## Padre Differential July 11, 2011

Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , , ,

I was all set to fire up the Choke Index again this year. Unfortunately, Derek Jeter foiled my plan by making his 3000th hit right on time, so I can’t get any mileage out of that. Perhaps Jim Thome will start choking around #600 – but, frankly, I hope not. Since Jeter had such a callous disregard for the World’s Worst Sports Blog’s material, I’m forced to make up a new statistic.

This actually plays into an earlier post I made, which was about home field advantage for the Giants. It started off as a very simple regression for National League teams to see if the Giants’ pattern – a negative effect on runs scored at home, no real effect from the DH – held across the league. Those results are interesting and hold with the pattern that we’ll see below – I’ll probably slice them into a later entry.

The first thing I wanted to do, though, was find team effects on runs scored. Basically, I want to know how many runs an average team of Greys will score, how many more runs they’ll score at home, how many more runs they’ll score on the road if they have a DH, and then how many more runs the Phillies, the Mets, or any other team will score above their total. I’m doing this by converting Baseball Reference’s schedules and results for each team through their last game on July 10 to a data file, adding dummy variables for each team, and then running a linear regression of runs scored by each team against dummy variables for playing at home, playing with a DH, and the team dummies. In equation form,

$\hat{R} = \beta_0 + \beta_1 Home + \beta_2 DH + \delta_{PHI} + \delta_{ATL} + ... + \delta_{COL}$

For technical reasons, I needed to leave a team out, and so I chose the team that had the most negative coefficient: the Padres. Basically, then, the $\delta$ terms represent how many runs the team scores above what the Padres would score. I call this “RAP,” for Runs Above Padres. I then ran the same equation, but rather than runs scored by the team, I estimated runs allowed by the team’s defense. That, logically enough, was called “ARAP,” for Allowed Runs Above Padres. A positive RAP means that a team scores more runs than the Padres, while a negative ARAP means the team doesn’t allow as many runs as the Padres. Finally, to pull it all together, one handy number shows how many more runs better off a team is than the Padres:

$Padre Differential = RAP - ARAP$

That is, the Padre Differential shows whether a team’s per-game run differential is higher or lower than the Padres’.

The table below shows each team in the National League, sorted by Padre Differential. By definition, San Diego’s Padre Differential is zero. ‘Sig95’ represents whether or not the value is statistically significant at the 95% level.

$\begin{tabular}{|r||r|r|r|r|r|} \hline \textbf{Team}&\textbf{RAP}&\textbf{Sig95}&\textbf{ARAP}&\textbf{Sig95}&\textbf{Padre Differential}\\ \hline PHI&0.915521&1&\textbf{-0.41136}&0&\textbf{1.326881}\\ \hline ATL&0.662871&0&-0.26506&0&0.927931\\ \hline CIN&\textbf{1.44507}&1&0.75882&0&0.68625\\ \hline STL&1.402174&1&0.75&0&0.652174\\ \hline NYM&1.079943&1&0.58458&0&0.495363\\ \hline ARI&1.217101&1&0.74589&0&0.471211\\ \hline SFG&0.304031&0&-0.15842&0&0.462451\\ \hline PIT&0.628821&0&0.1873&0&0.441521\\ \hline MIL&1.097899&1&0.74016&0&0.357739\\ \hline WSN&0.521739&0&0.17391&0&0.347829\\ \hline COL&1.036033&0&0.81422&0&0.221813\\ \hline LAD&0.391595&0&0.38454&0&0.007055\\ \hline FLA&0.564074&0&0.66097&0&-0.0969\\ \hline CHC&0.771739&0&1.31522&1&-0.54348\\ \hline HOU&0.586857&0&1.38814&1&-0.80128\\ \hline \end{tabular}$

Unsurprisingly, the Phillies – the best team in baseball – have the highest Padre Differential in the league, with over 1.3 runs on average better than the Padres. Houston, in the cellar of the NL Central, is the worst team in the league and is .8 runs worse than the Padres per game. Florida and Chicago are both worse than the Padres and are both close to (Florida, 43) or below (Chicago, 37) the Padres’ 40-win total.