Probability in Field Hockey

I have decided to center this mathematical exploration around the topic of sports and more specifically field hockey. When trying to decide on my exploration topic, my teacher advised me to think about things I am passionate about that I would enjoy spending time doing research on. Sports is something I am very invested in and when I thought more about that topic, I was immediately drawn to the idea of statistics in my current sport, field hockey. With my field hockey team's state championship game coming up, I kept contemplating how math plays into field hockey and the outcomes of games.

However, I wanted to go more specific than just how to predict who will win a field hockey game. Since scoring goals is so important in field hockey, I decided to investigate how math and statistics play into the success of a goal being scored. Is it possible to determine the best factors for a shot to be successful and score a goal?

I first thought about the factors I wanted to consider in my exploration such as frequency of shots and location of the shot. Does the number of shots at goal impact the number of goals scored in a game? And does the angle of the shot from the goal cage impact the success of that shot going in? In this exploration, I am to investigate how the number of shots taken in a field hockey game and the angle of the shot taken from the goal affect the probability that the shot will be scored in order to determine the ideal location and frequency of shots taken. To investigate this I amusing data that my team collected on shots taken and goals scored in that game throughout our recent past season. I am also using research done on angles in field hockey to help predict the best tangle for the shots.

There are other factors that go into whether a goal is scored or not such as the speed of the ball and the number of players around goal cage; however, I am choosing to focus only on frequency and angle of shots. Through this investigation, I hope to determine the ideal number of shots taken in a game to predict a certain goal number outcome and the best place to take these shots from on the field. The Game of Field HockeyField Hockey consists of 11 players from each team, including a goalie, with two teams playing against each other on the field at once. The game is played on a field with a length of 100 yards Alexanne O'Delland a width of 60 yards with two 25 yard lines and a centerline. The goal cages are7 feet high and 4 yards wide. The radius of the semi-circle is 16 yards which are measure from an imaginary center point of the goal line to the outside points on the semi-circle.

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