Thanks to Ultrasignup.com, I have been provided with a sample of everyone that has ran a 100 mile race as well as every other race they have ran. I am having a little trouble setting the data up for my ideal analysis which is a predictive model but have taken forays into the data. In particular, I was interested in exploring the relationship between age and ultra-marathon times. In an attempt to control for the distance, I segmented by 50k and 50 and 100 mile. I have provided three scatter-plots below with the associated fitted values plot.

For all the of the fitted lines, I have chosen to fit a polynomial, 2nd degree, for the functional form. The rationale behind this choice is that the relationship between age and race time is most likely non-linear in nature and is more likely u-shaped in nature. Meaning that as humans age their times will get faster but this relationship will slowly change until a turning point occurs at which times slow as age increases. The only downside is that interpreting the coefficients is more difficult…

From the three charts, the general take away is that as age increases we do see a increase in ultramarathon race times at all distances. However, what I find interesting is that the curvature of the fitted lines becomes less as the distance increases. At the 100 mile distance, there is very little curvature which suggests that the increase in race times associated with aging are fairly even across all ages. Thus as you age you are less likely to run 100 milers much slower than you did when you were younger! Not so much can be said for the 50K distance.

I will follow up this post later with an attempt to see the turning points for which times began to get drastically slower given aging. Let me know if you have any other interesting analysis questions you think I might be able to answer!

Well, as some might know I will soon be working for a tech start-up called JustAnswer. In short, the company is a Q&A website that connects individuals with question to qualified experts who can answer those questions. In there words, the mission ” is to help people, by providing the best online platform for people to access quality and compassionate Experts, conveniently and affordably. By doing so, we believe that we can improve the world.” I will be doing work related to search engine marketing (SEM). In researching this new subject matter, I have come across some interesting tools and articles that I would like to share.

First, I wanted to share the Google Research Blog which is a gold mine! I have found this to be an exceedingly interesting blog to follow but here are some of the fruits of my internet surfing.

Google Correlate applied to Ultras!

One cool tool that I stumbled across was Google Correlate, which allows you to upload a time-series or state cross-section and see what search term has the most similar search pattern. You can also search a specific term and see what other terms have the same search pattern. Naturally, being a ultra-runner, I had to explore the correlations in that arena. So, I tried two terms: “ultramarathon” and “Western States 100″. Here is what I found…

The search term correlated most highly with “ultramarathon” is “badwater” (an ultramarathon). This is a little surprising as I thought “Western States 100″ or something along those lines would be. So naturally, I had to try “Western States 100″.

While not the most correlated term one of the terms with the highest correlation was “double dipsea”.

As you will note in both of these charts, there are spikes around the beginning of July (“ultramarathon”) and the later part of June (“Western States 100″). In the first case, I am not sure which direction the causality flows but it certainly seems that searches for “badwater ultramarathon” spike significantly around the beginning of July which also happens to be around the dates of the race. Also of note is that the amplitude, for the search term “ultramarathon”, has generally been greater over time which suggests increasing interest in the sport! Likewise, we see spikes, in the second chart, towards the end of June when both Western States and the Double Dipsea occur.

While this tool is not really that interesting in terms of ultrarunning, it certainly has a lot of applicability to other subject matter. Here are a few links in which to explore the uses further…here and here and here. Also, you can find the whitepaper for Google Correlate here. Additionally, you can find some interesting forecasting papers from Hal Varian that utilize Google search data to forecast real data series both here and here.

Search Engine Marketing and Statistics

Lastly, I have found a variety of interesting papers that I thought I would share. The main focus of these papers is to assess ad effectiveness using a variety of controlled experiments using differing statistical analysis. Here they are:

Measuring Ad Eectiveness Using Geo Experiments

Evaluating Online Ad Campaigns in a Pipeline: Causal Models At Scale

Incremental Clicks Impact Of Search Advertising

Alright that is all I got for now. Enjoy.

To fulfill my, irrational, desire to record as much running data as possible, I undertook the task of recording everyday of running last year. The metrics I recorded were basic: time, distance, weight. Now that it is a full year later, I am trying to figure out what the heck I do with this data? So in a effort to do a little entertaining analysis, I thought I would provide some stats and charts for everyone to peruse. Let me know if you have any thoughts or ways to better present the data. I am always open to suggestions. I should state now, that these are very rough estimates and I am probably in gross need of brushing up on my statistics. With that being said take it with a grain of salt and enjoy…the 100 mile prediction is at the bottom!

Basic Metrics:

Total Yearly Miles: 1505.2
Highest Daily Mileage: 51.2
Highest Weekly Mileage: 62
Average Miles per Month: 99.7
Average Pace (min/mile): 8:50

Chart 1:

I think this is a somewhat obligatory chart and kinda just gives a sense of the year in terms of monthly totals. I added the moving average to provide a little smoothing of the data and to give a better sense of the average level given that month and the previous months values.

As you can tell, beginning in July I really started to get back into running after three months of zero to very low mileage. I escalated fairly quickly from July on and only tapered off in November due to vacations/injury/taper before North Face 50 on December 3rd. I can safely say that nearly half of the December total is due to North Face.

Chart 2:

I find this chart to be much more interesting and thought provoking than Chart 1. First, the chart is seeking to find the relationship between my pace and the distance I run. This is useful for the purposes of predicting how fast I will run at a particular distance. Obviously, the relationship is non-linear and in fact is more likely logarithmic or maybe even quadratic. Second, this plot provides an insight into the model that could be used to forecast race performance.

Getting down to the actual numbers, it is clear that the fit of the model to the data is somewhat lacking given the low R^2 and therefore the low amount of the variance in pace explained by distance. In its current form, I exclude races from the regression analysis simply because they are efforts that were outside the norm but I have included them in the plot. So this plot can be interpreted in terms of training. As such, the interpretation from this simple linear model is that for every mile run, the pace increases by .073 minutes per mile. Due to the excel handling of time, this is literally interpreted as an increase of 7.3% of a minute or 60*.073 = 4.38 seconds. Note that in an abstract sense, the constant (8.3324 or 8:20 min/mile) is the pace that would be run if I ran zero miles.

Chart 3:

The purpose of this exercise was to predict my 50 mile pace at North Face using my training data. I employ two models one linear and the other logarithmic. As is apparent, neither truly captures my race time. The differential for the linear model and my actual time is plus 1:42 min/mile and for the log model minus 00:21 min/mile. Again, the fit of these models is somewhat suspect given my naive regression analysis.

One potential way to improve the fit of the model is to use only race times. However, I only have five races this year. This suggests, I could use last year’s races as well to bolster the amount of data and therefore the statistical power. The only problem with this is the downward trend (faster pace) in race performance over time. One way to adjust for this is to introduce a time variable that would account for changes over time. Take for example the Pacifica 30k trail races I ran in 2010 and 2011, one I ran in 3:33:46 and the other in 2:56:19. I tend to believe that a large part of this improvement is due to an improvement in performance related to increased training. However, in my current model this improvement would not be accounted for. I plan to explore these improvements at a later date.

For now, I am looking for any helpful comments as I would like to develop a predictor for ultra times. I am not sure if there is anything out there yet, but would like to calibrate something. I am imagining the old model of the two mile time trial is not very accurate for anything beyond the 26.2 mile mark. That being said, I think I can develop something if I can get enough data from a variety of individuals or scrape the ultrasignup website. So, my first job will be to gather the appropriate data but I need to think about what data I need first (e.g. race times and distances). So be on your toes, you may be getting an email soon!

Alright, PREDICTION TIME. The two models I have constructed suggest that I will run between a 10:18 and a 15:40 min/mile pace for a 100 miles or to put the range in hours between 17:10 and 26:06. In a general sense, I consider these lower and upper bounds given my training. Obviously, race specific details such as elevation and altitude will change the time but I think this is a decent range albeit somewhat on the low end. In the case of Tahoe Rim Trail 100, I know that times in the 17, 18 and 19 hour range win the race, are fast and relatively few, so I am imagining something more towards the mid to top of the distribution meaning 22 hours and up. Anyway, only time will tell!

I will be sure to update this as the race gets closer and training progresses.

Last year, 2011, was a trying year for me in regards to running. I had set out to run numerous races and conquer my first 50 mile race: Lake Sonoma 50 miler. However, mother nature and my body had other plans at least for the first part of the year. In a somewhat serendipitous string of events, I ended up having pain on the outside of my both of my knees only days before the race. I wasn’t going to be able to run and was feeling very depressed. Then, I received an email notifying me that the race had been cancelled due to flooding. I was luckily afforded a reprieve and had planned to focus on healing. Then disaster struck, in a fluke accident, by fluke I mean inebriated, I ended up breaking a bone in my hand and it benched me for longer than I had anticipated.

Despite the setbacks, I rolled into July rested, healed, and with new resolve. I began running again slowly and was really feeling good again. This new found well-being coupled with mutterings from my running compatriots about tackling the North Face Endurance Challenge 50 miler, quickly prompted me to readdress my desire to run a 50 miler. After Lake Sonoma was cancelled, I had in my mind written off the year for ultras but deep down I was still hungering for it. So, I signed up for the North Face Endurance Challenge as did my girlfriend and a handful of other friends (one can be found here).

Without going into the nitty-gritty, I made it fairly unscathed to race day and with only one minor setback. Though nervous going into the race, it ended up being a banner day in which the weather was perfect, I felt great, ran a smart race, and had a superb pacer. All of this allowed me to run a great first 50 miler in a time of 8:46:47 (results here).

After my successful first 50 miler, I pretty much instantaneously got the itch to do another and to tackle a hundred miler. Thus, I have for the time being signed up for two races in  2012. One, is to revisit the Lake Sonoma 50 miler and the second is to run the Tahoe Rim Trail 100 mile race. The latter is my target race for the year and I am really looking forward to it. It is at altitude, so my sea level lungs will certainly be taxed. However, an exploratory run on the course, embed below but also the last of the year, wasn’t too taxing and I didn’t feel like I was struggling too much. This has given me hope that I will be able to adapt fairly well, but only time will tell.

I will work on putting up a running calendar and results here in the near future. I am sure I will also be running some other races this year, so will be sure to blog about those. Looking forward to 2012 and running some great races!

Naturally, Wednesday morning involves watching a few running related videos. Stumbled upon the Asics Youtube Channel and found two videos particularly moving/inspiring. One is trail related the other track.

Also thought I would pass along an article related to social media marketing my running buddy wrote. For someone that knows little about the subject and will soon be entering into the marketing world, I found it interesting and informative (link).

Enjoy.

Hello world, as some may know I used to blog over at Reddhead Flyfishing. Due to the narrow nature of the website name, I felt a need to expand and generalize my personal website. Thus, I have started this website. It is currently titled “Run Amok” but I am not certain the name will stick. Anyway, I plan to start posting regularly on a variety of topics. Much like myself, the content will be eclectic and hopeful entertaining. Let me know if you have any thoughts!