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:

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.