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Dynamic Programming in Sports

What is dynamic programming

It was introduced to us as a solution to the problems where we are unable to use greedy algorithms. The key point to apply dynamic programming in problems is to look at whether we are to break problem into smaller subparts and those subparts ends up in some case that we can solve. Dynamic Programming is generally useful in cases where in problems we can identify 2 things

1) Overlapping Subproblems 2) Optimal Substructure

If the problem doesn’t have Overlapping subproblems there is no use of dynamic programming In DP problems we need to find relationships among the participating entities that will server the purpose of dp transitions, define the dp state. DP state defines what our state at that given instance means.

To show how dp can be applied in the field of sports i have chosen the following situations, these situations are cricket and tennis

1. Predicting the score a team will make depending upon the overs left and wickets in hand. ex1
2. The way batsman should play to maximize run rate. ex2
3. The way batsman should target different balls to maximize run rate. ex3
4. Probability of chasing down the target with the given constraints. ex4
5. Serving analysis for games like tennis. ex5

Further Scope

1. An advanced win predictor, in example 4 i have made a simple win predictor but it can be improved by taking more factors into considerations. These factors are
   1. Recent form and the capability of the upcoming batsman.
   2. Recent form and the capability of the bowlers are expected to bowl.
   3. Record of the team while defending or chasing, this means a team might easily score 200 in first innings but might fail to score in 2 innings because of pressure of other factors like dew
   4. Average scoring rate of the grounds in example 4 the data is for 3 grounds and those have similar kind of pitches so this formula wouldn’t show efficient result when used in some other ground.
2. The combination of probability and dynamic programming is quite lethal, we have used it to make a strategy for batsman a similar can be done for a bowler where they have some strength and different bowls. A type of a delivery will result in decreasing the strength of the bowler and there would be expected runs that can be scored on that bowl. We would like to minimize the runs scored in his over that would be our ideal strategy.