# Scoring a race series

The Hocomock Swamp Rat just wrapped up the 7th bi-annual Grand Pricks series and Coach Guido has announced that this’ll be the last one (sadly, the HSR  is going away too).

Some people I know are thinking about starting their own series, and we were tossing around ideas on how such a series should be scored.  We’re talking about running, but the same thoughts can apply to biking or any other series of races.

First, you need to take a step back and think about what you want to reward. Totaling points up is the easy part – deciding on how to allocate points in an interesting way is the hard part.

In a race series, you want to reward runners in some fashion according to participation, speed, and if the races vary much, challange/difficulty.  I’d start by focusing on the balance between speed and participation. If the races are all on a track or all in a pool, difficulty doesn’t change much.  Otherwise, I’d use difficulty essentially as a tiebreaker. In a two race series, if two runners each win one race and finish last in the other, then the one who won the more difficult race should win out.

There are many ways to address the balance between participation and speed.  I’ll start with two.  Let’s call the first Plan A: You get “finishing points” according to where you finish in the race.  If there are 40 runners in the series, the winner in a race gets 40 finishing points, while the 40th (and last) runner gets 1.  Your “series score” is a percentage of the finishing points, based on the share of the races you finish. For example, with 40 runners in the series, runner A wins race 1 and gets 40 finishing points. He’s 1 of 1 in finishes, so he gets 100% of his points (40) for a score. Sadly, he misses race 2, so he still has 40 finishing points, but his series score drops to 20 (40 * 1/2). Now he wins race 3 (+40=80) and his score rises to 53.3 (80 * 2/3).

The other way (Plan B) is to add points for each race just for showing up. Suppose each racer starts with 10 attendance points. Then if 40 start, the winner gets 50 and the last runner gets 11.

The first is more complicated, but that might be fun. Essentially it means you lose points for not showing up, instead of staying where you were. More drama? Perhaps. Different, certainly.

I’d give finishing points based on the total of runners signed up for the series, not just the runners that show up for the race. In any race, the people that show up beat anyone who stays home sitting on the couch.  I’d give credit for that.  If 30 of forty show up for a race, first is still worth 40, not 30 (plus base attendance points, if any). 30th is worth 11, not one. Of course, you get 0 for not showing.

Personally, all else being equal, I’d like the person who shows up for all the races and finishes last every time to equal or just beat out the person who shows up only once and wins. Let’s assume 40 people and 5 races. Runner A wins one race and skips the rest. Runner B shows up for all races but finishes last every time.

With Plan A, Runner A ends up scoring 8 series points (40 * 1/5).  Runner B has 5 series points (1+1+1+1+1 * 5/5).

With Plan B, Runner A has 40 finishing points + (1*attendence points). Runner B has 5 finishing points + (5*attendance points). If you give everyone 9 points per race for showing up, Runner A scores 49 and Runner B scores 50, which is fine by me.

You can mix Plan A and B together and use both percents and attendance points to make things more fun!  Without any attendance points, Plan A weights attendance more than Plan B, so it takes fewer attendance points to even things out, if that’s what you want to do.

With Plan A, if you add in attendance points, you can add those attendance points in before or after you apply the attendance percentage.  Each attendance point counts more (and the numbers are simpler) if you add them in afterwards.

You can mix in difficulty by changing the number of attendance points or by assigning a difficulty multiplier to attendance points for each race. “Difficulty” is necessarily subjective, but that’s what makes this all fun.  This also lets you give bonuses for Rat traditions like nudity.

You can make all sorts of adjustments if you like.  For example, you can give extra finishing points to the winner to make first place worth proportionally more, if you think that everyone else is a loser of one degree or another.

Do you have any other thoughts or ideas?  Put them in the comments!

## 7 thoughts on “Scoring a race series”

• Jim Sweeney

FWIW, this is how the old CIVRA Series was scored. It rewards distance and participation as well as order of finish but necessarily against each other.

The percentile of your order of finish times the distance per race.

For example:
Runner 1 finishes 50th in a 5K with 1000 finishers:
Score = .95 X 3.1 = 2.945 points

Runner 2 finishes 623rd in the same race.
Score = .38 X 3.1 = 1.178

Runner 2 finishes 75th of 100 in a 15K
Score = .25 X 9.3 = 2.325 points

• rcharbon

Sweens,
So you’d have to run nine 5K’s to outweigh one marathon, or three 5K’s to match one 15K. And the runners who aren’t in the series affect the scoring. That doesn’t seem quite right. Of course, no system is equitable for everyone.

• Mark Kramer

Ah, Ray, it looks like you are about to be tossed on the horns of Arrow’s Impossibility Theorem.

Each race can be considered a preference vote or ballot for the runners. Even if you assume they are weighted equally, there is no “fair” system of determining the overall series winner. Much has been written on this paradox; I’ll just quote the first paragraph from Wikipedia:
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more discrete options, no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a certain set of criteria. These criteria are called unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of election theory as it is further interpreted by the Gibbard–Satterthwaite theorem.

In short, no “fair” voting system can be designed to satisfy these three criteria:

If every voter prefers X over Y, then the group prefers X over Y.
If every voter’s preferences between X and Y remain unchanged when Z is added to the slate, then the group’s preference between X and Y will also remain unchanged.
There is no “dictator”: no single voter possesses the power to determine the group’s preference.

• rcharbon

Now my head is spinning. I suppose in summing up a race series to declare a winner, we’re “converting the ranked preferences of individuals into a community-wide ranking”, if you consider the races to be the individuals that make up the community. When one runner (X) beats another (Y) in a race, that’s a preference for X as expressed by that race.

Sure, there’s no “right” system. Instead, there are systems that are better (or worse) matches for the prejudices of the people who set them up, no matter how arbitrary those prejudices may be. My prejudice is that no one (X) can finish ahead of another (Y) in series of races by only showing up for one race, no matter how well X does in that one race, if Y shows up for every race. The rest is mere detail 🙂

• Dan Solomon

the best and obviously only way to do it is to allow me to do it on a purely adhoc basis centered in drug-addled hippie socialist fuzzy thinking tempered by a soupcon of running knowledge and fundamental fairness–let me know when you want me to start

• Bob

Here’s what you do, you make up a few scenarios:

Great runner that smokes the field in only one race
Good runner that only does a few races
Average runner that does a lot
Slow runner that does them all

Survey the group and see how they should rank, then design the scoring accordingly. At least this way, those with a stake get to determine the scheme. What does the group consider to be most important?

Maybe include penalties for missing races.

• Dave Camire

I like the way we score the Good Times Series. Other then age/gender grading I think it is the most equitable way to score a series.

In this series cumulative points will be totalled at the end. Points are awarded based on a relative merit for a performance based on the fastest runner. The winner receives 1000 points and lesser points are awarded to each finisher based on time. Points are computed by dividing a runners’ time into the time of the first place finisher then multiplying by 1000.