(I do want to apologize beforehand for any confusion I may cause by this. I try my best to explain things that I think might be confusing for someone with less of a statistical background. I hope you all can get something good out of this and if you have any questions, don’t hesitate to ask me in the comments.)
Hello Everyone! I figured I would share this information with you. A while back I did a hypothesis test to see if Villanova, statistically, was a better shooter against us. What I found was discouraging to say the least. I ran three separate tests looking at Villanova's free throw shooting, three point shooting, and overall field goal
percentage. I gathered my data from Kenpom's website and went back three years to the beginning of Xavier's time in the Big East. I gathered in total the last 86 games Villanova played in, with the last game being Dec. 31st, 2015. Of the 86 games I collected, Villanova played us 6 times, and in those 6 games they averaged: 51.32%, 43.38%, and 75.48%, in field goal percentage, three point percentage and free throw shooting respectively. In the other 80 games, Villanova, on average, shot: 45.93%, 35.43%, and 72.98%, in field goal percentage, three point percentage and free throw shooting respectively. Using the above data, I ran a one sided , two sample T-Test to figure out if both averages came from the same mean. (Or in other words, I am testing to see if the shooting averages against Xavier fall within a reasonable range of Villanova's average).
What I found was Villanova, statistically, shot better against Xavier in their overall field goal percentage (FG%) and in their three point percentage (3PT%). At a .05 alpha level, I was able to reject the null hypothesis that Villanova’s overall FG% and 3PT%, against Xavier, was less than or equal to Villanova’s population average. (In other words, I can say that I am 95% positive that the two sample averages did not come from the same population and that Villanova’s overall FG% and 3PT%, against Xavier comes from a higher population average). Now with that being said, I do have to admit there is one problem with my test. Since I was unable to get 30 pieces of data between Villanova and Xavier, I cannot prove that this data is normally distributed around a mean or that it is not just random chance. I can say though, that in all of my years of doing hypothesis testing that it is very hard to pass a test at the .05 alpha level.
So know that I have dragged out all through the brutal statistical mumbo jumbo, I can ask you all why do you think this is the case? Xavier’s defense is susceptible to a hot shooter, but the odds of them consistently going hot against us was the point of my statistical analysis. There is something else wrong with this match up that allows for Villanova to shoot so well against us and it bothers me a lot. So at this point, I would love to hear you thoughts? Can y’all help me figure out why Villanova is a statistically better shooter against us?
(Also, I am sorry. I wanted to link my excel data to this post, but I have spent about an hour and I can't figure it out. So if anyone wants to see the data, I can e-mail it to you or hopefully learn how to post it for all to see.)