January 21, 2010

## Everything you always wanted to know about: Win Shares

The world of advanced baseball statistics can be an intimidating place for those of us who slept our way through advanced algebra or haven't been a follower of the Bill James revolution from the beginning.

Still, that doesn't mean that we should feel left out when it comes to another way of understanding and appreciating the game we all love. With that in mind, BLS stat doctor Alex Remington will explore a new advanced statistic each week during the offseason, providing a simple primer for the uninitiated.

Today's statistic: Win Shares

What Win Shares Means: Win Shares was first advanced in a book of the same name that Bill James wrote in 2002. It's an extension of an older stat of his called Runs Created that tries to measure the number of runs that a hitter has put on a scoreboard. (The earliest version of Runs Created was simply the product of OPS x Total Bases. Recent versions take many more offensive outcomes into consideration, including baserunning.)

Win Shares attempts to measure how many wins a hitter or pitcher has personally notched for his team in the standings. Unlike other new-school stats, Win Shares look quite explicitly at the standings: A 90-win team has more Win Shares to allocate than an 80-win team.

Win Shares are defined as 1/3 of a win — three Win Shares are equal to one team win. Why three? Well, the number is arbitrary. Since Win Shares are only whole integer values, James wanted to pick a number that was neither too small, so as not to lose a great deal of information in rounding, nor too big, because the estimators in Win Shares weren't precise enough to differentiate between 1/10 of a win and 2/10 of a win.

Win Shares have changed since they were first introduced. Bill James later introduced a stat called "Loss Shares" because Win Shares themselves are never negative. They have also been eclipsed in popularity by Tom Tango's WAR which was introduced in 2008.

It sounds like James is still tinkering with the formula and others have made tweaks too. However, Hardball Times, which carried Win Shares data for years, is no longer tracking them, having recently replaced their player pages with links to FanGraphs (which prefers to measure WAR instead).

How to calculate Win Shares: I'm just going to paraphrase Dave Studeman's definition over at Baseball Graphs, the best encapsulation of the method available on the web, because it's a long process. (If you want to know how long, read Brandon Heipp's fine-toothed walkthrough.) Win Shares for offense (batting and baserunning) and defense (pitching and fielding) are calculated separately and allocated proportional to the overall contribution that each made. That proportion is determined by calculating each player's marginal contribution to the whole.

The team's number of Win Shares is equal to its win total times three. To allocate team Win Shares, we look at Marginal Runs. The insight is similar to that in WAR for a replacement player — namely, that we only care about the runs scored and prevented by the team above and beyond what a minimally acceptable offense and defense would provide. This is preferable to starting from zero, because you can't start a game without nine men in your lineup. (Note: Win Shares themselves are allocated from a team's win total, and are NOT adjusted for replacement value. Hardball Times's Win Shares Above Bench, below, addresss this problem.)

Offensive Marginal Runs are equal to Team Runs Scored minus 52 percent of the League Average Runs Scored; Defensive Marginal Runs are equal to 152 percent of the League Average Runs Allowed minus Team Runs Allowed. Then, add them together and calculate the proportions: Offensive Marginal Runs divided by Total Marginal Runs, and Defensive Marginal Runs divided by Total Marginal Runs. The team's Win Shares are allocated proportionally to the offense and defense according to their percentage of the total Marginal Runs.

Next we do the same for each player. We calculate their marginal proportions using Runs Created per 27 Outs (RC/27, a measure of how many runs the player creates over the usual length of a game). Subtract 52 percent of the league average RC/27 from the player's RC/27, and adjust for ballpark; this gives us each player's marginal RC/27. Do this for every player on the team and add them all up. Then allocate the team's offensive Win Shares to each based on their proportion of the sum.

That leaves us pitching and defense, which we similarly have to separate. Pitchers are allocated runs based on the components of FIP, home runs, walks and strikeouts. Fielders are allocated runs based on extraordinary plays like passed balls, errors and double plays, as well as the a measure of how many routine plays the team converts into outs (we use a park-adjusted version of a stat called Defense Efficiency Ratio, which is like BABIP for fielders). However, the proportions are bounded: "Pitching never is credited with less than 60 percent, or more than 75 percent, of defensive Win Shares."

Just as we did with RC/27, we calculate each pitcher's marginal runs not allowed, as well as wins, losses and saves. Closers are given credit for their high-leverage innings. Then, pitchers are docked credit if they're truly awful hitters. Unearned runs are split evenly between pitchers and fielders. The most complicated part of all (!) is fielding, because each position has its own formula, involving calculations of things like errors, putouts, double plays, and assists. As usual, we allocate the Win Shares proportionally according to the player's marginal contribution to his team's fielding total.

I am not aware of a public explanation of the Loss Shares method (other than Tom Tango's rough assumption) — or of easily available measures of Loss Shares.

What Win Shares is good for: Unlike WAR (and other win-based measurements like Baseball Prospectus's WARP), Win Shares are allocated from a team's actual win total. As a result, they may be better for discussions about real-world awards like All-Star selections and MVPs, flawed as they are, than stats like WAR which seek to separate a player from his context as much as possible. Generally speaking, a 20 Win Share season (equal to 20/3, or about 6.7 team wins) is an All Star-type campaign; a 30 Win Share season (equal to 10 team wins) is an MVP-type season. (Note that the underlying win values in each of these are different from those in WAR. In WAR, an All Star-type campaign is usually between 4-6, and MVP is usually between 7 and 9.) As Studeman wrote in 2004, "The Win Shares system actually goes to great lengths to make sure the total contribution from all players equals the number of games his team actually won. None of the other stats do that."

When Win Shares doesn't work: It's a really long and complicated process for a stat that few people prefer to WAR, but instructive as a window into the mind of Bill James, one of baseball's great innovators — and also a cautionary tale for anyone thinking about devising her or his own stat. As Bill James himself admitted in 2008, six years after he introduced it, "There are some things about it that are fouled up." Hardball Times did some good work to tweak and improve Win Shares, such as the calculation of Win Shares Above Bench, which was basically an attempt to add a replacement adjustment (the Above Replacement in Wins Above Replacement) to Win Shares. But, as we've seen, they wound up giving up and simply switching to WAR.

Tom Tango believes that Win Shares (along with Loss Shares) are essentially a version of Pete Palmer's Linear Weights, which are also an inspiration for Tango's own wOBA and WAR, and asks: "Since we can derive Win Shares from Linear Weights, then why go through this whole exercise? Linear Weights is far easier to calculate." He's obviously a proponent of his own stat, but most baseball bloggers at this point would probably agree with him.

Why we care about Win Shares: Win Shares was a fascinating intellectual exercise, an attempt to derive a new total value stat that actually corresponded to a team's win total that wound up straddling the line between what I've been calling old-school and new-school: traditional metrics that measure what happened, like runs and wins, and new metrics that try to measure what should have happened in a neutral environment, controlling for things like park effects, defense, teammate strength, handedness, and so on. New-school stats are most popular among the hardcore fantasy baseball crowd, because they tend to be much better predictors of future performance. But because they attempt to control for context — and dumb luck — they're not necessarily great descriptors of what actually happened. Old-school stats reflect the scoreboard and standings. Win Shares tries to do a little of both.

Bill James is a great innovator, but he's also an employee of a major league team who's no longer able to do his best work in the public domain. Win Shares is not a perfect stat by any means and at this point, WAR is easier to find, easier to use, and more popular. Win Shares is an interesting answer to an interesting question: given the number of wins a team actually has, how can we figure out how they add up? This is just the beginning of the answer. Bill James is one of the best at asking good questions. Win Shares are a good start. But they also go to show that the first answer isn't always the best, even when it's offered by Bill James.

Previous lessons: BABIP, OPS+, FIP, wOBA, WPA, WAR, UZR, J-HOFFA

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