I wanted to develop a mathematical formula that would predict the probability of scoring a goal from anywhere in the soccer field. I kicked a ball many times from a single place to determine how straight I could kick. Then I created a formula based on statistics and trigonometry to calculate the probability of scoring from any distance and angle in the field. I then tested my formula by calculating the probability at eight locations and then going out to the field and kicking the ball from those locations. I found a good correlation between my formula and the actual results. However, I am having a hard time writing a hypothesis. I wrote three very different ones, and would like some advice as to the best way to write the hypothesis:
1.If kicking accuracy, the distance of the shot and angle from the goal affect the chances of scoring a goal, then a mathematical model can be used to predict the probability of scoring from any location on the field.
2.If the angle formed between the kicking location and the goal increases, my mathematical formula predicts that the probability of scoring will increase.
3.Once a player’s kicking accuracy is determined, the probability of scoring from anywhere in the field can be predicted mathematically using a formula based on statistics and trigonometry.
Thanks for your help, this is the last part of the puzzle missing, I hope I haven't done it backwards.
Writing a hypothesis for a math project
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MReis
- Posts: 1
- Joined: Tue Nov 24, 2009 7:37 pm
- Occupation: student 10th grade
- Project Question: Math Category: Can I develop a mathematical formula to predict the probability of scoring a goal from anywhere in the soccer field?
- Project Due Date: November 30
- Project Status: I am finished with my experiment and analyzing the data
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rgoelmsft
- Former Expert
- Posts: 25
- Joined: Fri Oct 23, 2009 2:31 pm
- Occupation: Software Engineer
- Project Question: n/a
- Project Due Date: n/a
- Project Status: Not applicable
Re: Writing a hypothesis for a math project
Very creative project idea; I love it.
There are a couple reasons you're having trouble coming up with a good hypothesis: 1.) You haven't chosen your independent or dependent variables. 2.) You did practically all of your experimentation before you decided what question you were trying to answer. This is not a bad thing ... just that you went about this a little differently than a typical science investigation project.
So, here's my suggestion. Just for a moment, forget that you've already done all this experimentation and developed a formula. Here are some ideas for interesting questions you might choose to ask:
1. In soccer, how is the probability of scoring a goal affected by the kicker's distance from the goal? (Independent variable is the distance from the goal.)
2. In soccer, how is the probability of scoring a goal affected by the kicker's angle facing the goal? (Independent variable is the kicker's angle.)
3. (or taking a slightly different approach) In soccer, how is a kicker's accuracy affected by the moisture on the field? (Independent variable is the moisture on the field.)
4. In soccer, how is a kicker's accuracy affected by the amount of ambient light available? (Independent variable is the amount of light.)
5. In soccer, is a kicker's accuracy correlated to his/her height, and if so, how? (Independent variable is kicker's height. Very difficult to isolate this variable though since you can't change somebody's height. Experimenting with different height players won't work since they'll each have a different amount of experience.)
6. In soccer, how is a kicker's accuracy correlated to the number of years they have been playing soccer? (Independent variable is the number of years playing the sport.)
7. In soccer, how is a kicker's accuracy affected by the amount of air pressure in the ball? (Independent variable is the air pressure.)
8. (... you get the idea ...)
Once you've chosen your question, THEN you're in a position to come up with your hypothesis, which is your guess as to what the answer will be. For example, for the above questions, an example hypothesis would read something like this:
1. In soccer, I predict that the probability of scoring a goal decreases as the kicker's distance from the goal increases. (Kind of an obvious one.)
2. In soccer, I predict that the probability of scoring a goal increases as the kicker's angle facing the goal increases.
3. In soccer, I predict that a kicker's accuracy goes down significantly when the field is wet.
4. In soccer, I predict that a kicker's accuracy is negatively affected by darkness.
5. In soccer, I predict that taller players are generally more accurate kickers than shorter players.
6. In soccer, I predict that players with more years of experience can kick more accurately.
7. In soccer, I predict that a ball that is inflated with a higher air pressure can be kicked more accurately than a ball with low air pressure.
Then, once you have your question and your hypothesis, you can design experiments and develop a procedure for answering your question using real data. I do not think you need to throw away all of your existing experimentation and your formula ... you should be able to find a way to incorporate all of that as part of your research. But my advice is ... don't use your formula as the starting point for developing your question and hypothesis.
(BTW, my advice above only applies if you are doing this project for a science class or science fair, where you are supposed to following the scientific method. If this is really just supposed to be a pure math project, then it's an entirely different story and we can discuss further.)
--Rajeev
There are a couple reasons you're having trouble coming up with a good hypothesis: 1.) You haven't chosen your independent or dependent variables. 2.) You did practically all of your experimentation before you decided what question you were trying to answer. This is not a bad thing ... just that you went about this a little differently than a typical science investigation project.
So, here's my suggestion. Just for a moment, forget that you've already done all this experimentation and developed a formula. Here are some ideas for interesting questions you might choose to ask:
1. In soccer, how is the probability of scoring a goal affected by the kicker's distance from the goal? (Independent variable is the distance from the goal.)
2. In soccer, how is the probability of scoring a goal affected by the kicker's angle facing the goal? (Independent variable is the kicker's angle.)
3. (or taking a slightly different approach) In soccer, how is a kicker's accuracy affected by the moisture on the field? (Independent variable is the moisture on the field.)
4. In soccer, how is a kicker's accuracy affected by the amount of ambient light available? (Independent variable is the amount of light.)
5. In soccer, is a kicker's accuracy correlated to his/her height, and if so, how? (Independent variable is kicker's height. Very difficult to isolate this variable though since you can't change somebody's height. Experimenting with different height players won't work since they'll each have a different amount of experience.)
6. In soccer, how is a kicker's accuracy correlated to the number of years they have been playing soccer? (Independent variable is the number of years playing the sport.)
7. In soccer, how is a kicker's accuracy affected by the amount of air pressure in the ball? (Independent variable is the air pressure.)
8. (... you get the idea ...)
Once you've chosen your question, THEN you're in a position to come up with your hypothesis, which is your guess as to what the answer will be. For example, for the above questions, an example hypothesis would read something like this:
1. In soccer, I predict that the probability of scoring a goal decreases as the kicker's distance from the goal increases. (Kind of an obvious one.)
2. In soccer, I predict that the probability of scoring a goal increases as the kicker's angle facing the goal increases.
3. In soccer, I predict that a kicker's accuracy goes down significantly when the field is wet.
4. In soccer, I predict that a kicker's accuracy is negatively affected by darkness.
5. In soccer, I predict that taller players are generally more accurate kickers than shorter players.
6. In soccer, I predict that players with more years of experience can kick more accurately.
7. In soccer, I predict that a ball that is inflated with a higher air pressure can be kicked more accurately than a ball with low air pressure.
Then, once you have your question and your hypothesis, you can design experiments and develop a procedure for answering your question using real data. I do not think you need to throw away all of your existing experimentation and your formula ... you should be able to find a way to incorporate all of that as part of your research. But my advice is ... don't use your formula as the starting point for developing your question and hypothesis.
(BTW, my advice above only applies if you are doing this project for a science class or science fair, where you are supposed to following the scientific method. If this is really just supposed to be a pure math project, then it's an entirely different story and we can discuss further.)
--Rajeev