sat, 28-sep-2019, 18:46

Introduction

At the 57th running of the Equinox Marathon last weekend Aaron Fletcher broke Stan Justice’s 1985 course record, one of the oldest running records in Alaska sports. On the Equinox Marathon Facebook page Stan and Matias Saari were discussing whether more favorable weather might have meant an even faster record-breaking effort. Stan writes:

Where is a statistician when you need one. Would be interesting to compare times of all 2018 runners with their 2019 times.

I’m not a statistician, but let’s take a look.

Results

We’ve got Equinox Marathon finish time data going back to 1997, so we’ll compare the finish times for all runners who competed in consecutive years, subtracting their current year finish times (in hours) from the previous year. By this metric, negative values indicate individuals who ran faster in the current year than the previous. For example, I completed the race in 4:40:05 in 2018, and finished in 4:33:42 this year. My “hours_delta” for 2019 is -0.106 hours, or 6 minutes, 23 seconds faster.

Here’s the distribution of this statistic for 2019:

//media.swingleydev.com/img/blog/2019/09/twenty_nineteen_histogram.svgz

There are several people who were dramatically faster (on the left side of the graph), but the overall picture shows that times in 2019 were slower than 2018. The dark cyan line is the median value, which is at 0.18 hours or 10 minutes, 35 seconds slower. There were 53 runners that ran the race faster in 2019 than 2018 (including me), and 115 who were slower. That’s a pretty dramatic difference.

Here’s that relationship for all the years where we have data:

//media.swingleydev.com/img/blog/2019/09/slower_faster.svgz

The orange bars are runners who ran that year’s Equinox faster than the previous year and the dark cyan bars are those who were slower. 2019 is dramatically different than most other years for how much slower most people ran. 2013 is another particularly slow year. Fast years include 2007, 2009, and last year.

Here’s another way to look at the data. It shows the median number of minutes runners ran Equinox faster (negative numbers) or slower (positive) in consecutive years.

//media.swingleydev.com/img/blog/2019/09/median_diff_one_year.svgz

You can see that finish times were dramatically slower in 2019, and much faster in 2018. Since this comparison is using paired comparisons between years, at least part of the reason 2019 seemed like such a slow race is that 2018 was a fast one.

Two-year lag

Let’s see what happens if we use a two-year lag to calculate the differences. Instead of comparing the current year’s results with the previous year for individual runners that raced in both years, we’ll compare the current year with two years prior. For example runners that ran the race this year and in 2017.

Here’s what the distribution looks like comparing 2019 and 2017 results from the same runner.

//media.swingleydev.com/img/blog/2019/09/two_year_histogram.svgz

It’s a similar pattern, with the median values at 0.18 hours, indicating that runners were almost 10 minutes slower in 2019 when compared against their 2017 times. This strengthens the evidence that 2019 was a particularly difficult year to run the race.

Median difference by year for all years of the two-year lag data:

//media.swingleydev.com/img/blog/2019/09/two_year_diffs.svgz

Remember that the dark cyan bars are years with slower finish times and orange are faster. 2019 still comes out as an outlier, along with 2013. 2007 is the clear winner for fast times.

All pairwise race results

If we can do one and two year lags, how about combining all the pairwise race results? At some point the comparison is no longer a good one because of the large time interval between races, so we will restrict the comparisons to six or fewer years between results. We’ll also remove the earliest years from the results because those years are likely biased by having fewer long lag results.

Here’s the same plot showing difference times in minutes for all pairwise race results, six years and fewer.

//media.swingleydev.com/img/blog/2019/09/all_through_six_median_diff_minutes.svgz

You can see that there’s a pretty strong bias toward slower times, which is likely due to people aging and their times getting slower. The conditions were good enough in 2007 that this aging effect was offset and people running in that race tended to do it faster than their earlier performances despite being older. Even so, 2019 still stands out as one of the most difficult races.

Here’s the aging effect:

##
## Call:
## lm(formula = hours_delta ~ years_delta, data = all_through_six)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -6.3242 -0.3639 -0.0415  0.3115  6.4441
##
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)
## (Intercept) -0.03390    0.01934  -1.752              0.0797 .
## years_delta  0.05152    0.00558   9.234 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8845 on 8664 degrees of freedom
## Multiple R-squared:  0.009745,   Adjusted R-squared:  0.00963
## F-statistic: 85.26 on 1 and 8664 DF,  p-value: < 0.00000000000000022

There’s a very significant positive relationship between the difference in years and the difference in marathon times for those runners (years_delta in the coefficient results above). The longer the gap between races, the slower a runner is by just over 3 minutes each year. Notice, however, that the noise in the data is so great that this model, no matter how significant the coefficients, explains almost none of the variation in the difference in marathon times (dismally small R-squared values).

Weather

The conditions in this year’s race were particularly harsh with a fairly constant 40 °F temperature and light rain falling at valley level; and below freezing temperatures, high winds, and snow falling up on Ester Dome. The trail was muddy, soft, and slippery in places, especially the single track and the on the unpaved section of Henderson Road. Compare this with last year when the weather was gorgeous: dry, sunny, and temperatures ranging from 39—60 °F.

We took a look at the differences in weather between years to see if there is a relationship between weather differences and finish time differences, but none of the models we tried were any good at predicting differences in finish times, probably because of the huge variation in finish times that had nothing to do with the weather. There are too many other factors contributing to an individual’s performance from one year to the next to be able to pull out just the effects of weather on the results.

Conclusion

2019 was a very slow year when we compared runners who completed Equinox in 2019 and earlier years. In fact, there’s some evidence that it’s the slowest year of all the years considered here (1997—2019). We could find no statistical evidence to show that weather was the cause of this, but anyone who was out there on race day this year knows it played a part in their finish times. I ran the race this year and last and managed to improve on my time despite the conditions, but I don’t think there’s any question that I would have improved my time even more had it been warm and sunny instead of cold, windy, and wet. Congratulations to all the competitors in this year’s race. It was a fun, but challenging year for Equinox.

tags: running  R  Equinox Marathon 
wed, 18-sep-2019, 13:14

Introduction

A couple years ago I wrote a post about past Equinox Marathon weather. Since that post Andrea and I have run the relay twice, and I ran the full marathon. This post updates the statistics and plots to include two more years of the race.

Methods

Methods and data are the same as in my previous post, except the daily data has been updated to include 2018. The R code is available at the end of the previous post.

Results

Race day weather

Temperatures at the airport on race day ranged from 19.9 °F in 1972 to 35.1 °F in 1969, but the average range is between 34.3 and 53.2 °F. Using our model of Ester Dome temperatures, we get an average range of 29.7 and 47.4 °F and an overall min / max of 16.1 / 61.3 °F. Generally speaking, 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 16 out of 56 race days, or 29% of the time, and measurable snowfall has been recorded on four of those sixteen. 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 sixteen years when it rained or snowed (1990, 1993, 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. Five of the 12 years where measurable precipitation fell at the airport and 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 nine race days, bringing the percentage up to sixteen 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 4.8 miles per hour. The highest 2-minute wind speed 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.

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 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 44 of 56 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 (most of 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.

Summary

The following stacked plots shows the weather for all 56 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.

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 five of the other years with liquid precipitation probably experienced snow on Ester Dome (1977, 1986, 1991, 1994, and 2016) 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. A CSV with this data can be downloaded from all_wx.csv

Date min t max t ED min t ED max t awnd prcp snow p prcp p snow
1963-09-21 32.0 54.0 27.5 48.2   0.00 0.0 0.01 0.0
1964-09-19 34.0 57.9 29.4 51.8   0.00 0.0 0.03 0.0
1965-09-25 37.9 60.1 33.1 53.9   0.00 0.0 0.80 0.0
1966-09-24 36.0 62.1 31.3 55.8   0.00 0.0 0.01 0.0
1967-09-23 35.1 57.9 30.4 51.8   0.00 0.0 0.00 0.0
1968-09-21 23.0 44.1 19.1 38.9   0.00 0.0 0.04 0.0
1969-09-20 35.1 68.0 30.4 61.3   0.00 0.0 0.00 0.0
1970-09-19 24.1 39.9 20.1 34.9   0.00 0.0 0.42 0.0
1971-09-18 35.1 55.9 30.4 50.0   0.00 0.0 0.14 0.0
1972-09-23 19.9 42.1 16.1 37.0   0.00 0.0 0.01 0.2
1973-09-22 30.0 44.1 25.6 38.9   0.00 0.0 0.05 0.0
1974-09-21 48.0 60.1 42.5 53.9   0.08 0.0 0.00 0.0
1975-09-20 37.9 55.9 33.1 50.0   0.02 0.0 0.02 0.0
1976-09-18 34.0 59.0 29.4 52.9   0.00 0.0 0.54 0.0
1977-09-24 36.0 48.9 31.3 43.4   0.06 0.0 0.20 0.0
1978-09-23 30.0 42.1 25.6 37.0   0.00 0.0 0.10 0.3
1979-09-22 35.1 62.1 30.4 55.8   0.00 0.0 0.17 0.0
1980-09-20 30.9 43.0 26.5 37.8   0.00 0.0 0.35 0.0
1981-09-19 37.0 43.0 32.2 37.8   0.15 0.0 0.04 0.0
1982-09-18 42.1 61.0 37.0 54.8   0.02 0.0 0.22 0.0
1983-09-17 39.9 46.9 34.9 41.5   0.00 0.0 0.05 0.0
1984-09-22 28.9 60.1 24.6 53.9 5.8 0.00 0.0 0.08 0.0
1985-09-21 30.9 42.1 26.5 37.0 6.5 0.14 2.1 0.57 0.0
1986-09-20 36.0 52.0 31.3 46.3 8.3 0.07 0.0 0.21 0.0
1987-09-19 37.9 61.0 33.1 54.8 6.3 0.00 0.0 0.00 0.0
1988-09-24 37.0 45.0 32.2 39.7 4.0 0.00 0.0 0.11 0.0
1989-09-23 36.0 61.0 31.3 54.8 8.5 0.00 0.0 0.07 0.5
1990-09-22 37.9 50.0 33.1 44.4 7.8 0.26 0.0 0.00 0.0
1991-09-21 36.0 57.0 31.3 51.0 4.5 0.04 0.0 0.03 0.0
1992-09-19 24.1 33.1 20.1 28.5 6.7 0.01 0.4 1.26 23.0
1993-09-18 28.0 37.0 23.8 32.2 4.9 0.29 4.1 0.37 0.3
1994-09-24 27.0 51.1 22.8 45.5 6.0 0.02 0.0 0.08 0.0
1995-09-23 43.0 66.9 37.8 60.3 4.0 0.00 0.0 0.00 0.0
1996-09-21 28.9 37.9 24.6 33.1 6.9 0.06 1.2 0.26 0.0
1997-09-20 27.0 55.0 22.8 49.1 3.8 0.00 0.0 0.03 0.0
1998-09-19 42.1 60.1 37.0 53.9 4.9 0.00 0.0 0.37 0.0
1999-09-18 39.0 64.9 34.1 58.4 3.8 0.00 0.0 0.26 0.0
2000-09-16 28.9 50.0 24.6 44.4 5.6 0.00 0.0 0.30 0.0
2001-09-22 33.1 57.0 28.5 51.0 1.6 0.00 0.0 0.00 0.0
2002-09-21 33.1 48.9 28.5 43.4 3.8 0.00 0.0 0.03 0.0
2003-09-20 26.1 46.0 22.0 40.7 9.6 0.00 0.0 0.00 0.0
2004-09-18 26.1 48.0 22.0 42.5 4.3 0.00 0.0 0.25 0.0
2005-09-17 37.0 63.0 32.2 56.6 0.9 0.00 0.0 0.09 0.0
2006-09-16 46.0 64.0 40.7 57.6 4.3 0.00 0.0 0.00 0.0
2007-09-22 25.0 45.0 20.9 39.7 4.7 0.00 0.0 1.05 0.0
2008-09-20 34.0 51.1 29.4 45.5 4.5 0.00 0.0 0.08 0.0
2009-09-19 39.0 50.0 34.1 44.4 5.8 0.00 0.0 0.25 0.0
2010-09-18 35.1 64.9 30.4 58.4 2.5 0.00 0.0 0.00 0.0
2011-09-17 39.9 57.9 34.9 51.8 1.3 0.00 0.0 0.44 0.0
2012-09-22 46.9 66.9 41.5 60.3 6.0 0.00 0.0 0.33 0.0
2013-09-21 24.3 44.1 20.3 38.9 5.1 0.00 0.0 0.13 0.6
2014-09-20 45.0 51.1 39.7 45.5 1.6 0.36 0.0 0.00 0.0
2015-09-19 37.9 44.1 33.1 38.9 2.9 0.01 0.0 1.49 0.0
2016-09-17 34.0 57.9 29.4 51.8 2.2 0.01 0.0 0.61 0.0
2017-09-16 33.1 66.0 28.5 59.5 3.1 0.00 0.0 0.02 0.0
2018-09-15 44.1 60.1 38.9 53.9 3.8 0.00 0.0 0.00 0.0
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