Discussion: Covid math problem - race format

Local race organizers have put on races with two different formats. In one format, people are started in waves ranked in terms of speed, say equal amounts of 5-12 minute mile pace runners, and in the other the waves are comprised of a random sample of racers speed.

Lets say there is one person in a field of 200 who has Covid, and racers are started in waves of 4 every 15 seconds, and the length of the race is 10 miles.

In which format is one more likely to to be exposed to the individual who has Covid? In which format is the exposure going to be longer?

Easy, as long as you have a fixed value for how long you need to be within a given distance of the virus carrier, or you could define this as a weighted distance, so that 1m or less is max risk, going down to zero at maybe 10 m behind. (Unless there is a tail-wind you will not be exposed to a carrier who is behind you.)

Integrate the risk/distance curve over the time it takes to pass, and you'll find that the risk is pretty much linear in the passing time. If you also have a hard cutoff like the "15 min within 2m" rule used for the Apple/Google tracking app, you'll quickly realize that the Covid risk from outdoors events is extremely low unless you run in tightly packed groups.
I.e. yet another win for orienteering, with individual starts and no real pack running, at least not within a meter or two.

But you'll only 'realize the risk is extremely low' if you accept the arbitrary app parameters. What do they really know? I'm personally using the '15 seconds within 2 meters' rule. Or less. Yes, it does make orienteering attractive.

Anyway, I didn't want to get bogged down in the details, just wanted to know if there was an analytical mind out there that could determine which model was generally more safe, assuming that proximity and duration are negatives.

The trains will both arrive at the station at the same time.

Graeme Ackland has probably already written a paper about this.

I almost had a first draft of the paper, but the optimal solution requires no drafting.

@graeme: NICE!
(And a Happy New Vaccinated Year to all of you!)

I like 'the trains will arrive at the station at the same time' meaning to me that both courses are risky. (boots on the ground observation: I think the pace-graded starts are the safer, if you are among the fastest or slowest especially, nobody passes you) The answer, my friends, is blowing in the wind.

The counter to that, of course, is that if there's somebody the same speed as you, then you stay near that person for the whole race in the pace-graded starts. In your example, everyone who is about the same speed as Covid Marvin spends a lot of time in his vicinity.

Best plan: interval starts, with the fastest going first. People the same speed maintain their spacing, and otherwise the field just spreads out. But that wasn't one of the options.

This is the standard challenge facing every organiser compiling the one minute start interval startlist for cycling time trials. As drafting is banned, the passed rider must allow the passing rider a 30m gap after they are passed, so that they gain no drafting advantage.

Participants provide the organiser with their PB. One solution is for the organiser to divide the entries into ten groups of similar ability, one of each group is placed in each of the ten minute blocks, and placed in that block to be away from riders of close ability. So the best riders start ten minutes apart, as do the worst, etc.

JJ, that is what I was trying to describe above. I apologize for my poor language skills! I totally agree. But that was not the model that was selected for one race. The objection was that while the potential frequency of exposure would be less, the duration of exposure could be longer. I don't necessarily agree, but that's how it was explained to me. They may not have considered that even if two runners are separated by just a few seconds in their mile pace, they will soon be a good distance apart after the start. If one runner ran 8 min miles and the other 8:16, after 100 meters or so they could be 4-5 meters apart, and they would have only run a few seconds together before they achieved the 'official' social distancing number. And start them 6' apart in the first place and even that goes away.

And if there's a stiff crosswind, all concerns may go out the window.