So we've looked at two sports, baseball and cricket, and now we're going to run exactly the same exercise. Look at the relationship between win percentage and Pythagorean expectation for a third sport that is basketball. We're going to use NBA data for the 2018 season. So, and we're going to use exactly the same process as we used in the previous two cases. So let's get going. So, first, we load up the packages, next we load up the data. This is slightly different data frame here and we have all of the games for each team in each season. And what we have here is the various statistics relating to the performance of the teams. But we also have in this data frame, something to know. Each team appears twice for each game, first as the home team and then as the away team. So in that sense, we have twice as many rows as we have games. So whereas before we needed to separate out and create two data frames for home team and away team, actually, this has already been done for us in this data set. That's a difference that it's worth remembering as we move on. You can either have a data frame, which identifies an individual game where you have two teams. And then, if you want to measure the performance of each team, do you need to separate them out? Or you have a data frame where each game appears in two rows, one for the home team and one for the visiting team. So, in this data frame, we have two rows for each game. So also, this data frame includes more data than we need, and we just want to focus on regular season NBA games. So we take that subset here, we can see the list of variables that we have in our data here. Again, we've got many more variables than we need. We're also going to drop rows with missing variables. We don't want to include those in analysis, and so we can drop those here using dropna. And then we identify each game where the team wins with the value one, which means that, of course, it's either win or lose situation. So that is way, if you didn't win, you have a zero, which represents a loss. So that enables us to count up the statistics and the values for each team. So now here, instead of creating dudes two data frames and merging them. We actually can create just one data frame using a group by for team name, with the results for each team, the points scored and the points against again, it's a sum. But we don't need to do the teams as home, team and away team because that's already been sorted out for us. So we just have a list of teams again. This list is going to be 30 rows long term. So, now we look at the data, so we've got actually 29 teams, so we have one missing team in our data here. But that doesn't matter too much in this context. And we have the result, the number of wins for the team across the seas, the number of points scored and the number of points against. And out of that, we can create the win percentage again. Every team plays 82 games, so the win percentage is just the value for the result divided by 82. And we have the Pythagorean expectation, which is as before, points scored squared divided by the sum of points scored squared and point conceded squared. So we have our data in the format that we want to analyze it. And so we do the same things we did before. Now, with our statistical analysis, we first run a rail plot to see what the relationship looks like. And you can see that list looks very similar now to the baseball example. Not at all like the cricket example. And if we run our regression, you'll see that the regression results are also rather similar to what we found in the baseball case. We can see here the coefficient on the Pythagorean expectation. We can see a very large t statistic and a P value of 0.000 which essentially means this is highly statistically significant. And we have up here in our square 2.943, so, and even closer fit in that sense than we saw with the baseball data. So in that sense, we found that when we look at the NBA, we get a very similar result. And maybe that's because again we have similar amounts of data to the amount that we had in baseball. Or maybe it's because again, the scoring rules work more like baseball than they work like crickets. So again that gives us pause for thought is what might really be behind the relationship that we observe here. So now we've done three sports. Let's look at one more. Let's look at english football and see what the relationship looks like there.
