Tennis Statistics

Court Pace Index Explained

How Hawkeye Measures The Speed of a Tennis Court

In 2016 Tennis TV started publishing a new metric for showing the speed of the courts at the Masters 1000 tournaments: Court Pace Index.

Since then they've regularly shown us the data at each tournament, often with a comparison to the speed of the same tournament last year and to other Masters 1000 venues during the season.

You can see a screenshot of the data below which in this example was showing the speed of 2018 World Tour Finals compared to previous years:

London-Updated

What is Court Pace Index?

The court pace index is calculated from the coefficient of friction (forces pressing the ball and court together), and the coefficient of restitution (how much the ball compresses on impact). The mathematical equation is as follows:

CPI=100(1-μ)+150(0.81-e)

  • Where μ is the coefficient of friction
  • e is the coefficient of restitution

In simple terms,  it measures the speed of the ball right before impact with the surface and the speed at which it leaves the surface.

Does Court Pace Index Factor in the Conditions?

When I first saw the word ‘Index' I assumed that it had to factor conditions as that word implies it's covering absolutely everything.

However, now the formula is published we can see it only factors in the coefficient of friction and restitution so it's purely about the surface.

I'm not a physicist but I assume you could say it partly includes conditions as it's measured during real tournament play. But the conditions have basically zero time to impart any real difference on the ball as the speed is measured as soon as it leaves the surface. 

They do have the data to look at how conditions affect the ball though as with a big enough sample size across tournaments you could see how much speed a ball that was hit at the same point, speed, RPM and trajectory lost by the time it crossed the net for example.

Serves seem to make the most sense here as the vast majority of contact points are going to fall within a very small area. You could map Federer's serves from one tournament, overlay that with serves from another tournament, find near exact matches and compare how much speed they lost. 

Wind speed & direction, temperature, altitude and humidity. What else would need to be recorded for a fair comparison?

Hawkeye currently tracks and has the following data to hand:

  • Min/Average/Max ball speed
  • The speed of the ball at the contact point
  • The speed of the ball at the net
  • The speed of ball into/out of bounce
  • The speed of the ball at the baseline
  • The speed of the ball at the apex point

What other possibilities can you think of here?

Why Does The Court Speed Up During a Tournament?

One of the components of a tennis courts top coat is sand. This gives the court a rough texture and is used to dictate how quickly or how slowly a court will play.

A tennis court is always at it's roughest when it's brand new. When it is played on during a tournament, friction from the player's shoes wears the particles down making the surface smoother. A smoother surface is quicker as there's less friction when the ball makes contact with it.

How Does Hawkeye Work?

Hawkeye was originally developed for Cricket but it actually took off first in the world of tennis and has been officially used in Grand Slams since 2006.

It works via a system of ten cameras dotted around the tennis court, 5 at each end each filming at 60 FPS. The frame by frame footage these camera's collect is then triangulated to give the 3D location of the ball and can be used to determine whether the ball was in or out.

Because it's tracking every single shot across an entire match from when it leaves the racquet and when it bounces, it can also be used to calculate how the surface is impacting the speed of the ball.

Is Court Pace Index Different from the ITF's Court Pace Rating?

Yes.

Court Pace Index is calculated from Hawkeye data at the tournament itself.

Court Pace Rating is used by the ITF to categorise surfaces, essentially for people laying ITF approved courts at their venue or tournament. It's a buying guide, not a measure of speed at each tournament.

Just because the ITF classify Plexcushion as a certain speed, does not mean it's that speed at the tournament where it is used. The underlying surface, top coat, tournament requests, and many other factors can impact the surface. 

So whilst they are calculated similarly they aren't the same. The CPR of Court Pace Rating is usually done on a sample piece of the court with a Sprite or a Sestee in a lab setting. It's rarely done during a tournament or at the venue itself as the equipment is a.) expensive and b.) difficult to transport.

Is Court Pace Index Accurate?

Given Hawkeye operates with an average error of 3.6mm I'd say so. It might not be perfect but it's clearly the most accurate method of assessing the speed of a court right now in the world of tennis.

The only flaw I've seen to date is that the numbers aren't always the same on each graphic. For example, this year in London, the numbers shown had completely changed compared to the ones that had been shown in Paris 2 weeks earlier for the same tournaments. This was apparently down to a calculation error which was updated and the graphic shown in Paris revealed to be incorrect.

Questions? Corrections? Ideas? Let me know in the comments.

Jonathan

Huge fan of Roger Federer - I'll pretty much try and watch all his matches from Grand Slam level right down to ATP 250. When I'm not watching or tweeting about tennis I play regularly myself and use this blog to share my thoughts on Fed and tennis in general.

35 Comments

    1. In fact, after about 3 years without a title, this is my first title of 2018. A least I’m in elite company and I’m very happy. Obviously, it’s disappointing I did not win more but 1 is better than 0. Perhaps the regular winners have been put on a silent ban by Jon?

      Maybe I’ll have a great 2019. 🙂

  1. I’m wondering what everyone thought of Hawkeye doing all the line calls in Milan? Should the ITF get rid of lines people? What if the system fails?
    Thanks for the post, Jonathan. I thought you were on holiday in the Maldives.

  2. A bit of physics: first and foremost, courts are neither “slow” or “fast” because they don’t move at all. haha. Moving objects are.

    Second: the coefficient of restitution determines how high the ball bounces. It is lower on surfaces that deform in a plastic way (think of plasticine). Best example: grass. It is higher on very hard surfaces that don’t deform and is also high on elastic surfaces (think of a trampoline). Clay is a high bouncing surface because it compresses vertically very little.

    Third: the friction coefficient is more tricky to explain. In fact there are two of them.
    -The static coefficient is what you feel when your shoe soles are stuck to the ground. It also the one that causes the racquet strings to spin the ball. It’s high on “sticky” surfaces and low on “sliding” surfaces. If it is high, it also causes the ball to invert its backspin to topspin at bounce: a lot of inversion on sticky surfaces, very little on sliding surfaces. See grass: Fed’s slices are deadly on grass because the ball bounces with very little inversion (if at all) of its initial backspin. Combine that with the low bounce and there you have it.
    -The dynamic coefficient: this is what you feel when you are sliding (both surfaces moving relative to each other). It is the phenomenon where the ball energy is lost. It is the lowest on grass. It’s higher on hard courts. On clay it’s different matter because the loose particles act as rough bearings that dissipate a lot of the ball energy (both linear speed and spin). That’s why almost every shot on clay is a rally reset: aggressive players have a hard time because the surface dissipates most of the energy they put on the ball. Does this sound familiar?… RG, anyone?…

    Finally: the more different the two coefficients are (static and dynamic; the latter is *always lower*), and also the higher the static one, the more you are likely to injure yourself. Think when you are sliding: as you slow down, suddenly the sole sticks and your ankle snaps. Ouch. If you can predict when the static coefficient takes charge, you should be fine and stop the slide before the slide stops you.
    On clay the two coefficients are closer to each other and it’s easier to control the slide. Less difference=less snap.
    Cheers.

    1. Nice.

      So how do you think Hawkeye could produce a true speed metric that factors in conditions? Is it even possible or are there too many variables?

      Assuming they can match X number of serves from one tournament to another that have the exact same speed, spin and trajectory, and wind speed is negligible, then they can work out how the other variables impact speed?

      So say an indoor event: If a serve was 120mph at both events. The temperature was 21 degrees and humidity the same. But one was 500 metres higher above sea. They could work out the impact altitude has?

      1. I think that there are too many variables. If you think about the spin solely, you need 3 variables: the angular speed (in rpm, Hz, doesn’t matter) and the orientation of the spin axis, which requires 2 angles itself. It seems to much gum to chew.

        To use the hawkeye data we should eliminate all the variables that it cannot measure, or better: make them constants from one experiment to the next.
        With no spin on the ball, constant temperature, pressure, RH, etc, a reduction in the linear speed (of the ball) after impact would fit nicely our perception as to what is a “slow” or a “fast” court.

        “Would” is the word, because there’s a monster lurking: consider a sticky hardcourt. Upon bounce, the ball will acquire top spin (it always does). This can *only* be done at the expense of the translation energy (I won’t write down the equations here… Suffice to say that the total kinetic energy is translation + rotation). If you hit a flat ball onto a sticky court, it will slow down. If you hit it with top spin such that the bottom of the ball has zero velocity relative to the ground, it will not slow down. If you hit it with backspin, it will slow down *a lot*.

        As for higher altitudes: all other things being constant, the lower air pressure and density would reduce aerodynamic drag, so, yes, the ball will be less braked by the air. It will also be a bit more inflated and bouce higher! (unless you use balls filled at a lower pressure…)

      2. “If you hit it with top spin such that the bottom of the ball has zero velocity relative to the ground, it will not slow down. ”

        What’s the science here? Surely any ball that bounces is decelerating after the bounce?

  3. Thanks Jonathan & Rui! Awesome explanation. Too bad physics wasn’t this interesting in school.

    It’s truly amazing how fast the top players are able to calculate all these variables as they move from game to game, court to court, tournament to tournament, surface to surface.

    1. I don’t think so. If you look across the calendar year, the surfaces aren’t much different in terms of terms of speed or how they perform. So there is very little adaptation required…. when did you last see a player really change their game across surfaces? Rarely.

      It’d be more interesting if the surfaces were variable, then it would be amazing to see how players cope. Right now it’s if you’ve played on one surface, you have played on them all.

      Sure little changes and you might make a tiny adjustment, but it’s certainly tiny. You can rock up to tournaments, and after a couple of practice sessions be ready to go.

      There’s perhaps only grass that needs more change with footwork, but even then the surface is so rock hard now that’s debatable too.

  4. Add barometric pressure? Effects would be similar to altitude, but where altitude is fixed, bary pressure is variable.

    Suspect it may be combinations of all the variables that have been discussed that result in the varying subjective impressions the players give of how the courts are playing. Rui has talked about some factors that might impact the ball’s performance upon bouncing. Actually that might be an interesting comparison – what changes do we see, say, in Fed’s serve stats day to day – is there measurable time to impact w racquet from toss, time to impact w surface from racquet strike? If as younsay you could compare those numbers in known-same-spit serves, you might get some usable info about the atmospherics – because up,until that first impact with the surface, of course, there’s no impact from the court itself at all. Then maybe you could subtract those non-court effects from observed effects that DO reflect ball performance. Dunno, does sound daunting.

    I’m thinking you did a post a while back that also talked about the balls themselves & the impact they had. I would expect barometric pressure effects to maybe be most felt with respect to the type & characteristics of the ball. Even more daunting.

    1. That’s why coaches repeat time and again “watch the ball”. If you do, your eyes, ears, hands, feet (in fact all your senses) will collect an amazing amount of information, and process it in real time at a lightning speed so you can react accordingly. Our bodies do know very well physical phenomena (you don’t need to speak or hear to ride a bike). In school we “just” formalize it mathematically and bring it to the conscious level.

      1. Nice! How amazing that the brain understands all this intuitively so beautifully. I remember having a very, very hard time with idealized rigid bodies alone during my first classical mechanics course in grad school, and we are talking about objects that change shape at will here!

    2. Yeah I’m thinking of more variables every time I think about it, and of course the balls make a difference too in terms of their weight, age of ball which I totally forgot when writing above.

      Maybe it just too complext to do with any reliability.

  5. I catched an article regarding the upcoming Hopman Cup 2019 yesterday.
    According to the committed players Fed’s Group B will be pretty competitive including
    – USA (Tiafoe)
    – Greece (Tsitsipas)
    – Great Britain (Norrie)

    compared to Group A including
    – Germany (A.Zverev)
    – France (Poullie)
    – Australia (Ebden)
    – Spain (Ferrer)

    1. There it is, the match of the millennium everone is waiting for: hot-headed Stefanos vs grumpy-old-Roger!
      Now, seriously, I hope Stefanos gets a grip on himself. Last time he nearly broke both hands on the pause between games (against Alex-the-Minotaur, if I remember well). And a headset met his creator…

  6. The court speed discussion takes us into serious tennis “geekdom”, especially with the detailed reference to some of the physics involved in the game. It largely confirms what we see during tournaments, but what it doesn’t – and can’t – tell us is how well players respond to the variation in conditions. Clearly, some are are more suited to certain conditions than others. Like quite a few here, I have become rather tired at the general slowing of court surfaces in recent years that have suited the attrition baseliners – especially the parade of claycourt specialists. However, the game variable that interests me the most, and the one that is at he heart of competition, is what goes on between the players’ ears. The great imponderable in any sporting contest.

    1. Yeah, for some of the players it seems that at times a big black hole develops between the ears!
      Other times it’s a short circuit, a power out, or fast neuron rotting…

  7. I think CPI is not worth a shit. Something for the public to watch and not understand anything. Bongo camera tells more 😉
    CPI is not a measure for court pace, but for a players mix. Let Lopez play Niculescu and then Nadal play Thiem or Federer play Djokovic. On the same court, one after other, so all conditions are quite the same. But the game is different. The same players mix can produce different CPI on same day, because something like standard match does not exist. And if Lopez plays Djokovic, Niculescu plays Nadal and Thiem plays Federer, the result will be different as well. CPR uses standard conditions with 1 player (machine) and the routine is the same for every court. Not the CPI. It measures two parameters and completely ignores, who is playing, has one a big serving day and serves at 140 mph or it’s bad day and he serves only 110.
    I would prefer to see CPI for a given player and a match. This could help me understand the game, no matter, how the court “plays”. Paraphrasing Rui – only players play, I have never seen a court playing something or one court playing directly another court. So we don’t need players at all. Hahaha …

      1. I know, what they are measuring. I knew it before but I have read carefully your explanation. Maybe I’m missing something. Are measurements made during real matches or just like for CPR,, using standard ball throwing machine? If they measure real game, it’s obvious for me, results are not comparable with other courts/tournaments, different years (because not only the court changes, the players mix changes and the way everyone plays changes too.
        If it’s so much worth for you to post statements about my understanding capability instead of explaining, what I maybe misunderstood, it’s up to you. Whatever.

  8. “The court pace index is calculated from the coefficient of friction (forces pressing the ball and court together), and the coefficient of restitution (how much the ball compresses on impact). The mathematical equation is as follows:”
    Are these parameters equal for every player and every shot? “Forces pressing the ball …” depend on the surface AND on the shot, so they are individual. Averaging them gives a result for given players mix and a mix of matches played. Next year another mix comes and everything changes even if nothing changed in the surface.
    Yes, thy measure what they call “court pace”.. This is not worth a shit even to compare Federer playing London in some subsequent years or even days/matches/opponents.

    1. Incredibly cynical and statistically you seem to be dismissing the notion of a big data average, which is very dangerous thinking.

      The CPI is updated across the tournament as play continues. So what you really see is a figure that starts during day 1 and regularly increases to peak on day 7 (as Jon explained). In other words, the more play happens, the larger the dataset used to generate the figures you get.

      No adjustment is made for courts speeding up, so the CPI increases across the week, but with negative curvature, because fewer matches get played day on day.

      What you seem to be saying is that it doesn’t take into account how players play, which is 100% true, but that doesn’t make it a worthless statistic. It just tells you on average across a week how much a ball slows down off a shot. Year on year the mixture of shot type and pace doesn’t vary that much when taken as a whole (again, seriously read up on summary statistics), so the numbers are perfectly reliable.

      As your next post obviously says, you seem to think this post was made to say “courts are slow so of course Roger doesn’t win”. Jesus, how blinkered do you think we are? You really don’t think people who love watching tennis might actually find some tennis information interesting? The stat doesn’t tell us much about who should win a given match. What it does say is on average how difficult returning a shot hit in exactly the same way with the same pace is. And that is definitely worth analysing.

  9. Court as such has no pace. Pace is an effect of the surface and the shot. If this is to be seen as an objective measure, it’s only good to explain, why Federer didn’t win – the court is guilty.

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