Our Daily Bleg: How to Handicap a Multi-Race Challenge?

From a reader named Kevin O’Toole comes a bleg that needs input from people with experience in the realms of running, races, and maybe Olympic competition. (We tussled with Olympic medal counts here; and Justin Wolfers harnessed your collective wisdom when he ran the Stockholm Marathon.) Here’s Kevin’s story:

For the past few years, I’ve had some ongoing bets with friends at work (a supply-chain management company in Atlanta) around weight loss and fitness — just to stay in shape and keep it interesting. We’ve refined things based on the concept we liked at StickK.com (haven’t been there in a while, but I heard about it on Freakonomics).

Last fall we had a bet around a 5K race, which my team lost. We want an opportunity to redeem ourselves, and being the engineering types we are (you should see our 5MB college-football pool spreadsheet), we’ve decided to complicate things a little and do four races with two teams of two.

The races will be run in the following order: 10K, 1 mile, 5K, and half-marathon (at least 12 weeks after the 5K). This is a good mix of speed and endurance, with spacing to minimize risk of injury and optimize training.

The challenge is this: we don’t think we should pick the winner based on total time. We want to reward the speed runners if they can win big at those races and reward the distance runners if they can put in time on the long races. If you just go by time, then 30 seconds in the mile or 1 minute in the 5K won’t count as much as 90 seconds in the half-marathon (or, conversely, the distance runner would have an advantage there).

Both teams are a mix of running experience: Andrew (five marathons and many 5K’s and 10K’s) paired with David (one 5K and one 10K), versus Kevin (a few 10K’s and 5K’s, and two half-marathons) and Eric (four marathons and many 5K and 10K races).

We want all four times to count toward the total for each race and for the overall, but straight-up time puts the emphasis too heavily on the 10K and half-marathon. What do people think would be a good handicap system? Some point system with a points-per-second factor based on race length? Some combination of total time with a factor based on the length of the race?

Please help Kevin as best as you can. Send you own future blegs here.


Are the races being run officially timed and reported on? Are the races being run the same? What about offering points based on their standing (you can further handicap them based on age group.) So, if someone finishes 10th out of 20 people they would get a score of .5, but if they scored 1st they would only have a .05.

If they are running different races, then maybe award based on decile or performance relative to the winning time? I always consider it a good race if I finished no more than 1.5 times the winning female time.

C. Larity

Since you're clearly college football fans, why reinvent the wheel? Steal the old BCS formula that factored in strength of schedule and victory margin. In other words, use a point system to give additional points to those who do exceptionally well in a certain event (i.e. breaking your PR in a mile by :05, or beating your 5K best by :15).


Without putting much thought into it:

For each race, each runner gets points according to how far their time is form the average time of the four runners. So the winner might be 5% better than the average time, so get 5 points. The other three runners might get positive or negative points depending on how people finish.

Repeat for each race.

Add 100 to the final score if people care about being negative.

travis ormsby

You could convert the times into z-scores based on a population whose times are representative of each runner.

Whover is the most standard deviations ahead would be the winner.


Can't you normalize the times to a standard time-- say 1 hour is the winner's time for each race-- and then scale all the other times accordingly?

Levi Funk

Divide the individual's time by the distance of the race. Do this for all 4 races and add up the total number. This should be a fair index.

Matt Kromer

The following link has a tool that projects what your time would be for races of different distances based on your time for a single distance.

This tool attempts to account for the fact that you cannot hold the same pace over longer distances. (For example, a 5:00 mile is a 2:49 marathon).

My recommendation would be to use this calculator to calculate equivalent race 1-mile race paces, and take the average of the four.


Peg the winner's time on each race as 100(%) and give them 100 points. Give points to the other three on each race based on where they finished (105%, 107.2%, etc.). After all four races everyone will probably have between 400 and 450 points, lowest score wins.


Along the z score approach, somebody already has a great z score for running. Jack Daniels, world's best running coach, not the whiskey, has a number that describes rate of oxygen consumption, VDOT. It's a good objective measure of your race performance. He spent a lot of time assigning VDOTs for a whole bunch of races. You can take the times from the various races, google vdot calculator, enter your race times, get a vdot, average them and pick a winner.


Since you are engineers, I'd recommend a progressively curved point system along the lines of the one used for events scoring in the decathlon. Also see the rationale behind this system here.


The easiest thing to do is to multiply all race times together, to get a grand total product for each person. Lowest score wins. Shaving 1% off of any one race will reduce a player's total score by 1%. Shaving 1% off of all four races is about as useful as shaving 3.94% (almost 4%) off of any one race.

An equivalent method (in the sense that it will always give the same winner) is to sum the logarithms of the different times. A 1% improvement on any given race will lower your score by about .01 (if you use a natural logarithm), or (.01/ln10=.004365) if you use the base 10 logarithm.


Percentile finish versus age-class.

That is, if you finish 25th versus 100 in your age-class, then are in the 75th percentile. Same thing if you finish 2nd in an age class of five racers. (The catch is that if you're in a small category small changes make a big difference.)

Add up the finishes, top percentile wins.


Several above have suggested awarding points based on the winning margin as a fraction of the length of that race. This seems to have the most intuitive appeal but I doubt it would really work in practice. Runners get injured - they twist ankles, get cramps, and otherwise pull up lame in all manner of creative ways. One injury (seemingly likely in 16 person-races) could seriously distort such a system.

I would suggest a points system based on the ranking in each race (i.e. 3 points for placing first, 2 for second, 1 for third). You could alter these point values based on your preferences. For instance, if you want to encourage specialization, you could award more points to first place. If you deem some races more important than others, award more points for those. There are many possibilities but we'd have to know more about your goals.

The solution isn't perfect. Like the other suggestions, it would allow for a blowout. Ideally, you want both teams to have a chance to win up to the last race.

Of course, you could just play basketball...



Use paces based on the MacMillan chart or something similar rather than absolute run times - that will let you equalize across the different races (i.e. that - I'm making up numbers, too lazy to pick real ones! - 8:10 pace in a 10K equals 8:32 pace in a half-marathon) and reward the winning teams for speed, but with conversions for different distances: i.e. it's a tie if person X runs 8:10/mi. in the 10K and person Y runs 8:32/mi. in the half.



Calculate the speed of each runner during each race, in actual mph, to 3 decimals.
Add those together.


Perhaps throw it on a curve? If you are confident that no one's going to tank to throw off the curve, the percentage difference between the winner and the last place finisher or between the winner and the field, multiplied by the log of the distance -- to make each second of pace maintained over the longer distance worth more -- should create a system that takes into account the distance delta and the talents of the collection of runners.


Here's my suggestion:

Find a reference race that all teams agree on: recent Olympic results, a well known competition (World Championships or a well known marathon). Run statistics on the times and figure out an average and sigma values.

Take the race results, and determine the deviation as if the result was in the reference competition.

Add the individual results and average for the team.

Paul Clapham

I used to rate my own times in those races by calculating my time as a multiple of the current world record for the distance. I guess that's a crude form of what the site linked to by #7 does, but it worked pretty well for me.


To help runners train, there exists tables that given the runner's VO2max (or some other proxy like a "VDOT" measurement), give the time the runner should be able to complete various distances. I can tell you that these are spookily accurate.

Perhaps you can use such a table to normalize the distances. For example, on a table I have handy, a VDOT of 50 corresponds to,

1 Mile: 5:50
5 km: 19:57
10 km: 41:21
1/2 mar: 1:31:35

(Notice the times are not linear with distance. Everyone knows it's harder to run a marathon at 5 minute-mile pace than a single mile.)

You could then do something like this to attempt to say, normalize the 5km time to a marathon,

((actual time) - 41:21)(1:31:35)/41:21

So for example, if you ran the 10km in 41:11, 10 seconds faster than the reference VDOT, that's equivalent to 22 seconds faster for a half-marathon. Notice we are scaling times, not distances. You can then normalize all distances to one, say the half, and whomever has the fastest normalized sum wins.

I'm sure the VDOT charts I've seen are just generated from some empirical equation. If you can find that, you may figure out an even easier or better way. Using VDOT, you can even handicap individual runners by using different numbers for each runner.



As an example of percentile finish, I just pulled up a popular 5k in Sacramento. For the 20-29 male age class there were 50 finishers. The winning time for the age group was just over 16 minutes. A very respectable time, say 25 minutes would get you 18th place, or 64th percentile.

If your teams are grouped into similar age groups, then evenly matched racers might finish 18th and 20th and be scored accordingly. Generally, you'll see tight bunching at the top of the age groups and more spread at the bottom, meaning top racers really have to run well to score well and beginners have room for a lot of improvement quickly.