By Jiacheng Ren and Haolin Wang
Go Dores: Final Shot Strategy proposal
BY Jiacheng Ren and Haolin Wang
All Vanderbilt Basketball fans have faced the situation like this: Vanderbilt Commodores was 2 point behind in the second half and we get the ball. There was only 15 seconds left to make the final shot. Shall we make a two-point basket to tie the game or shoot a three to end it now?
To answer this question, we must know the probability to score a two-point and a three-point shot. Apparently, it is relatively easy to take a two-point shot than a three pointer because it is easier to score when shooting nearer to the basket and the defense might be more focused on preventing us shooting a three-point shot. However, even if we made the two-point shot, we still have to play in the overtime game. Unfortunately, we have a very poor overtime game winning record, which would almost compromise our effort on making the two-point shot. On the other hand, we have top three-point shooters in the whole country. Perhaps, the chance of scoring a three would be slim since our opponent would put more attention on preventing us shooting a three. We might be better off to let our John Jenkins or Jeffery Taylor to win the game right away.
In order to find the best chance to win the game, we need to know the key factors that could possibly influence the result. According to Bill Hanks, a 32-year-experienced basketball coach, “the final shot by a team is dictated by five factors.” The first one is the time on the clock, which dictates how much time the shooter have for the final shot and how complicated your final play could be. We will ignore this factor in this project to simplify our analysis. The second factor is foul situation, and we will also simplify this factor by assigning a fixed probability of getting fouled based on Hanks’s experience. “The closer a player is to the basket, the higher the chance of a foul.” The third factor is the players. Assuming in this scenario, the players in the game are Jenkins, Taylor, Ezeli, Tinsley and Goulbourne. The table below shows the stats of the players. The fourth factor is the placement of the ball and the fifth factor is the defense. We will ignore these two by making assumptions in the scenario. In addition, we would like to add another key factor because what we are interested in is not only making the last shot, but also winning the game. This factor would be our overtime performance. By gathering data from the web, we can know the ranking of the two teams and our expectation to win in the overtime. Sadly, we lost all 3 overtime games this season.
Player FG% FT% 3P%
John Jenkins .474 .837 .439
Jeffery Taylor .493 .605 .423
Festus Ezeli .539 .604 .000
Brad Tinsley .474 .855 .415
Lance Goulbourne .456 .680 .309
First of all, we can apply hypothesis test on the overtime winning chance. H0 will be we have a 50% chance and HA will be the chance is less than 50%. For the shooting, we will run simulations which, for example, let Jenkins shoot 3 point for 100 times and let Ezeli attempt a close range shot for 100 times. We will also run a simulation to see if we get a foul or not. The approximate chance of foul can be concluded from the database of ESPN. At last, we consider all of our simulations and find out what’s the expectation of each different final play strategies.