Tuesday, May 12, 2009

What Are the Odds?

Now that we know how many bases a double is worth for each arrangement, let's figure out the average value of a double. In math terms, the equation looks like this, where B is the average number of bases hypothetical teammates advance on a double:

B = 0* (% nobody on) + 2.5*(% 1st) + 2*(% 2nd) + 1*(% 3rd) + 4.5*(% 1st and 2nd) + 3.5*(% 1st and 3rd) + 3*(% 2nd and 3rd) + 5.5*(% loaded)

The coefficients are just the number of bases teammates advance from each arrangement on a double.

We just need to find a way to figure out what those percentages are. Fortunately, ESPN has some ridiculous stat-keepers who record how many plate appearances a hitter gets with each baserunning arrangement. Unfortunately, they only do it on a player-by-player basis, nothing league-wide. (And league-wide is what I'm looking for.)

So...I just have to take a good cross-section of hitters across different leagues, at different spots in their batting order, and on both good and crappy-hitting teams. I chose to honor the following 6 hitters:

Freddy Sanchez (top/NL/crappy)
Luke Scott (middle/AL/decent)
Ryan Howard (middle/NL/good)
Orlando Cabrera (top/AL/decent)
Mark Ellis (bottom/AL/crappy)
Jason Kendall (bottom/NL/good)

Using their summed 2008 stats, I got the following percentages for coming to bat with the following arrangements:

Nobody on: 56.6%
1st: 17.5%
2nd: 9.7%
3rd: 2.9%
1st and 2nd: 6.4%
1st and 3rd: 2.3%
2nd and 3rd: 2.0%
Loaded: 2.6%

Now we can calculate that sum from above. The total number of bases that the average double is worth is... 3.25 bases. This is actually a little higher than what OPS tells us it's worth, which is about 3 bases (1 for OBP, 2 for SLG).

So that's how I calculated the number of Bases Advanced a double is worth. Later I'll post how many Bases each of the other plate outcomes is worth and show you all my formula for Bases Advanced.

Feedback is welcome! So if there's something you think I fucked up or overlooked, lemme know.

How Valuable Is a Double?

(...Or a walk, hit-by-pitch, single, triple, home run, stolen base, sacrifice, or non-strikeout?)

As I claimed yesterday, the value of a plate appearance is assessed by the number of bases a hitter moves himself and his teammates. Well, it's pretty easy to tell the number of bases a batter moves himself with any one of those actions. The hard part is figuring out how far teammates advance in an average plate appearance through each of those actions.

While watching a game, it's pretty easy to tell. When Mark Teixeira doubles home Derek Jeter from 3rd and Johnny Damon from 2nd, he's created 5 Bases Advanced (2 for himself, 1 for Jeter, and 2 for Damon). But we want to know how much a generic double is worth. In order to do that, we need to invoke some basic baseball knowledge and a little math.

The basic idea is this: there are 8 possible baserunning arrangements for a batter when he comes to the plate (nobody on, man on 1st, man on 2nd, man on 3rd, men on 1st and 2nd, 1st and 3rd, 2nd and 3rd, and the bases loaded), and we can predict how many total bases all runners will advance from each arrangement for a particular outcome at the plate. What we need to do is determine the probability that a hitter will come up in each of those situations, and then find the average number of Bases Advanced.

Take a double, for example. Obviously, the batter advances himself 2 bases. And the runners?
Nobody on: Uhh, there's nobody on. 0 Bases.
Man on 1st: Advances to at least 3rd base, scores 50% of the time. 2.5 Bases.
Man on 2nd: Scores. 2 Bases.
Man on 3rd: Scores. 1 Base.
1st and 2nd: Guy on 2nd scores, guy on first scores half the time. 4.5 Bases.
1st and 3rd: Guy on 3rd scores, guy on first scores half the time. 3.5 Bases.
2nd and 3rd: They both score. 3 bases.
Loaded: Guys on 2nd and 3rd score, guy on first scores half the time. 5.5 Bases.

But wait. We're not done. Now we need to know the odds that a batter comes up with each of those arrangements.

Monday, May 11, 2009

Bases Advanced

The object of baseball is to score more runs than the bad guys. Seems simple enough. But when it comes to evaluating individual players, we have a really, really hard time figuring out exactly how valuable that guy is to his team's ability to score runs.

The challenge of baseball statistics is to determine a hitter's contribution to the runs his team scores, irrespective of the performance of his teammates. Clearly, RBIs and runs scored are heavily dependent on your teammates' ability to get on base or drive you in. Therefore, a useful hitting statistic should somehow ignore what the guys in front of or behind you have done.

The other challenge is to distill totals like hits, walks, and home runs into the value they add to a team's ability to score runs. How valuable is a walk versus a base hit? How valuable is a stolen base?

I postulate that a hitter's value comes in his ability to advance both himself and his teammates around the bases, and that his value is directly proportional to the total number of bases both he and his teammates advance as a result of his plate appearances.

How to turn this idea into an actual stat...well, I'll get to that later.

Sunday, May 10, 2009

Welcome!

Welcome to my blog, everyone! This is a place for me to jot down my random baseball (or maybe non-baseball) thoughts, and for you guys to discuss them with me. It'll probably be a lot about strategy and statistics, but who knows, maybe I'll get adventurous and tackle the (ughhhh) steroid issue.

You all know I'm a Red Sox fan, but I'll try not to be too much of a homer. That said, I'll probably spend more time talking about the Sox than any other team, just because I know them better and would have more interesting things to say. Not that I expect you to find this interesting or anything.

But hey, hopefully I'll spark a little lively debate.