# Court Pace Index and its use in tennis

In tennis grass and hard courts are fast, clay is slow. This is a statement which is carved in the minds of even the most novice tennis fan. But what exactly proves this statement? Simply by pitching the ball on the court and measuring its speed is not enough. There are various hard turfs to choose from and different clay courts with varying speeds. Even the grass courts are of different types based on the type of grass used. So which is the fastest or slowest grass, hard or clay court and how can we get a correct interpretation of this stat?

Court Pace Index is a measure that looks into various factors and breaks down these entities in determining the speed of a court. If we take a mathematical viewpoint, CPI is calculated by the formula:
CPI=100(1-μ)+150(0.81-e) Where μ is the coefficient of friction and e is the coefficient of restitution.
Let us make our task easier by considering the different factors that laid down the basis of the formula given above.

1) Altitude
Higher the altitude, faster the court. This is because the density of air at a higher altitude allows the ball to drift quickly. Temperature also plays an important role as the true density of a region will change compared to its original altitude. The court speed is faster in Madrid even though its CPI is more when compared to Monte Carlo. Monte Carlo is played at 97 feet while the tournament in Madrid is played at 2,188 feet.

2) Temperature
Higher the temperature, faster the court. This is because air density is inversely proportional to the temperature. An increase in temperature will allow the ball to float in the air at a quicker rate. Consider the Australian Open where the intense heat drains the players. But its hard court usually generates a quicker pace compared to the hard court at US Open.

3) Indoor/Outdoor events
The indoor courts showcase a faster gameplay compared to the outdoor events. A major portion of this factor relies on the sub-type of the turf used. Speeds can vary on a Decoturf hard court, Plexicushion Prestige and Greenset Grand Prix court.

4) Type of ball used
The wide range of walls used and the amount of pressure loaded in them coupled with their core weight can affect their speed on the court. The ball’s behaviour can also depend on the manufacturer. A Wilson ball is usually faster than a Slazenger ball.

5) CPI itself
There are multiple courts that host a particular event. The average CPI of all the courts determines the pace rating of that tournament and not only the Centre court. Besides, the CPI is not a stagnant entity and can change every year. For example, Indian Wells’ CPI in 2016 was 30. In 2017, it has dropped down to 27.3 which indicates a slower court.

The CPI rating analyzes the speed of courts in five categories:
Category 1: Slow court: CPI <29Category 2: Medium slow court: CPI 30-34Category 3: Medium court: CPI 35-39Category 4: Medium-Fast court: CPI 40-44Category 5: Fast court: CPI >44

Based on the 2016 scores, Shanghai is the fastest among the Masters tournaments. In the grand slams, Australian Open is the fastest falling under the medium-fast category.

A drastic rise in the CPI score was observed in the World Tour Finals last year. Played om Greenset Grand Prix, this tournament was the second fastest in terms if court pace after Shanghai. Here is a comparison data of the World Tour finals’ CPI held in the past few years.

All statistical analysis considered, it may seem that ultimately it all comes down to the way the courts are fabricated. The range obtained for different types of hard courts, clay courts and grass courts are a test to a player’s adaptability.