Get To Know An Advanced Stat: Win Shares

Over the first few weeks of the season, we looked at why certain advanced stats are more useful than their basic stat predecessors. Metrics like True Shooting Percentage, Rebound Rate and others we discussed are fairly simple to explain in words and numbers, but there are a handful of much more complex all-encompassing basketball stats that most of us don't really understand despite the fact that we cite them in nearly all of our arguments.

On that note, let's dive back into the 'Get To Know An Advanced Stat' series with Basketball Reference's Win Shares. And to break it all down, here's a Q&A with Basketball Reference's David Corby:

Q: How exactly did the concept of Win Shares and its development come about?

Corby: Basketball win shares were developed by Justin Kubatko, the founder of Basketball Reference. We've never spoken but I imagine that the appeal had to do with the lack of (relatively) easily computed uber stats in basketball. I can think of Kevin Pelton's WARP and Dave Berri's Wins Produced, which are ideological kins of Win Shares, in that they consider a player's offense and defense and attempt to explain his total contribution, which they measure as wins. Many readers will recognize that the Win Shares statistic was established in baseball's Sabermetric community. Basketball hasn't been shy from borrowing its terms, the term Win Shares was still available, and Justin had a useful concept that fit that name. Voilà.

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Q: Often times, we'll throw around numbers like Win Shares in NBA debates without really knowing what those stats entail. Stats like True Shooting Percentage and Rebound Rate can be easily explained by average fans with a simple calculation, so how would you explain Win Shares to fans as simply as possible?

Corby: Generally, Win Shares is an effort to credit a player's total measurable contribution to his team's win total during the season - in this sense, it isn't shy about being an all-in-one statistic.

For the layperson, it's meant to be conceptually simple - that is, one Win Share should reflect the offensive and defensive contributions of a player that have led to one win during the season.

While the computation is complicated, the importance of its component statistics are well known to any basketball fan. On offense this includes field goals, assists, and free throws - and credit is also given for offensive rebounds that enable point production. On defense, things are a little more vague but the player receives credit for possessions where his team prevents a score and where the player himself contributes a stop. The formula for stops is itself somewhat complicated, but generally a stop is awarded through easily understood events like steals, blocks, and defensive rebounds.

My point here is to emphasize that all of the common counting stats are there, and a player that makes well-rounded contribution on offense and defense will do well in the system. The magic of Win Shares is that the final computation tempers these counting stats by contextual factors that are generally beyond a player's control, and it packages these contributions into an easily understood metric (a contributed "win").

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Q: Can you tell us about that final computation you mentioned that 'tempers the counting stats?'

Corby: As an example, in computing offensive win shares a component statistic is "points produced". Rather than simply add the points that a player scores (FT + FG2 * 2 + FG3 * 3), it seems better policy to recognize those actions that enable a player's scoring and split credit accordingly. In this case, we understand that a player's point production is dependent upon teammates contributing assists and offensive rebounds. Thus, in calculating points produced a 2-point field goal will be worth less than two points, because we award some of that credit to his teammates.

Win Shares is disciplined about accounting for these kinds of events.

Another example is recognition that player's counting stats depend strongly upon a team's style of play. Most fans, whether they tend to enjoy statistics or not, are able to recognize that some teams play at a much faster pace than others. This being the case, we need to account for the relative value of a point produced for a team that tends to accumulate more possessions than other teams in the league, or the opposite case. This is an important observation and something that Win Shares accounts for. Consider last year's Pacers team, which played with a very low tempo and whose players had correspondingly fewer scoring chances than other teams in the league. This fact tends to diminish the counting stats of Paul George and others, but Win Shares doesn't punish them for this fact.

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Q: How do you get from all of those simple numbers you mentioned on offense and defense to the final product of how many offensive or defensive 'win shares' a player has contributed?

Corby: Well, it's somewhat complex. The first step is to understand some fairly well known advanced statistics like Points Produced, Defensive Rating, and how to estimate a team's offensive possessions. I won't write those formulas here, but they're available in our site's glossary and also in Dean Oliver's book (Basketball On Paper), to which Win Shares component statistics owe their origin. If somebody did this by hand, it would take them several sheets of paper (not recommended). However, they can be computed, if somewhat tediously, in a spreadsheet. At that point you can do the final calculation by following our methodology explained here: http://www.basketball-reference.com/about/ws.html.

The best way to answer your question is to emphasize the crux of the Win Shares calculation, which is the concept of marginal production. We calculate both a marginal offensive figure and a marginal defensive figure for each player, which is a way to value their production - that is, how well they produce points and prevent scoring - relative to league figures.

Then we calculate the Win Shares by dividing the sum of the player's marginal point production by his team's marginal points per win. In this way, we distribute a team's Win Shares in a way that sum to the team's actual win totals.

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Q: One of the advantages of Win Shares seems to be that, as you mentioned, a player's teammates and other factors they can't control like pace, are taken into account, as well as the fact that the calculations are such that a team's roster would have its Win Shares add up to the team's win total.

In other words, it all makes sense. So how would you say Win Shares stacks up against other all-encompassing advanced stats like PER or VORP/WARP? What would you say are the strengths and flaws of Win Shares?

Corby: Win Shares does well for itself because it's useful and easy to understand conceptually. It's also comprehensive, that is, it includes a player's offense and defense, which lends it some versatility. A fan can reasonably cite Win Shares as an argument for player awards like the All-Star game or MVP, or career distinctions like the Hall of Fame. Another selling point is that it's a low-bias statistic because it corrects for the tendencies of an era or a player's team.

That said, PER and VORP are useful in their own way, too, and we don't necessarily view Win Shares as being in the ring with those statistics. Basketball Reference publishes PER and it's something that I use frequently. It's straightforward and, like Win Shares, conceptually simple. But it doesn't attempt to measure individual player defense and it isn't cumulative, which of course it isn't designed to be because it's an efficiency metric. This means that a player fares no better according to PER having played 30 minutes/games compared to a player that played 10 minutes/game.

Understand that Win Shares has its own drawbacks. As an example, a component of defensive Win Shares is a player's individual defensive rating, of which a component is the team's defensive rating. To some extent, then, a player's Win Shares are partly subject to the vagaries of his current team. A player will tend to have fluctuations that are a consequence of lineup changes, a trade, or other factors that affect his team's defensive performance, and which are surely larger than differences in the player's underlying contribution.

Also understand that basketball Win Shares differs from its baseball cousin. Baseball Win Shares necessarily add up to a multiple of a team's total wins. Basketball Win Shares come close, but team wins aren't an actual component of its calculation so it's more accurate to consider their total an estimate. For example, the Sixers' roster right now has something like 11.5 Win Shares, but the team has 15 real wins. These differences tend to be small in most cases - I simply cherry-picked a large one which will probably iron itself out - but the point is that basketball Win Shares aren't able to provide an air-tight accounting.

I'll step back for a moment and suggest that basketball statistics tend toward the extremes in how much they measure. The examples here of PER and Win Shares use a limited number of measurable, discrete inputs, and thus accept certain limits to their application. Analysis of plus/minus statistics might represent the next frontier of analysis, but it grapples with the opposite problem, namely the sheer amount of statistical noise encompassed by everything that happens on the court.

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Q: When you say that in addition to correcting for the tendencies of a team, Win Shares also corrects for the tendencies of an era, what do you mean?

Corby: What I mean by eras is the tendency of certain styles of play to predominate or diminish over a span of years. For example, the NBA has featured a slower pace of play in the 1990s and 2000s than it did in the 1970s and 1980s (though it's been rising over the last few years). Pace refers to the number of possession that teams use in the course of a game, which affects scoring totals and other counting stats. The components of Win Shares rise or fall with these changes in the context, so when a player produces 10% more points in one season than a player from an era when league scoring averages were correspondingly lower, Win Shares will recognize the same marginal offensive contribution for each player. That is, all else being equal, the players will be awarded equal credit.

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Q: You mentioned plus/minus stats as the possible next frontier. Do you mean stats like Adjusted Plus/Minus and Regularized Adjusted Plus/Minus? And what do you mean by the 'statistical noise encompassed by everything that happens on the court' when discussing these plus/minus stats?

Corby: Concerning plus/minus stats, those are the ones that I was referring to, yes. I brought these up as a way to distinguish the approach of Win Shares. Plus/minus stats are obscured by any number of factors, for example, multicollinearity, sample size issues, strength of opponents, and a lot of randomness. I understand that the research gets pretty sophisticated by using multi-year spans of data and careful regression techniques. As an approach, it's ambitious and comprehensive of all factors that lead to scoring and preventing scoring. This breadth distinguishes the approach from Win Shares and others, which are comparatively modest and begin with a set of easily computed, measurable inputs.

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Q: Is there a player whose Win Shares figures surprise you, either on offense, defense or in total? Maybe a player you didn't expect the numbers to be kind to, or a player you thought would have better win share numbers? And does that affect your perception of the player at all?

I was surprised to see Kevin Love, David Lee and Carlos Boozer around the top-20 in defensive win shares, but considering that defensive rebounding is a key component of the metric, it makes sense.

Corby: There are a lot of surprises when you look at the list. Carlos Boozer's a good example, certainly. Having outsized component counting stats, like rebounds and blocks, lead to players like Ben Wallace and Marcus Camby having higher Win Share rates (per 48 minutes of play) than players like Jason Kidd, which might be surprising to casual fans. Along similar lines, Dennis Rodman fares pretty well.

Getting back to my point in a previous answer about how defensive Win Shares are distributed, there's a tendency to reward playing lots of minutes on good defensive teams, even if there's scant evidence for a player's actual defensive abilities. A good example is this year's Pacers team, which leads the NBA in defensive rating, and currently has four of the top six players in Defensive Win Shares. Opponent misses and non-assigned turnovers get attributed equally to all players, so Lance Stephenson and David West benefit greatly from the influence of Roy Hibbert and Paul George, and thus currently measure as better defenders than players like Kevin Durant and Dwight Howard. Like most fans, I don't personally believe that's the case but in the absence of detailed defensive measurement this is the best we can do while maintaining conceptual simplicity. It's a trade-off.

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Read more in the Get To Know An Advanced Stat series:
Offensive/Defensive Rating
Effective Field Goal Percentage and True Shooting Percentage
Rebound Rate
Advanced Assist Measures
Individual defense