.7 45.5
2015‑09‑19 37.9 44.1 2.9 0.01 0.0 1.49 0.0 33.0 38.9


The weather for the 2016 race was just about perfect with temperatures ranging from 34 to 58 °F and no precipitation during the race. The airport did record 0.01 inches for the day, but this fell in the evening, after the race had finished.

Appendix: R code


 race_dates <- read_fwf("equinox_marathon_dates.rst", skip=5, n_max=54,
                        fwf_positions(c(4, 6), c(9, 19), c("number", "race_date")))

 noaa <- src_postgres(host="localhost", dbname="noaa")
 # pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
 #                               WHERE station_name = 'UNIVERSITY EXP STN'"))
 # pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
 #                               WHERE station_name = 'COLLEGE OBSY'"))
 pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
                               WHERE station_name = 'FAIRBANKS INTL AP'"))

 race_day_wx <- pivot %>%
     inner_join(race_dates, by=c("dte"="race_date"), copy=TRUE) %>%
     collect() %>%
     mutate(tmin_f=round((tmin_c*9/5.0)+32, 1), tmax_f=round((tmax_c*9/5.0)+32, 1),
            prcp_in=round(prcp_mm/25.4, 2),
            snow_in=round(snow_mm/25.4, 1), snwd_in=round(snow_mm/25.4, 1),
            awnd_mph=round(awnd_mps*2.2369, 1),
            wsf2_mph=round(wsf2_mps*2.2369), 1) %>%
     select(number, race_date, tmin_f, tmax_f, prcp_in, snow_in,
            snwd_in, awnd_mph, wsf2_mph)

 week_before_race_day_wx <- pivot %>%
     mutate(year=date_part("year", dte)) %>%
     inner_join(race_dates %>%
                copy=TRUE) %>%
     collect() %>%
     mutate(tmin_f=round((tmin_c*9/5.0)+32, 1), tmax_f=round((tmax_c*9/5.0)+32, 1),
            prcp_in=round(prcp_mm/25.4, 2),
            snow_in=round(snow_mm/25.4, 1), snwd_in=round(snow_mm/25.4, 1),
            awnd_mph=round(awnd_mps*2.2369, 1), wsf2_mph=round(wsf2_mps*2.2369, 1)) %>%
     select(number, year, race_date, dte, prcp_in, snow_in) %>%
     mutate(week_before=race_date-days(7)) %>%
     filter(dte<race_date, dte>=week_before) %>%
     group_by(number, year, race_date) %>%

 all_wx <- race_day_wx %>%
     inner_join(week_before_race_day_wx) %>%
            snow_label=ifelse(snow_in>0, '*', NA),
            pweek_snow_label=ifelse(pweek_snow_in>0, '*', NA)) %>%
     select(number, year, race_date, tmin_f, tmax_f, tavg_f,
            prcp_in, snow_in, snwd_in, awnd_mph, wsf2_mph,
            pweek_prcp_in, pweek_snow_in,
            snow_label, pweek_snow_label);

 write_csv(all_wx, "all_wx.csv")

 madis <- src_postgres(host="localhost", dbname="madis")

 pafa_fbsa <- tbl(madis,
   WITH pafa AS (
     SELECT dt_local, temp_f, wspd_mph
     FROM observations
     WHERE station_id = 'PAFA' AND date_part('month', dt_local) = 9),
   fbsa AS (
     SELECT dt_local, temp_f, wspd_mph
     FROM observations
     WHERE station_id = 'FBSA2' AND date_part('month', dt_local) = 9)
   SELECT pafa.dt_local, pafa.temp_f AS pafa_temp_f, pafa.wspd_mph as pafa_wspd_mph,
     fbsa.temp_f AS ester_dome_temp_f, fbsa.wspd_mph as ester_dome_wspd_mph
   FROM pafa
     INNER JOIN fbsa ON
       pafa.dt_local BETWEEN fbsa.dt_local - interval '15 minutes'
         AND fbsa.dt_local + interval '15 minutes'")) %>% collect()

 write_csv(pafa_fbsa, "pafa_fbsa.csv")

 ester_dome_temps <- lm(data=pafa_fbsa,
                        ester_dome_temp_f ~ pafa_temp_f)

 # Model and coefficients are significant, r2 = 0.794
 # intercept = -2.69737, slope = 0.94268

 all_wx_with_ed <- all_wx %>%
                              tmin_f*ester_dome_temps$coefficients[2], 1),
                              tmax_f*ester_dome_temps$coefficients[2], 1))

 make_gt <- function(outside, instruments, chamber, width, heights) {
     gt1 <- ggplot_gtable(ggplot_build(outside))
     gt2 <- ggplot_gtable(ggplot_build(instruments))
     gt3 <- ggplot_gtable(ggplot_build(chamber))
     max_width <- unit.pmax(gt1$widths[2:3], gt2$widths[2:3], gt3$widths[2:3])
     gt1$widths[2:3] <- max_width
     gt2$widths[2:3] <- max_width
     gt3$widths[2:3] <- max_width
     gt <- gtable(widths = unit(c(width), "in"), heights = unit(heights, "in"))
     gt <- gtable_add_grob(gt, gt1, 1, 1)
     gt <- gtable_add_grob(gt, gt2, 2, 1)
     gt <- gtable_add_grob(gt, gt3, 3, 1)


temps <- ggplot(data=all_wx_with_ed, aes(x=year, ymin=tmin_f, ymax=tmax_f, y=tavg_f)) +
   # geom_abline(intercept=32, slope=0, color="blue", alpha=0.25) +
   geom_rect(data=all_wx_with_ed %>% head(n=1),
            aes(xmin=-Inf, xmax=Inf, ymin=-Inf, ymax=32),
            fill="darkcyan", alpha=0.25) +
               color="darkorange", alpha=0.50, linetype=2) +
               color="darkorange", alpha=0.50, linetype=2) +
               color="darkorange", alpha=0.50, linetype=1) +
               color="darkorange", alpha=0.50, linetype=1) +
   geom_linerange(aes(ymin=ed_min_temp_f, ymax=ed_max_temp_f)) +
   # geom_smooth(method="lm", se=FALSE) +
   geom_linerange(size=3, color="grey30") +
   scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015, 2)) +
   scale_y_continuous(name="Temperature (deg F)", breaks=pretty_breaks(n=10)) +
   theme_bw() +
   theme(plot.margin=unit(c(1, 1, 0, 0.5), 'lines')) +  # t, r, b, l
   theme(axis.text.x=element_blank(), axis.title.x=element_blank(),
         axis.ticks.x=element_blank(), panel.grid.minor.x=element_blank()) +
   ggtitle("Weather during and in the week prior to the Equinox Marathon
            Fairbanks Airport Station")

 prcp <- ggplot(data=all_wx, aes(x=year, y=prcp_in)) +
     geom_bar(stat="identity") +
     geom_text(aes(y=prcp_in+0.025, label=snow_label)) +
     scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015)) +
     scale_y_continuous(name="Precipitation (inches)", breaks=pretty_breaks(n=5)) +
     theme_bw() +
     theme(plot.margin=unit(c(0, 1, 0, 0.5), 'lines')) +  # t, r, b, l
     theme(axis.text.x=element_blank(), axis.title.x=element_blank(),
           axis.ticks.x=element_blank(), panel.grid.minor.x=element_blank())

 pweek_prcp <- ggplot(data=all_wx, aes(x=year, y=pweek_prcp_in)) +
     geom_bar(stat="identity") +
     geom_text(aes(y=pweek_prcp_in+0.1, label=pweek_snow_label)) +
     scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015)) +
     scale_y_continuous(name="Pre-week precip (inches)", breaks=pretty_breaks(n=5)) +
     theme_bw() +
     theme(plot.margin=unit(c(0, 1, 0.5, 0.5), 'lines'),
           axis.text.x=element_text(angle=45, hjust=1, vjust=1),

 rescale <- 0.75
 full_plot <- make_gt(temps, prcp, pweek_prcp,
                      c(7.5*rescale, 2.5*rescale, 3.0*rescale))
 pdf("equinox_weather_grid.pdf", height=13*rescale, width=16*rescale)

 fai_ed_temps <- ggplot(data=pafa_fbsa, aes(x=pafa_temp_f, y=ester_dome_temp_f)) +
   geom_rect(data=pafa_fbsa %>% head(n=1),
               aes(xmin=-Inf, ymin=-Inf, xmax=(32+2.69737)/0.94268, ymax=32),
               color="black", fill="darkcyan", alpha=0.25) +
   geom_point(position=position_jitter()) +
   geom_smooth(method="lm", se=FALSE) +
   scale_x_continuous(name="Fairbanks Airport Temperature (degrees F)") +
   scale_y_continuous(name="Ester Dome Temperature (degrees F)") +
   theme_bw() +
   ggtitle("Relationship between Fairbanks Airport and Ester Dome Temperatures
           September, 2008-2013")

 pdf("pafa_fbsa_sept_temps.pdf", height=10.5, width=10.5)

 fai_ed_wspds <- ggplot(data=pafa_fbsa, aes(x=pafa_wspd_mph, y=ester_dome_wspd_mph)) +
   geom_point(position=position_jitter()) +
   geom_smooth(method="lm", se=FALSE) +
   scale_x_continuous(name="Fairbanks Airport Wind Speed (MPH)") +
   scale_y_continuous(name="Ester Dome Wind (MPH)") +
   theme_bw() +
   ggtitle("Relationship between Fairbanks Airport and Ester Dome Wind Speeds
           September, 2008-2013")

 pdf("pafa_fbsa_sept_wspds.pdf", height=10.5, width=10.5)
tue, 07-jan-2014, 15:27
Equinox Marathon finish

Equinox Marathon finish

It’s the beginning of a new year and time for me to look back at what I learned last year. Rather than a long narrative, let’s focus on the data. The local newspaper did a “community profile” of me this year and it was focused on my curiosity about the world around us and how we can measure and analyze it to better understand our lives. This post is a brief summary of that sort of analysis for my small corner of the world in the year that was 2013.


2013 was the year I decided to, and did, run the Equinox Marathon, so I spent a lot of time running this year and a lot less time bicycling. Since the race, I’ve been having hip problems that have kept me from skiing or running much at all. The roads aren’t cleared well enough to bicycle on them in the winter so I got a fat bike to commute on the trails I’d normally ski.

Here are my totals in tabular form:

2013 Exercise Totals
type miles hours calories
Running 529 89 61,831
Bicycling 1,018 82 54,677
Skiing 475 81 49,815
Hiking 90 43 18,208
TOTAL 2,113 296 184,531

I spent just about the same amount of time running, bicycling and skiing this year, and much less time hiking around on the trails than in the past. Because of all the running, and my hip injury, I didn’t manage to commute to work with non-motorized transport quite as much this year (55% of work days instead of 63% in 2012), but the exercise totals are all higher.

One new addition this year is a heart rate monitor, which allows me to much more accurately estimate energy consumption than formulas based on the type of activity, speed, and time. Riding my fat bike, it’s pretty clear that this form of travel is so much less efficient than a road bike with smooth tires that it can barely be called “bicycling,” at least in terms of how much energy it takes to travel over a certain distance.

Here’s the equations from Keytel LR, Goedecke JH, Noakes TD, Hiiloskorpi H, Laukkanen R, van der Merwe L, Lambert EV. 2005. Prediction of energy expenditure from heart rate monitoring during submaximal exercise. J Sports Sci. 23(3):289-97.

Male : ( − 55.0969 + (0.6309hr) + (0.0901w) + (0.2017a))/(4.184)60t
Female : ( − 20.4022 + (0.4472hr) − (0.0901w) + (0.074a))/(4.184)60t


  • hr = Heart rate (in beats/minute)
  • w = Weight (in pounds)
  • a = Age (in years)
  • t = Exercise duration time (in hours)

And a SQL function that implements the version for men (to use it, you’d replace the nnn and yyyy-mm-dd with the appropriate values for you):

--- Kcalories burned based on average heart rate and number
--- of hours at that rate.
CREATE OR REPLACE FUNCTION kcal_from_hr(hr numeric, hours numeric)
RETURNS numeric
LANGUAGE plpgsql
AS $$
    weight_lb numeric := nnn;
    resting_hr numeric := nn;
    birthday date := 'yyyy-mm-dd';
    resting_kcal numeric;
    exercise_kcal numeric;
    resting_kcal := ((-55.0969+(0.6309*(resting_hr))+
                    (0.2017*(extract(epoch from now()-birthday)/
    exercise_kcal := ((-55.0969+(0.6309*(hr))+
                     (0.2017*(extract(epoch from now()-birthday)/
    RETURN exercise_kcal - resting_kcal;

Here’s a graphical comparison of my exercise data over the past four years:

It was a pretty remarkable year, although the drop in exercise this fall is disappointing.

Another way to visualize the 2013 data is in the form of a heatmap, where each block represents a day on the calendar, and the color is how many calories I burned on that day. During the summer you can see my long runs on the weekends showing up in red. Equinox was on September 21st, the last deep red day of the year.


2013 was quite remarkable for the number of days where the daily temperature was dramatically different from the 30-year average. The heatmap below shows each day in 2013, and the color indicates how many standard deviations that day’s temperature was from the 30-year average. To put the numbers in perspective, approximately 95.5% of all observations will fall within two standard deviations from the mean, and 99.7% will be within three standard deviations. So the very dark red or dark blue squares on the plot below indicate temperature anomalies that happen less than 1% of the time. Of course, in a full year, you’d expect to see a few of these remarkable differences, but 2013 had a lot of remarkable differences.

2013 saw 45 days where the temperature was more than 2 standard deviations from the mean (19 that were colder than normal and 26 that were warmer), something that should only happen 16 days out of a normal year [ 365.25(1 − 0.9545) ]. There were four days ouside of 3 standard deviations from the mean anomaly. Normally there’d only be a single day [ 365.25(1 − 0.9973) ] with such a remarkably cold or warm temperature.

April and most of May were remarkably cold, resulting in many people skiing long past what is normal in Fairbanks. On May first, Fairbanks still had 17 inches of snow on the ground. Late May, almost all of June and the month of October were abnormally warm, including what may be the warmest week on record in Alaska from June 23rd to the 29th. Although it wasn’t exceptional, you can see the brief cold snap preceding and including the Equinox Marathon on September 21st this year. The result was bitter cold temperatures on race day (my hands and feet didn’t get warm until I was climbing Ester Dome Road an hour into the race), as well as an inch or two of snow on most of the trail sections of the course above 1,000 feet.

Most memorable was the ice and wind storm on November 13th and 14th that dumped several inches of snow and instantly freezing rain, followed by record high winds that knocked power out for 14,000 residents of the area, and then a drop in temperatures to colder than ‒20°F. My office didn’t get power restored for four days.


I’m moving more and more of my work into git, which is a distributed revision control system (or put another way, it’s a system that stores stuff and keeps track of all the changes). Because it’s distributed, anything I have on my computer at home can be easily replicated to my computer at work or anywhere else, and any changes that I make to these files on any system, are easy to recover anywhere else. And it’s all backed up on the master repository, and all changes are recorded. If I decide I’ve made a mistake, it’s easy to go back to an earlier version.

Using this sort of system for software code is pretty common, but I’m also using this for normal text files (the docs repository below), and have starting moving other things into git such as all my eBooks.

The following figure shows the number of file changes made in three of my repositories over the course of the year. I don’t know why April was such an active month for Python, but I clearly did a lot of programming that month. The large number of file changes during the summer in the docs repository is because I was keeping my running (and physical therapy) logs in that repository.

Dog Barn

The dog barn was the big summer project. It’s a seven by eleven foot building with large dog boxes inside that we keep warm. When the temperatures are too cold for the dogs to stay outside, we put them into their boxes in the dog barn and turn the heat up to 40°F. I have a real-time visualization of the conditions inside and outside the barn, and because the whole thing is run with a small Linux computer and Arduino board, I’m able to collect a lot of data about how the barn is performing.

One such analysis will be to see how much heat the dogs produce when they are in the barn. To estimate that, we need a baseline of how much heat we’re adding at various temperatures in order to keep it at temperature. I haven’t collected enough cold temperature data to really see what the relationship looks like, but here’s the pattern so far.

The graph shows the relationship between the temperature differential between the outside and inside of the barn plotted against the percentage of time the heater is on in order to maintain that differential, for all 12-hour periods where the dogs weren’t in the barn and there’s less than four missing observations. I’ve also run a linear and quadratic regression in order to predict how much heat will be required at various temperature differentials.

The two r2 values shows how much of the variation in heating is explained by the temperature differential for the linear and the quadratic regressions. I know that this isn’t a linear relationship, but that model still fits the data better than the quadratic model does. It may be that it’s some other form of non-linear relationship that’s not well expressed by a second order polynomial.

Once we can predict how much heat it should take to keep the barn warm at a particular temperature differential, we can see how much less heat we’re using when the dogs are in the barn. One complication is that the dogs produce enough moisture when they are in the barn that we need to ventilate it when they are in there. So in addition to the additive heating from the dogs themselves, there will be increased heat losses because we have to keep it better ventilated.

It’ll be an interesting data set.


Power consumption is a concern now that we’ve set up the dog barn and are keeping it heated with an electric heater. It’s an oil-filled radiator-style heater, and uses around 1,100 Watts when it’s on.

This table shows our overall usage by year for the period we have data.

Yearly electricity use
year average watts total KWH
2010 551 4822
2011 493 4318
2012 433 3792
2013 418 3661

Our overall energy use continues to go down, which is a little surprising to me, actually, since we eliminated most of the devices known to use a lot electricity (incandescent light bulbs, halogen floodlights) years ago. Despite that, and bringing the dog barn on line in late November, we used less electricity in 2013 than in the prior three years.

Here’s the pattern by month, and year.

The spike in usage in November is a bit concerning, since it’s the highest overall monthly consumption for the past four years. Hopefully this was primarily due to the heavy use of the heater during the final phases of the dog barn construction. December wasn’t a particularly cold month relative to years past, but it’s good to see that our consumption was actually quite low even with the barn heater being on the entire month.

That wraps it up. Have a happy and productive 2014!

sun, 04-aug-2013, 09:35
How will I do?

How will I do?

My last blog post compared the time for the men who ran both the 2012 Gold Discovery Run and the Equinox Marathon in order to give me an idea of what sort of Equinox finish time I can expect. Here, I’ll do the same thing for the 2012 Santa Claus Half Marathon.

Yesterday I ran the half marathon, finishing in 1:53:08, which is an average pace of 8.63 / 8:38 minutes per mile. I’m recovering from a mild calf strain, so I ran the race very conservatively until I felt like I could trust my legs.

I converted the SportAlaska PDF files the same way as before, and read the data in from the CSV files. Looking at the data, there are a few outliers in this comparison as well. In addition to being ouside of most of the points, they are also times that aren’t close to my expected pace, so are less relevant for predicting my own Equinox finish. Here’s the code to remove them, and perform the linear regression:

combined <- combined[!(combined$sc_pace > 11.0 | combined$eq_pace > 14.5),]
model <- lm(eq_pace ~ sc_pace, data=combined)

lm(formula = eq_pace ~ sc_pace, data = combined)

     Min       1Q   Median       3Q      Max
-1.08263 -0.39018  0.02476  0.30194  1.27824

            Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.11209    0.61948  -1.795   0.0793 .
sc_pace      1.44310    0.07174  20.115   <2e-16 ***
Signif. codes:  0***0.001**0.01* ‘ ’ 1

Residual standard error: 0.5692 on 45 degrees of freedom
Multiple R-squared: 0.8999,     Adjusted R-squared: 0.8977
F-statistic: 404.6 on 1 and 45 DF,  p-value: < 2.2e-16

There were fewer male runners in 2012 that ran both Santa Claus and Equinox, but we get similar regression statistics. The model and coefficient are significant, and the variation in Santa Claus pace times explains just under 90% of the variation in Equinox times. That’s pretty good.

Here’s a plot of the results:

As before, the blue line shows the model relationship, and the grey area surrounding it shows the 95% confidence interval around that line. This interval represents the range over which 95% of the expected values should appear. The red line is the 1:1 line. As you’d expect for a race twice as long, all the Equinox pace times are significantly slower than for Santa Claus.

There were fewer similar runners in this data set:

2012 Race Results
Runner DOB Santa Claus Equinox Time Equinox Pace
John Scherzer 1972 8:17 4:49 11:01
Greg Newby 1965 8:30 5:03 11:33
Trent Hubbard 1972 8:31 4:48 11:00

This analysis predicts that I should be able to finish Equinox in just under five hours, which is pretty close to what I found when using Gold Discovery times in my last post. The model predicts a pace of 11:20 and an Equinox finish time of four hours and 57 minutes, and these results are within the range of the three similar runners listed above. Since I was running conservatively in the half marathon, and will probably try to do the same for Equinox, five hours seems like a good goal to shoot for.

sat, 27-jul-2013, 08:03
Gold Discovery Run, 2013

Gold Discovery Run, 2013

This spring I ran the Beat Beethoven 5K and had such a good time that I decided to give running another try. I’d tried adding running to my usual exercise routines in the past, but knee problems always sidelined me after a couple months. It’s been three months of slow increases in mileage using a marathon training plan by Hal Higdon, and so far so good.

My goal for this year, beyond staying healthy, is to participate in the 51st running of the Equinox Marathon here in Fairbanks.

One of the challenges for a beginning runner is how pace yourself during a race and how to know what your body can handle. Since Beat Beethoven I've run in the Lulu’s 10K, the Midnight Sun Run (another 10K), and last weekend I ran the 16.5 mile Gold Discovery Run from Cleary Summit down to Silver Gulch Brewery. I completed the race in two hours and twenty-nine minutes, at a pace of 9:02 minutes per mile. Based on this performance, I should be able to estimate my finish time and pace for Equinox by comparing the times for runners that participated in the 2012 Gold Discovery and Equinox.

The first challenge is extracting the data from the PDF files SportAlaska publishes after the race. I found that opening the PDF result files, selecting all the text on each page, and pasting it into a text file is the best way to preserve the formatting of each line. Then I process it through a Python function that extracts the bits I want:

import re
def parse_sportalaska(line):
    """ lines appear to contain:
        place, bib, name, town (sometimes missing), state (sometimes missing),
        birth_year, age_class, class_place, finish_time, off_win, pace,
        points (often missing) """
    fields = line.split()
    place = int(fields.pop(0))
    bib = int(fields.pop(0))
    name = fields.pop(0)
    while True:
        n = fields.pop(0)
        name = '{} {}'.format(name, n)
        if'^[A-Z.-]+$', n):
    pre_birth_year = []
    while True:
            f = fields.pop(0)
            print("Warning: couldn't parse: '{0}'".format(line.strip()))
            if'^[0-9]{4}$', f):
                birth_year = int(f)
    if'^[A-Z]{2}$', pre_birth_year[-1]):
        state = pre_birth_year[-1]
        town = ' '.join(pre_birth_year[:-1])
        state = None
        town = None
        (age_class, class_place, finish_time, off_win, pace) = fields[:5]
        class_place = int(class_place[1:-1])
        finish_minutes = time_to_min(finish_time)
        fpace = strpace_to_fpace(pace)
        print("Warning: couldn't parse: '{0}', skipping".format(
        return None
        return (place, bib, name, town, state, birth_year, age_class,
                class_place, finish_time, finish_minutes, off_win,
                pace, fpace)

The function uses a a couple helper functions that convert pace and time strings into floating point numbers, which are easier to analyze.

def strpace_to_fpace(p):
    """ Converts a MM:SS" pace to a float (minutes) """
    (mm, ss) = p.split(':')
    (mm, ss) = [int(x) for x in (mm, ss)]
    fpace = mm + (float(ss) / 60.0)

    return fpace

def time_to_min(t):
    """ Converts an HH:MM:SS time to a float (minutes) """
    (hh, mm, ss) = t.split(':')
    (hh, mm) = [int(x) for x in (hh, mm)]
    ss = float(ss)
    minutes = (hh * 60) + mm + (ss / 60.0)

    return minutes

Once I process the Gold Discovery and Equnox result files through this routine, I dump the results in a properly formatted comma-delimited file, read the data into R and combine the two race results files by matching the runner’s name. Note that these results only include the men competing in the race.

gd <- read.csv('gd_2012_men.csv', header=TRUE)
gd <- gd[,c('name', 'birth_year', 'finish_minutes', 'fpace')]
eq <- read.csv('eq_2012_men.csv', header=TRUE)
eq <- eq[,c('name', 'birth_year', 'finish_minutes', 'fpace')]
combined <- merge(gd, eq, by='name')
names(combined) <- c('name', 'birth_year', 'gd_finish', 'gd_pace',
                     'year', 'eq_finish', 'eq_pace')

When I look at a plot of the data I can see four outliers; two where the runners ran Equinox much faster based on their Gold Discovery pace, and two where the opposite was the case. The two races are two months apart, so I think it’s reasonable to exclude these four rows from the data since all manner of things could happen to a runner in two months of hard training (or on race day!).

combined <- combined[!((gd_pace > 10 & gd_pace < 11 & eq_pace > 15)
                       | (gd_pace > 15)),]

Let’s test the hypothesis that we can predict Equinox pace from Gold Discovery Pace:

model <- lm(eq_pace ~ birth_year, data=combined)

lm(formula = eq_pace ~ gd_pace, data = combined)

     Min       1Q   Median       3Q      Max
-1.47121 -0.36833 -0.04207  0.51361  1.42971

            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.77392    0.52233   1.482    0.145
gd_pace      1.08880    0.05433  20.042   <2e-16 ***
Signif. codes:  0***0.001**0.01* ‘ ’ 1

Residual standard error: 0.6503 on 48 degrees of freedom
Multiple R-squared:  0.8933,    Adjusted R-squared:  0.891
F-statistic: 401.7 on 1 and 48 DF,  p-value: < 2.2e-16

Indeed, we can explain 65% of the variation in Equinox Marathon pace times using Gold Discovery pace times, and both the model and the model coefficient are significant.

Here’s what the results look like:

The red line shows a relationship where the Gold Discovery pace is identical to the Equinox pace for each running. Because the actual data (and the prediced results based on the regression model) are above this line, that means that all the runners were slower in the longer (and harder) Equinox Marathon.

As for me, my 9:02 Gold Discovery pace should translate into an Equinox pace around 10:30. Here are the 2012 runners who were born within ten years of me, and who finished within ten minutes of my 2013 Gold Discovery time:

2012 Race Results
Runner DOB Gold Discovery Equinox Time Equinox Pace
Dan Bross 1964 2:24 4:20 9:55
Chris Hartman 1969 2:25 4:45 10:53
Mike Hayes 1972 2:27 4:58 11:22
Ben Roth 1968 2:28 4:47 10:57
Jim Brader 1965 2:31 4:09 9:30
Erik Anderson 1971 2:32 5:03 11:34
John Scherzer 1972 2:33 4:49 11:01
Trent Hubbard 1972 2:33 4:48 11:00

Based on this, and the regression results, I expect to finish the Equinox Marathon in just under five hours if my training over the next two months goes well.

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