We always use this word, ‘hypothetical’ in multiple contexts in which we come up with an imaginary or a real-world problem and arrive at a solution by taking in multiple factors affecting that problem. When it comes to sports, we often knowingly or unknowingly talk a lot about hypotheses, where we either try and predict a team’s score or a player’s current form.

Rohit Sharma has been India’s backbone for the past 10 years and has been their most consistent opener since then. But there has been a decline in the consistency of his performances ever since the England series in 2021. His long list of injuries is also a factor in his declining performance, but India would definitely want him to regain his form with the world cup on its way.

### Hypothesis Testing

Let us have a statistical take on Rohit’s performance in the ODIs using the concept of Hypothesis Testing. This blog tends to get a bit technical but we have tried our best to explain in simple words. Hypothesis Testing refers to a statistical technique which is used to investigate our ideas or theories by using data. There are two types of hypotheses we use in this testing.

• Null Hypothesis: This is the theory or hypothesis that is going to be tested on whether it’s true or not. Our Null Hypothesis is – ‘Rohit Sharma is an In-Form batter’. Statisticians usually try to reject the null hypothesis and they accordingly formulate statements.
• Alternate Hypothesis: This covers everything else that is not covered by the Null Hypothesis and Statisticians usually try to accept the alternate hypothesis. Our Alternate Hypothesis is –  Rohit Sharma is not an In-Form batter’.

In order to conduct the hypothesis testing, we have 2 different methods, The Z-test and the T-test. We usually use the T-test when we don’t have the value of population variance (i.e: the variance in the overall population data) and we usually use the T-test if we have a sample population size of less than 30. Since we are considering only the last 10 ODI’s of Rohit’s career and since we don’t know the population variance (ie; variance of all his scores in ODI), we can use the T-test method.

We also have a term called significance level (alpha) which determines the probability that we reject the null hypothesis and this value is usually 0.05 which is considered to be a rule of thumb. Once we have determined this value, we have something called the T table from which we have to find the value corresponding to the number of samples and significance level considered. Using the table, we find out that the value is 1.833.

### T-test Implementation

Now, we use a T-test statistic and the formula is given below.

Here, X̄: sample mean, µ: population mean, S: sample standard deviation, n: number of sample size.

After performing the calculation based on Rohit Sharma’s sample performance, we find that the T-test statistic value is -1.937. Now here, this value lies outside the range of specified values i.e: it lies outside the range of 1.833 and -1.833 and thus, we can reject the null hypothesis. Since we are rejecting the null hypothesis, we are accepting the alternate hypothesis. Therefore, ‘Rohit Sharma is not an In-Form batter’ for team India in ODIs in recent years.

### Conclusion

What makes Hypothesis testing very interesting is that, according to stats, Rohit Sharma has a batting average of 37 in the last 10 ODI innings, but this test proves that the batting average metric doesn’t give a full picture of his impact for team India in recent times. When it comes to quality players like Rohit Sharma, A decent batting average of 37 could also imply that the benchmark set by them in their previous performances has been very high that his recent performances are considered to be below-par.