Sunday, January 7, 2018

In Defense of Jason Brown

Full disclosure: I've been rooting for Jason Brown to make the Olympic team for months. Ever since I saw he was planning a Hamilton routine, I've been dying to see that routine performed at the Olympics. So what follows is entirely, entirely self-serving. I'm aware of that.

The U.S. National Figure Skating Championships just concluded (except for ice dancing), and Nathan Chen won the men's event, which I knew would happen since he won the last one by 55 points. (Only 40 points this time.) Jason Brown... did not win, or finish second, or finish third. His free skate today was frankly kind of disastrous, and left him in sixth place. Tomorrow morning the three selections for the U.S. men's Olympic team will be announced, and sixth place is a long way back to end up making a three-man team.

But the U.S. figure skating authority say that they do not just take the top three skaters from Nationals. Instead they consider a "body of work" consisting of the following events:
  • 2018 U.S. Championships
  • 2017 Grand Prix Final
  • 2017 World Championships
  • 2017 Grand Prix Series
  • 2017 Four Continents Championship
  • 2017 Challenger Series
  • 2017 U.S. Championships
  • 2017 World Junior Championships
  • 2017 Junior Grand Prix Final 
Roughly speaking, this year's Nationals along with last year's GP Final and Worlds make up the top tier, the most recent GP series and Four Continents are the second tier, and the remaining competitions are third-tier.

Jason Brown did very poorly at the very most important event on this list. He finished behind Ross Miner (silver medal at Nationals) and Vincent Zhou (bronze), either of whom could make the team over him, as could Adam Rippon, who finished fourth (and got the rather strange pewter "medal"). But the rest of his body of work is significantly better than that of either Ross or Vincent. The same is true of Rippon. So it's easy to feel that the selection committee, in making sense of this mess, has to either treat Nationals as the only competition that mattered or give it no weight at all.

But that's what math is for.

Because I can't stop pondering the question of whether Jason should or will be selected, I thought I would construct a unified metric to try to evaluate each contender's total body of work and see who "deserves" the spot according to those metrics. Below are my attempts at doing just that.



Let's start with how each individual finish will be represented. We can't use raw score, because people haven't competed in the same number of events. It's not fair to just give Jason an extra 253.81 points for his performance at the Grand Prix Final, when neither Vincent nor Ross made that event. But at the same time it's not fair just to take each skater's average score, including say that mediocre 253.81 in Jason's figure: it's to his credit that he was at the GP Final and the others weren't. He shouldn't lose ground overall to them just because he didn't skate perfectly there.

So I think the thing to do is use ordinal finishes. But because this wants to be a cumulative stat, in order to use ordinal finishes we have to take the reciprocal. So you get 1 point for winning, half a point for finishing second, a quarter point for finishing fourth, etc. That's kind of arbitrary but it makes good intuitive sense, and it emphasizes finishing up at the very top compared to worrying about seventh versus eighth place, which feels right.

The next question is how to weight the different events. But I have a spreadsheet I can fiddle with so I can run lots of different models and see what pops out.

First, here's one that treats each Tier One event as being worth 3 points, each Tier Two event as worth 2 points, and each Tier Three event as worth 1 point. (For the GP series, that means one point for each of the two events.)
  • Nathan Chen, 12.5
  • Jason Brown, 3.345
  • Vincent Zhou, 3.361
  • Adam Rippon, 2.683
  • Ross Miner, 1.867
Jason makes the team!

Now here's one giving 2018 Nationals 9 points, 2017 GP Final 8 points, 2017 Worlds 7 points, 2017 GP series 6 points (3 per event), 2017 Four Continents 6 points, 2017 Challenger Series and Nationals 2 points each, and the two junior events 1 point each:
  • Nathan Chen, 34.167
  • Jason Brown, 8.75
  • Adam Rippon, 7.517
  • Vincent Zhou, 7.083
  • Ross Miner, 5.4
Jason makes the team!

All the assumptions I've made have been arbitrary, but they've also I think been fairly neutral. I've taken what the U.S. Figure Skating authorities have said they care about and used sensible numbers to represent those criteria. And under either assumption, Jason doesn't just make the team, he's in second. The question really seems to be whether Adam or Vincent should get the third spot after him (and sorry Ross Miner but you just aren't deserving). Now maybe you think that's unfair to Adam because he missed events last season with injury, not just poor performance. That's fair. But I'm not seeing an argument for Vincent over Jason.

Let's see, in fact, just what I have to do in order to build such an argument. Taking the graduated weighting from the second model, let's see how much I need to add to the weights for 2018 Nationals before Jason doesn't make the team.

Answer: 20. I need to weight Nationals at 20 points, out of what would then be 53 total points, before Jason misses the team by my metric. It's also now worth significantly more than the two other Tier One events added together.

Now maybe that's how it should be. Nationals used to be the only selection criterion, after all. Maybe it makes sense to weight Nationals as 50%, and everything else as 50%. (Which would make it Nathan/Ross/Vincent, no question.) But if Nationals is really just one of three Tier One events, that are all of roughly equal value, then I think it becomes tough to argue Jason doesn't deserve one of those spots.

We shall see. But I feel a lot more comfortable thinking that Jason maybe deserves one of the spots than I did before I sat down to do this exercise.

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