Wednesday, June 29, 2016

A Close-Up Look at the Baseball Statistic wOBA (Part 1)

Baseball statistics can give us important information about MLB players. Today, I will begin my discussion of baseball statistics, with a focus on wOBA, one of the more interesting baseball stats.

Various statistics have been used in MLB as indicators of a hitter’s “offensive value.” One such stat is batting average, which is the number of Hits divided by the number of At Bats.

A more recent — and more sophisticated statistic — is OBP (On-Base Percentage). It adds walks, hit by pitches, and sacrifice flies to the batting average formula. OPB is calculated by adding Hits, Walks, and Hit by Pitches and dividing that sum by At Bats, Walks, Hit by Pitches, and Sacrifice Flies.

Another more recent — and even more sophisticated statistic — is wOBA, which stands for Weighted On-Base Average. Its formula contains Walks, Unintentional Walks, Intentional Walks, Hit by Pitches, Sacrifice Flies, and At Bats, but instead of the total Hits, it contains the number of singles, doubles, triples, and homers. Plus, it adds something called “linear weights,” a sabermetric term used to indicated the “weighted value” of each of the following: BB, HBP, 1B, 2B, 3B, HR.

Here is the wOBA formula for the 2013 MLB season, taken from fangraphs.com:
wOBA = (0.690×uBB + 0.722×HBP + 0.888×1B + 1.271×2B + 1.616×3B + 2.101×HR) / (AB + BB – IBB + SF + HBP)
These are its linear weights: 0.690, 0.722, 0.888, 1.271, 1.616, 2.101.

The above linear weights resulted from analyzing the baseball data for the 2013 MLB season.

Say you wanted to find the Mets' wOBA for the 2013 season. For uBB you would substitute, how many unintentional walks the team had; for HBP you would substitute how many times a Met was hit by a pitch; for 1B you would substitute how many singles the team's players hit, and so on.

The linear weights for the 2013 season as of June 28 follow.
wBB: 0.690
wHBP: 0.722
w1B: 0.888
w2B: 1.271
w3B: 1.616
wHR: 2.101

What does 0.690 mean?

It indicates how much a walk contributed to a team’s run production in 2013. Specifically, each walk added (approximately) 0.690 runs to the team’s runs scored total. Thus 100 walks would add (approximately) 69 runs.

Similarly, the linear weights in 2016 as of June 28 are these:
wBB: 0.691
wHBP: 0.721
w1B: 0.879
w2B: 1.243
w3B: 1.571
wHR: 2.019

Note the differences between the 2013 and 2016 linear weights.

For a view of how linear weights have changed with seasons, see this table on fangraphs.com.

Notice that a double does not produce twice as many runs as a single. If it were, in 2016 a double’s weight would be 0.879 x 2 or 1.958, not 1.243. Similarly, a triple’s linear weight is not three times that of a single, a homer’s is not four times that of a single, and a homer is not twice that of a double.

What does the wOBA formula reveal about current Mets players?
To be continued