Statistical Skier

That was the question in a comment I got the other day.

So here’s the situation. Devon Kershaw currently has 953 WC points, Petter Northug has 1199. Northug is apparently going to skip the next two weekends of WC racing in order to prepare for the Vasaloppet. Could Kershaw catch and overtake Northug in that time, and then hold onto second place through the rest of the WC season?

There is a ton of uncertainty in answering questions like this, so bear with me as I make some assumptions. Specifically, let’s assume that,

• Northug skips the WC races in Poland and Lahti, and also the Drammen sprints, but contests every remaining race on the schedule.
• Kershaw skis all the remaining races on the schedule.

Northug will be missing three sprints and two distance races. The remaining races consist of one sprint (Stockholm), three distance races (Oslo, first two stages of World Cup Final) and the World Cup Final overall stage results. (I’m not quite sure why the final handicap start stage of the World Cup Final isn’t listed in the WC points PDFs. In keeping with FIS’s sclerotic approach to race formats and scheduling this would be the only stage race event that doesn’t award WC points.)

So presumably Kershaw would have to make up the point gap, plus some breathing room since we probably can’t expect him to beat Northug in every remaining WC race.

The gap is currently 246 WC points. How many points above this would he need to feel safe in keeping Northug at bay?

So far this season when they’ve raced directly against each other, Northug has scored an average of about 13 more WC points per distance race and around 6 more WC points per sprint race. (I checked whether I needed to track point differences in regular vs stage WCs separately due to the different point scales, but the numbers turn out more or less the same.)

Naively carrying that forward would suggest that Kershaw would need a cushion of at least 45 WC points, not including the WC points awarded in the WCF overall. If we assume that Kershaw is unlikely to finish ahead of Northug in those overall standings, we’d need to tack on another 20-30 WC points as a conservative estimate.

So at the end of the day, let’s call that a grand total of around 315 WC points that Kershaw would need to pick up in the next three weekends alone.

That would mean averaging around 63 WC points for each of the next five races, through Drammen. (Third place is worth 60 points.) So if Kershaw really wants to control his own destiny here he doesn’t have much room for even the occasional 4th or 5th place finish.

However, due to the extremely non-linear nature of WC points, small changes in each athlete’s schedule, or a handful of unusually good or bad performances could alter this number considerably.

Suppose, for instance, that Northug wrecks himself in the Vasa, and develops some sort of minor illness. Then when he returns he’s a little flat and and has 1-2 really poor performances, outside the top 15. In this scenario Kershaw would have to pick up fewer WC points than the current gap of 246, since he’d still be outscoring Northug in the final four races.

So if you toss the assumption that Northug will continue to ski as well as he has the rest of the season, things look vastly more optimistic for Kershaw. He could conceivably only need to pick up 200 WC points while Northug is absent. He could probably do that in five races with a string of top tens, and the occasional podium.

In the end, though, you sort of have to put your money on Northug here. As the guy with the lead at the moment, and also just the stronger skier overall, he’s the one with the room for an occasional bad race or misstep. No matter what Northug does, Kershaw’s the one who’ll have to ski more or less flawlessly in basically every single remaining race. Which doesn’t leave much room for error.