Now we're going to look at the relationship in English football or soccer as it's called in North America. Here we've got a slightly different problem with the data we're going to look at. In order to have more data, we can look at teams playing across different competitions at the same time. Now that's not something we could do with baseball. For example, if we wouldn't be unlikely to look at the same relationship between major league baseball and minor league baseball at the same time. Minor league baseball is a lower level of baseball competition and we wouldn't tend to mix up the data from two competitions. But in soccer, we might be actually tempted to do that. One reason is the phenomenon of promotion and relegation. Teams move between levels from season to season based on performance, the best teams in a lower-division are promoted and replace the worst teams in a higher division each year. In some sense, we can think of the hierarchy of leagues in soccer as being related to each other and in fact, in some sense, participating in the same competition, particularly if we look at competition over time. Here we're going to look at English soccer, and we're going to look at the four divisions which are connected through the system of promotion and relegation. We're going to see whether we have the same pythagorean expectation in relation to this data. Again, we follow the same processes we followed before. We'll load the packages, and then we'll load the data. You can see here that we have actually a rather stripped down form at the data, so we've got a relatively small number of variables. Let's look at the variables we've got. Again, for each team we've got the games played, the home team, the away team, the goals scored, the goals against, and the result. But remember also here in the game of football, unlike most of the other sports we've looked at, a draw or a tie is a very common occurrence. The results here are H, that means home win, A, away team win, or D, that means a draw or a tie and we have a lot of those games. The other thing to notice is we have the first column here is DIV means division, and then the EPL means English Premier League, and then at the bottom here you can see FL2, which means Football League 2, there are in fact four divisions in our data, and we've combined all of those in one dataset, so we have 2,000 rows. Again, a nice large dataset of the similar to what we had with baseball and basketball. Now what we're going to do is we're going to code the value of the result. Now we're going to have three results in our data. We're going to have a home win which will give a value of one, or we could have an away win which would have a value of zero for the home team. Obviously a one for the away team if they're the winners, and then the third possibilities we can have a drawer or tie and we're going to get that a value 0. We're going to call a draw equal to half a win. Using that convention, we can then construct win percentages as well in the world of soccer. Let's run that and create these variables. We're going to have the count variable again in order to see the number of games played. Now, we're back in the world that we were in in the first two sets of analysis when we looked at baseball and cricket where we've got each game is a single row, so we have to sort out the performance of each team as a home team and as an away team. You can see here the value for each team's performance across the season. We're looking at the number of home wins, games played at home full-time, home goals scored full-time, away goals scored, and so forth as the home team. We got 92 teams in total in the dataset, that's the all of the teams in the four divisions of the league competition. Now we do the same thing, the mirror image for the teams. As away teams again, we've got the team names and the games played. The number of away wins, goal score, goals against. Bearing in mind, we've got now draws as half wins in this dataset and we now do the merge where we put these two things together. We now have our combined values for wins, games played, goals for, goals against, both as home team and away team. We add those up to give the total number of wins, total goals, total games played, total goals scored, and total goals conceded. We have that as we did in baseball and cricket. Then finally, we create the values for win percentage, wins divided by number of games scored plus the Pythagorean expectation, goals scored squared divided by the sum of goals goals scored squared and goals conceded squared. Then we have our DataFrame, again the same format, but this time now we have 92 teams in our dataset. We can do a rail plot again here. What we can do is add something extra in our row plot. Because each of these teams come from a different division, potentially, we could actually code that in our data and create a plot which shows each division as a different color in the DataFrame. If you actually run this here, then look at what we get. You can see here it's color-coded and allows us to see where each team in each division is located on this chart. But once again, we get the very clear relationship that we saw in the baseball and basketball data. We see this very strong linear relationship between Pythagorean expectation of win percentage. In our soccer data, even though the structure of the competition is rather different, we see exactly the same relationship emerging. When we run our regression, again, we look at the coefficient on Pythagorean expectation, we have a value for the coefficient and we can see it's statistically highly significant. We have a very large T-statistic and a p-value of 0.000 again. When we look at the R squared up here, we can see an R squared of 0.93 for which tells us that our Pythagorean expectation is capturing a very large fraction, almost all the variation in lead position that we can find. What we've shown this time is that again, even if we look at a very different competition we look at the world of soccer, we still find the same relationship we found in baseball and basketball which is telling us really this Pythagorean expectation seems to be a fairly common feature of all sports and the only outlier appears to be cricket data. What we're going to do next is something a little bit extra compared to what we've done so far. So far, we've said that Pythagorean expectation seems to be a pretty good proxy for winning if you want to know whether a team is winning, but you don't know the number of wins, but somebody tells you the Pythagorean expectation, you wouldn't be a far wrong in most cases from saying, well, the winning percentage is probably close to their Pythagorean expectation. But that's a rather backward-looking way of thinking about it. We are thinking about looking at past performance. What about the future? Could we use Pythagorean expectation to predict what the outcome is going to be of games in the future. That's what we're going to look at in the final session of this week, we're going to look at seeing whether we can use this as a forecasting tool.
