And of course we’ll plot the regression line.<\/p>\n
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1. Prepare the data.<\/h4>\n
Begin with the imports. We’ve worked with pandas<\/em> and Matplotlib<\/em> many times on the blog. Making a new appearance is SciPy<\/em>, which we’ll use for the regression.<\/p>\n The dataset can be downloaded from Kaggle<\/a>. It contains team stats from every NFL game going back to 2002.<\/p>\n Get started by reading the dataset and converting its Since we’re interested in calculating how turnovers affect the final score, we’ll set up the regression like this:<\/p>\n Notice we’ve arbitrarily decided to work from the perspective of the home team. This helps us avoid double-counting games!<\/p>\n Create two new columns to contain said variables.<\/p>\n After that, restrict the dataframe to the most recent 10 years of games. Football fans know how much the sport has changed throughout its history. Limiting analysis to the most recent decade, while not perfect, should better represent the modern game while still providing plenty of data points.<\/p>\n Now it’s time to perform a simple linear regression. Doing regressions by hand is extremely tedious, but with Python it’s as easy as passing two iterables into Pass the appropriate dataframe columns into If you print This means each turnover is worth about 4.5 points<\/span> to the final score margin.<\/strong><\/p>\n Be careful not to interpret it as a causal relationship. Although turnovers almost certainly cause<\/em> a change in the final score, it would be overstating the capabilities of our methods. Strictly speaking we’re only observing the variables’ correlation.<\/p>\n Also notice that Next we’ll plot all data points along with the regression line. Start by creating a pair of lists to hold the regression line data. A straight line only really needs two ordered pairs. We can use The Matplotlib<\/em> code is fairly straightforward. We create two axes<\/em>, one each for the scatter plot and line plot.<\/p>\n I like to use a square window for regressions: A few more notes about the figure:<\/p>\nimport pandas as pd\r\nfrom scipy.stats import linregress\r\nimport matplotlib.pyplot as plt<\/pre>\n
date<\/code> column to datetime format.<\/p>\ndf = pd.read_csv(\"nfl_team_stats_2002-2020.csv\", parse_dates=[\"date\"])<\/pre>\n
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df.loc[:, \"turnover_margin\"] = df[\"turnovers_away\"] - df[\"turnovers_home\"]\r\ndf.loc[:, \"score_margin\"] = df[\"score_home\"] - df[\"score_away\"]\r\n<\/pre>\n
df = df[df[\"date\"] > pd.Timestamp(\"July 1 2011\")]<\/pre>\n
\n2. Linear regression.<\/h4>\n
scipy.stats.linregress()<\/code>. This function returns five values but we’re interested in three:<\/p>\n\n
slope<\/code>\n\n
intercept<\/code>\n\n
r_value<\/code>\n\n
![\"\"](\"https:\/\/wollen.org\/blog\/wp-content\/uploads\/2021\/09\/regression_equation-300x56.png\")
<\/a><\/p>\nscipy.stats.linregress()<\/code>:<\/p>\nslope, intercept, r_value, p_value, std_err = linregress(df[\"turnover_margin\"],\r\n df[\"score_margin\"])<\/pre>\n
slope<\/code> and intercept<\/code> values you’ll find:<\/p>\nslope = 4.53\r\nintercept = 1.96<\/pre>\n
intercept<\/code> is clearly non-zero. That’s because we’re analyzing the data from the perspective of the home team. In the NFL, home field advantage is worth a couple points. In a game of two equally matched teams with no turnover advantage, you’d expect the home team to be favored by approximately 2 points.<\/p>\n
\n3. Plot the data.<\/h4>\n
min()<\/code> and max()<\/code> to easily match a line to the scatter plot.<\/p>\nx_regression = [min(df[\"turnover_margin\"]), max(df[\"turnover_margin\"])]\r\ny_regression = [n * slope + intercept for n in x_regression]<\/pre>\n
figsize=(8, 8)<\/code>. And whenever possible, locate (0, 0) at the center of the window. In other words since the x-axis extends to +7, it should extend to -7 as well.<\/p>\n\n
alpha<\/code> (transparency) to scatter plots when there are many overlapping points.<\/li>\nwollen_dark<\/code> style. It will be linked at the bottom of this post.<\/li>\n<\/ol>\nplt.style.use(\"wollen_dark.mplstyle\")\r\n\r\nfig, ax = plt.subplots(figsize=(8, 8))\r\n\r\nax.scatter(df[\"turnover_margin\"], df[\"score_margin\"],\r\n color=\"#FFF\", s=30, alpha=0.5)\r\n\r\nax.plot(x_regression, y_regression,\r\n color=\"#D50A0A\", linewidth=3.0,\r\n label=f\"y={slope:.2f}*x{intercept:+.2f}\")\r\n\r\nax.set(xticks=range(-7, 8), xlim=(-7.25, 7.25), xlabel=\"Turnover Margin\",\r\n yticks=range(-60, 70, 10), ylim=(-62, 62), ylabel=\"Score Margin\")\r\n\r\nax.set_title(\"NFL Turnovers & Final Score | 2011\u20132020\")\r\n\r\nax.text(4.5, -36, f\"R\u00b2 = {r_value**2:.4f}\",\r\n {\"fontname\": \"Ubuntu Condensed\", \"fontsize\": 12, \"color\": \"#000\"},\r\n bbox={\"boxstyle\": \"round\", \"facecolor\": \"#FFF\", \"linewidth\": 0.25, \"alpha\": 0.9, \"pad\": 0.25})\r\n\r\nplt.legend(loc=\"upper left\")\r\n\r\nplt.show()<\/pre>\n
![\"\"](\"https:\/\/wollen.org\/blog\/wp-content\/uploads\/2021\/09\/nfl_turnovers_scoring.png\")
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