## Thursday, December 01, 2011

### How To Handicap Defense In Baseball

Hitting and pitching, they both play a big role in how you should handicap a baseball game. The often forgotten and important piece of the puzzle is defense. Just how much does the removal or addition of a good defensive player effect the likely outcome (think win probability) of a single baseball game?

I am sure there are many ways of solving this problem. The method I am going to use is a theoretical one. First let's take a swag at how many runs per season a good defensive player saves over an average defensive player. I think 20 runs per season is a good conservative number for a good (think Brett Gardner) and a bad one (think Raul Ibanez) costing his team 20 runs per season.

20 runs over a 162 games averages out to around 0.123 runs per game. If we set our run environment to 9 runs per game, which is fairly accurate but the round number makes the math easier, we get a 50/50 game having 4.5 runs for both Team A and Team B. On Vegas with no juice this would be a -100/+100 game on the Money Line (ML). Now let's assume an average defensive player on Team A is replaced with a player who the only difference is, is that he is a +20 (runs saved per season) player. Team A now scores 4.5 runs per 27 outs but Team B now only scores (4.5 - 0.123) 4.377 runs per 27. Using the pythagorean formula for a quick and dirty win probability calculation Team A now has a win probability of 51.3853%. So his glove is worth approximately 1.39% win expectancy. On the Vegas ML the -100/+100 (no juice) line would now look like -106/+106.

This would mean that if we instead put a -20 run defensive player in, instead of the +20 player. We would see Team A get a 48.6147% win probability and be on the other side of the -106/+106 line, for a whopping drop in win expectancy of 2.46% in this example. Of course things are effected a little bit differently based on the run environment and type of pitcher pitching. An infielder in a low run environment game playing behind a ground ball pitcher will have a bigger effect on the game outcome than he would in a game being played in a higher run environment with a strikeout pitcher who sees very few balls put in play.

These are all things to take into consideration and each defensive replacement must be looked at on a case by case basis, but for a rough calculation replacing a great fielder with an average one will cost your team a little over 1% in win probability and replacing a great fielder with a very bad one will cost you around 2.5% in win probability, looking at defense only.