# 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 withDavid(one 5K and one 10K), versusKevin(a few 10K’s and 5K’s, and two half-marathons) andEric(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.

## Greg

I can't find the article right now. I believe that it was in Running Times or Marathon & Beyond a month or two ago. There used to be a race that was all in one day that consisted of a 100 meter, 400 meter, 1 mile and a marathon. There may have been a 5k in there too. I don't recall. I think the article indicated the scoring system.

## Jonathan

Since there's only two teams it's head-to-head.

For each race calculate the dominance percentage as (winnertime - losertime / losertime) * 100%. The loser gets a score of zero for the race, the winner gets a score of whatever the formula above kicks out and since you're using a ratio the overall distance and time don't matter, only the relative greatness of the victory.

sum the scores for all four races, highest number wins.

## Jonathan

er, my bad with the failure to recognize negatives, but you get the idea. just tweak it so it makes sense.

## challenger

ok- let's assume a race between a few people. Each one has a personal challenge they wish to meet specific to themselves- yet connected with others. Their handicaps are quite different. The One with the greatest advantage over the others, also has a huge amount of weight to lose and a little that she cannot remember. For her it's mostly about loss.

The others (as far as I know) have alot to gain.

so x is the amount of time in the day that each person has to work on their challenge.

Seems impossible to develop a handicap situation.

The best scenario as I see it- is for her to share her results, the one memory loss may come back to her and if not - maybe at another time-

## Michael Giberson

Sounds like a task for David Pennock and pals at Yahoo! Reseach. Pennock and co-authors have written papers on "Pricing Combinatorial Markets for Tournaments", "Betting on permutations", and "Computational aspects of prediction markets."

A multi-race scoring system seems like their kind of thing.

## JimmyO

multiply all times by 6 and then divide by the normalized coefficient of 2 standard deviations from the null value squared. this factors all times back to its mutually exclusive denominator. high score wins

## Sam Carter

The way they do it in most track meets is based on points granted in order of finishing. Normally, just the top 3 finishers are scored in a head-to-head competition like yours, but in races with larger number of teams, they might score more places. Typically, 1st place is worth 5 points, 2nd place is worth 3 points, 3rd place is worth 1 point, and 4th or lower is worth nothing. You sum up the points from all the different races, and then the team with the most points wins.

In your particular case, the teams are Andrew & David vs. Kevin & Eric. Say for example, that order of finishers in the first race was: Andrew, Kevin, David, and then Eric. In that case, the team of A&D would get 6 points (5+1), and K&E would get 3 points (3+0). Then the points from the 2nd race are added, and so forth, until the last race is won.

In this scheme, it's truly a race, and beating a member of the other team by 1 second or 1 hour is the same. Time is not important, it's just important to win.

## Mike

In track and field duel meets, its 5 points for a win, 3 points for second, 1 point for third and butkus for anything else. There are usually 6 competitors per event - 3 from each team.

In the conference championships each place has a similar point value - usually 10-8-6-4-2-1

Another option is decathlon scoring. Each performance is given a point value - I had the feeling the scoring tables were originally based on the world record in each of the events at some time but maybe not. Unfortunately, the events you chose are all part of the decathlon (and I would add some throwing and jumping into your contest) :)

http://en.wikipedia.org/wiki/Decathlon

Good Lucj

## Matt

After each race, determine the ratio of each finisher's time to the world record for that race. Sum the ratios for each race, and the team for the lowest ratio wins. To simplify, I'll demonstrate with the 1m and half marathon. Say the WR times are 3 min. and 1hr, respectively. Runner A runs the mile in 5 min and the half in 2 hrs. His score would be 5/3+2/1 =3.66. Runner B runs the mile in 7 min and the half in 1:30. His ratio would be 7/3+1.5/1=3.83. Runner A would be the winner, since his ratio is lower.

## kuri

Keep it simple. Four runners, right? First place in each race is 4 points, second place 3, third place 2, and fourth place 1. After all the races are finished, the team with the highest score wins.

## HedgeHog

here's a link to the 2006 age graded tables - use them to score each individual, handicapped for age!

http://www.masterstrack.com/blog/archives/000785.html

## EdM

Cindy and Paul have it right. Base the results off of the percent of the current world record. Several endurance sports use that formula todetermine seedings or qualifying times.

As an exercise physiologist though, I disagree with you choice of races. Assuming no one shows up to a race inadequately trained, the person/team fastest over 5k will be fastest over 10k and 1/2 marathon as well. I'd say with 90% confidence that that same person/team will also win the mile. All of this based on the relative contribution of aerobic metabolism at each race distance. Throw a 100m dash in there in place of the 10k to even it up even if just a little.

## Olli

All of your systems seem overly complicated. Why not just copy the system used in a number of sports: give points according to your order. For example in formula 1, the winner gets 10 points, second 8, 3rd 6, 4th 5, etc.

In the spirit of competition, I would think winning a race against the opposing team is more important than the finishing time.

## Matt

Cross country scoring format: one point for first place, two for second, etc. The lowest team score wins. You'll either need an equal number of runners on each team, or score only the top 5 (or six, or seven, whatever you like) finishers. This method, of course, emphasizes finishing ahead of another runner rather than the margins of victory, which changes the emphasis of the race from finishing with a personal best time to beating another runner to the finish.

## Craig L

My suggestion -- simply average the miles per minute in each race of each participant. A 5k at 24 minutes is roughly an 8 minute mile. Likewise a half marathon at 1:45 is also roughly an 8 minute mile.

Average all four numbers together. Add the two teammates together. Lowest combined average wins.

Any of the suggestions related to relative standing in age group will be too dependent upon keeping all of the races similar. Plus, 5k's and half-marathon are generally more popular than the other distances.

Second best to me is some form of simple rank ordering. 1st place among the 4 paticpants gets 5 points, 2nd gets 3, 3rd gets 1, and 4th gets 0. This is the same for all four races, but doesn't seem to accomplish the goal of allowing a dominant win in one event to count more than the others.

## Metalate

How does the decathlon scoring work? That includes a mix of race lengths. I'm afraid that the suggestion to divide by race time still makes the long races too important. The 100m should have all times within a second or two (10-20%), but it's certainly possible someone could lose the half-marathon by 30 minutes, which is probably a much bigger percentage.

## Erin

I think you should pick the runner with the coolest last name.

Erin

## shaman

index each race back to the world record time at that distance. the team with the lowest average index wins.

## SammyC

I would say ignore most of these suggestions and look into how they score the Decathlon.

The Decathlon has a similar problem, but to an even greater degree: how do you compare a 10 second win in the mile, versus a 2 inch win in the high jump, versus a 3 foot win in the discus.

I'm not an expert, I don't really understand the exact forumla they use in the decathlon, but you can check it out here:

http://www.iaaf.org/mm/Document/Competitions/TechnicalArea/ScoringTables_CE_744.pdf

Here is my simplified version, inspired by my limited understanding of decathlon scoring: The winning time in the race is worth 1000 points, the last time is worth 1 point. Calculate all times inbetween accordingly, rounding to whatever place you prefer.

## Morten

The World Speed Skating Champion is crowned after four races: 500m, 1500m, 5000m and 10000m. So this is exactly analogous to this bleg. The winner is decided on the method suggested by comment 6. Time divided by distance for each race. So 1sek on 500m translates to 20sek on the 10k.

Good luck!