Why A Single Is Half a Home Run

Max from Boston asks on behalf of his dad: It strikes us that slugging is measured inaccurately in that a double isn't necessarily worth twice a single, a triple isn't necessarily worth 50% more than a double, a homer may be worth more than 2 doubles, etc.  Is there any data regarding the possible value of a weighted slugging pct.?

Is there any data? Ha! The pale-skinned basement-dwellers responsible for much of the sabermetric research over the last generation have trolled every piece of datum from all 400,000 MLB games played since 1876; analyzed each across 49 criteria; subjected them to 11 statistical tests, applied two dozen filters; pickled them in proprietary solutions for 48 hours, rolled them in flour, egg and bread crumbs and sauteed them on high heat until crispy and brown on the edges. 

There is more known about shortstop Leo Cardenas' ability to go from first-to-third on a single for the Cincinnati Reds in 1967 than about Toronto mayor Rob Ford's whereabouts last Thursday. Is there any data!

In fact, Max has opened a window into what seamheads call linear weights, exactly the calculation that Max has outlined. With runners on first and second, a double scores two runs, just as a triple does. Leaving the yard produces three -- not four -- times as many runs as a single, and the single leaves a runner just 90 feet from home. So what is the relative value of these events?

Going for Third on A Double? Hardly Worth It
Denied girlfriends after years playing video games, the stubby-fingered geeks have instead focused their pursuits on sifting through every occurrence in baseball history and determined how often and how many runs have scored when these hits (and all other events like fly outs, strikeouts, HBP, errors, etc.) have been involved. These are the relative values, assigning a walk/HBP a vaue of one:

Single ~ 1.25
Double ~ 1.75
Triple ~ 2.25
HR ~ 2.75

Are you shocked that a homer is worth less than three walks and less than two-and-a-quarter singles? Part of the value of each of these accomplishments is in their ability to not cause an out, of which there are a finite number allotted each team per game. 

And Now, To Actually Answer the Question
So back to slugging percentage. Clearly just adding up total bases to derive slugging percentage, and therefore OPS, glorifies yard barkers and diminishes the accomplishments of slap hitters. We documented this in March.

There are now better measures than slugging percentage and OPS that are defined by these linear weights. wOBA and True Average are one-stop shopping linear weights measurements of overall offensive performance that include park adjustments and other sanded edges, all rolled up into a number that looks like OBP (wOBA) or batting average (TAv). Here's an example of how wOBA can correct a misconception created by Max's slugging percentage discovery:

Last year, Adam Dunn produced an OPS 48% better than league average. That's awesome. But his wOBA was just .331 -- slightly better than average. Matt Carpenter, whose OPS was lower but whose hit distribution included many fewer home runs and many more singles, doubles (55) and triples (seven), produced a wOBA of .381.

In other words, OPS says Dunn was a great hitter last season and Carpenter a good one. wOBA shows us that Dunn was an above-average offensive performer while Carpenter was a downballot MVP candidate.