Weighted Stolen Base Runs (wSB) estimates the number of runs a player contributes to his team by stealing bases, as compared to the average player. In other words, it is the base stealing counterpart to wRAA. As with wRAA or other linear weights-based metrics, zero is average. A value above zero indicates that the player has contributed more runs than the average player would have given the same number of opportunities; a value below zero indicates that player has contributed fewer runs than an average player given those opportunities.
FanGraphs calculates wSB by comparing each player’s stolen base runs created per opportunity with league average stolen base runs created per opportunity. Therefore:
wSB = (SB * runSB) + (CS * runCS) – (lgwSB * (1B + BB + HBP – IBB))
League stolen base runs (lgwSB) is:
lgwSB = (SB * runSB + CS * runCS) / (1B + BB + HBP – IBB)
As with all linear weights-based metrics, the runs values (i.e. runSB and runCS) are estimates. In this case, the run value of a stolen base is set at .2 runs for all seasons. The run value of a caught stealing changes from year to year to reflect the changing value of runs and outs over the season.
runCS = – (2 x RunsPerOut + 0.075)
Runs Per Out is simply runs scored in the season divided by outs in the season. The seasonal constants for wSB can be found alongside the wOBA constants here. For 2014, lgwSB was 0.00377 and RunsPerOut was 0.151.
Obviously, stealing base is a positive action and getting caught is a negative one. You’d always like to move up a base and you would never like to make an out, but just counting stolen bases and caught stealings misses some important nuance. If you steal 10 bases and get caught 10 times during a season, your stolen base actively has actually cost your team runs because the value of advancing one base is smaller in magnitude than the cost of making an out. You might get a chance to move up later in the inning but you cannot un-make an out.
Enter wSB. Instead of just looking at a player’s stolen base count or their stolen base rate, wSB attaches run values to stealing a base and getting caught, and then compares it to league average. That way, you know if the player is adding value or costing his team runs. This is merely a mathematical estimate of something you know internally. You would rather have someone go 25 for 25 than someone who steals 40 but gets caught 19 times.
As a rule of thumb, you want to have at least twice as many SB as CS to break even, but that number bounces around based on the run environment.
How to Use wSB:
wSB is easy to read and easy to use. Zero is always league average for that season and it is measured in runs above or below average. This means a player with a +5 wSB has been worth five more runs than the average player given that player’s stolen base activity and opportunities. Generally, you see values between -3 and +6 for full time players, but that isn’t written in stone.
It’s important to remember that wSB only measures stolen base-type base running (i.e. not first to third, etc) and that it is not a measure of skill, but rather of outcomes. You won’t normally see a bad runner have a +5 season, but there are a lot of variables that influence stolen base outcomes so a +2 player might not be better than a +1 player going forward. Also, wSB treats every opportunity equally, even though the circumstances of the game will change how valuable a steal is or how costly an out is, making wSB like wRAA. If you want context dependent base running, it’s built into RE24.
Compared to seasonal wRAA, the spread between the the best and worst individual wSB is not that large. In recent years, the wSB leaders have usually been a bit over five runs above average, and the trailers are usually two or three runs below average.
Since 1950, only 22 times have players have had a single-season wSB of 10 or greater. The very best wSB seasons in modern baseball have been about 15 runs above average. The very worst have been about five runs below.
Things to Remember:
● wSB is baselined against the league average for a given year, meaning it can be used it to compare players from different eras. Zero is always league average for that year.
● Official statistics were not kept consistently for caught stealing until sometime in the 1950s. For many seasons prior to the mid-1950s, there are no records of caught stealing currently available. This situation might change in the future as the data is reconstructed. In the meantime, keep that in mind when looking at the wSB totals for players and seasons prior to the mid-1950s; use those numbers with caution.
● wSB is context neutral and is not park or opponent adjusted. Getting caught by Yadi Molina in a 0-0 game is the same as being caught by Derek Norris in a 10-0 game to wSB.
Links to Further Reading:
Matt Klaassen reads and writes obituaries in the Greater Toronto Area. If you can't get enough of him, follow him on Twitter.