Reaction times in sports
M.V.N. Murthy, The Institute of Mathematical Sciences, Chennai

The world cup football fever has come to an end. Long after this world cup is over, we will be talking about some extraordinary goals, saves. Some images refuse to fade, like the Argentina's goal keeper Sergio Romero's extraordinary saves during the penalty shoot out in the Argentina - Netherlands semi-final match. You may also remember Messi's fraction of a second stop during the penalty kick which confused the Netherland's goal keeper. These are just some examples; there will be many more from this world cup as it was with earlier editions as with many other sporting events. The photo shows Sergio Romero stopping a goal kick in World Cup semifinal match between Argentina and Netherlands.
You may also be a cricket fan, then you will probably remember how Virender Sehwag smashes Dale Stein's scorcher of a ball in the first over. If you are an athletics fan, then you will remember Usain Bolt getting off the blocks as soon as the starting gun sounds.
In every sport, like tennis, badminton, table tennis, some images stick. Each of the event mentioned above, and many more, involve what is called the reaction time, or how fast does an athlete or a player responds to a particular stimulus to be able to play the game at his or her best. Often a difference of a fraction of a second is the difference between victory or defeat. These times can be calculated by simple physics using the distance and speed which are easily measured. It is a part of the sports training where science is used extensively to get the best out of people. Improving reaction times is just one aspect of the use of science in sports along with fitness regimes and such.
Let us look at football. In a penalty shootout how much time does a goal keeper have to be able to stop the ball? The shooter places the ball in front of the goal at a distance of 12 yards (about 11 metres, yes that is the unit used in football). A top class player like Messi or Muller would hit the ball at around 130 km/hour speed. This gives about 0.3 seconds for the goal keeper to stop the ball as you can easily calculate.
In cricket, with Stein bowling at 150 km per hour, the reaction time over a distance of 22 yards is about 0.5 seconds for a Sehwag or Sachin to react. Similarly in Tennis the fastest serve will be around 200 km per hour. If you do the math correctly, you will see that the person receiving the serve has about 0.3 seconds to return. Now you can do this for table tennis, badminton and many other games. In all these cases the reaction time available is around 0.3-0.5 seconds for the best of sports persons. In fact the game would be boring if the reaction time is much larger, of the order of 5 or 10 seconds.
Interestingly, these estimated reaction times are realistic though challenging even at the top level of competition. In fact it turns out that the best reaction times for males is around 0.15 second and for females it is slightly higher, around 0.20 seconds. As you may easily realise, the best is reached around the age of 20 for both genders. It is almost a plateau between the age of 25 to 40, on the average it is about 0.175 seconds, for males, as seen from the graph.
In general, the reaction times calculated above is only one of the many things to keep in mind. Let us go back to penalty shootout's in foot ball. We got a reaction time of 0.3 seconds just by knowing the distance and speed of the ball. But this is not all. The ball could head anywhere in the goal. Goals are placed at the centre of goal line. The goal posts are symmetrically placed 7.3 metres apart with a height of about 2.44 metres. So the goal keeper has to decide which way the ball is moving in this window and stop the kick. This places an additional demand on the reaction time. As a result many goal keepers resort to guessing which way the ball moves ahead of the kick and move accordingly.
The game of guessing involves lot of statistical analysis- what is the preference of the shooter, is he left footed or right footed, which way is he looking? This is what the Coaches or managers analyse by watching video footages of earlier games so that the goal keeper is well informed. Even after this there is an element of chance. Which is why stopping a penalty shoot is one of the most difficult things in the game of football.
These observed reaction times (averaged over large samples presumably) has an interesting application in Athletics and Swimming. Often athletes move very swiftly and get disqualified. You are not supposed to make any deliberate movement before the starting gun is sounded. In fact, if there is any response in less than one tenth of a second after the starting gun is sounded, the athlete or swimmer will be disqualified. This is called a false start. This is because such a reaction would necessarily involve a movement before the sound of the gun. Even the fastest sprinters like Usain Bolt have a response time that is slightly more than 0.1 second. An analysis was done on the reaction times of sprinters at the 2008 Beijing Olympics. The result showed that male and female sprinters can achieve reaction times of 0.109 and 0.121 seconds in one out of 1,000 starts. There were fewer false starts among female athletes than with male athletes.
Therefore in the science of Sports rapid reactions to visual or audio signals are considered extremely important. By analysing various aspects of skills and experience, the reaction times can be improved and hence performance can be improved.