On The Line

Sometimes odd detail captures my attention and offers up what I think maybe is a puzzle, though it is not one to anyone else.  This post will illustrate.   I watched a good deal of tennis on TV last week.  I saw both of the Williams sisters matches when losing to Karolina Pliskova, who is a very gangly player but also a very effective server.  I also saw the women's final where Pliskova lost to
Angelique Kerber.  And I watched the men's final between Stan Wawrinka, the eventual winner, and Novak Djokovic, the number one rated men's player.

In this post I will focus on the use of a 'challenge' by a player to question the ruling by a lines person or by the umpire that was unfavorable to the player.  Each player gets a quota of challenges per set, I believe there are 3 of those.  If the challenge goes against the player, that challenge has been used up.  If the player is right, the player gets to keep the challenge.  Near the end of the set a player might use a challenge simply to get a bit of a breather, knowing that the challenge will be lost.  The set is near conclusion and getting the breather is a good tactical move.  Earlier in the set, challenges are a scarce commodity so they are hoarded unless the player feels an injustice has been done.  Then the challenge is used to right a seeming wrong.

Unlike in pro football where humans arbitrate the challenge based on the video replay, in pro tennis the challenge is entirely technology mediated, by a system called Hawk-Eye.  For the fan watching the match on TV, or on the big screen at the stadium, Hawk-Eye shades in a bit of the tennis court, presumably where the ball touched.  If the shaded area overlaps the line, the ball is called in.  Otherwise, the ball is called out.  Hawk-Eye has the last word on the matter.  The announcers treat that last word as if it is infallible.  Here I'm wondering if such deference is warranted.

In particular, both during the semifinal match between Serena Williams and Karolina Pliskova as well as during the final between Pliskova and Kerber, Chris Evert, a truly great player in her day and now one of the announcers who called these matches, consistently saw balls as out that Pliskova would challenge and that Hawk-Eye would confirm were in, sometimes by only a sliver.  Chris Evert talked about her failing eyesight.  She's older than I am, but by less than 1 month.  I can identify with this sense that our skills are deteriorating but that our judgments are still basically sound.  So how can it be that Chris Evert and Hawk-Eye were in such discord?  And what is it that Hawk-Eye actually does to determine that gray shaded area that marks the court? 

There seem to me to be two issues that are related but distinct to consider.  The first is the duration in which the ball is in contact with the court.  The second is the part of the surface area of the ball that is in contact with the court during this time interval.  Mis-measurement of either of these can be a source of error.

And here is the fundamental problem, both for Hawk-Eye and for human judgement on the matter.  The view is from above, looking down on the court.  This is not determined by sensors at court level.  So some inference must be made, about when the ball touches the court and how much of the ball touches the court, based on the view from above.  (Hawk-Eye relies on 10 different cameras, but they are all from above.)  In a hypothetical world where there are sensors built into the court that track when the ball touches and how much of the ball touches, the shaded area might be different from what Hawk-Eye produces.

Now we've reached the limits of my knowledge of physics and all else that matters in this domain.  But I wonder if this particular technology is biased in a way that favors Pliskova.  She is known to hit a flat ball (one with less spin) and on her serve, in particular, she gets a different angle than most of the other women players because she is so tall.  Do these things matter?

Human judgment on these matters is marred not just by failed eyesight from old age but by something called parallax, that results because we're looking at this from an angle, not from directly above.   For Pliskova, who is taller, the angle is not quite as severe.  So she may be more accurate in her judgments than other players put into the same situation.  But parallax is still an issue, even for her.  Hawk-Eye relies on some triangulation algorithm from multiple camera views that presumably adjusts for the parallax, which is why it is trusted.

Moving away from the technology and toward the human side of the equation, I'd like it for Chris Evert to perform better in this dimension, as her being a contemporary would give me more of a sense that I can still do it and not screw up, whatever doing it means at the moment.  So here I'm rooting for Chris and against Hawk-Eye.  Who else will take up that cause?