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Efficiency In The World Of Basketball As 'Effective Damage Per Second' In World Of Warcraft

For a number of analyses on WNBA awards, I've used a metric called Valuable Contributions Ratio (VCR) created by David Sparks.

I've described why it's useful to measure the value of rookies and most improved player candidates before, but explaining the metric itself can sometimes be a challenge.

Then Shannon offered a great analogy from World of Warcraft (WoW): effective damage per second. Bear with me as I have never even played WoW, but I think Shannon (@sgc72) has offered an interesting way to visualize exactly what this VCR metric is.

A screen shot from World of Warcraft fight with the Damage Per Second meter highlighted.

World of Warcraft

I'm not going to spend much time describing WoW because there are so many people that spend so much time with that game that you can probably find an explanation that works for you. Also, Wikipedia exists.

But in short, WoW is a "massively multiplayer online roleplaying game" (MMORPG), which is "a genre of role-playing video games in which a very large number of players interact with one another within a virtual game world." I'm not a big gamer, but the way I understand these games is Gauntlet (one of my favorite NES games that I never owned) on steroids - you're going on quests as a team, fighting a lot of vile creatures, and developing your individual character along the way. Believe it or not, I'm most familiar with WoW from studies of the game by educational researchers about how it facilitates the development of collaboration skills and even literacy.

Anyway, as a game in which the goal is to fight and hopefully destroy things, one would assume that the efficiency with which a character does so is pretty important.

Damage per second

Damage per second (DPS) is really exactly what it sounds like, Wowpedia defines it as, "...a measure of the damage dealt by a person or group over one second. DPS is a more practical measure of damage output than plain damage, as it allows characters of differing levels and classes to effectively compare their damage output." In plain(er) language, DPS takes your total damage and divides it by the number of seconds you personally were active in the fight. If your character dies or stops fighting for some other reason, your DPS may still be high, even though your overall damage is low, because it is a small sample time.

A graph of one player's DPS in WoW.

Predictably, damage in WoW is just any sort of spell or weapon attack that hurts a target. ZAM describes the five ways in which DPS can be used in the game from a measure of either character or weapon efficiency as well as a verb (which is awesome).

You can visit Wowpedia for the mathematical details of calculating DPS in its various forms, but the importance of DPS (especially for our purposes) is what ZAM writes as follows:

A character's DPS is defined as the amount of damage they deal across a certain amount of time. If a player deals 300,000 damage to a boss during 5 minutes (300 seconds), then they would be averaging 1000 damage-per-second. Since different factors can influence how long the battle takes, such as how well the other players in the battle are doing, it is not fair to simply compare a raw amount of damage. On another day, another player might deal 320,000 damage, but take 6 minutes (360 seconds) to do it. Even though they dealt more damage, they had more time available, and were not as efficient during the time the battle took. In fact, they were dealing 320,000/360 = 889 DPS. The first player was about 11% more effective. This is why DPS is the most significant quality for measuring damage output.

However, the problem with relying solely on DPS as a measure of effectiveness is that if you can only sustain that for 5 seconds, one might surmise that you wouldn't be very good at killing things because your team might need you for a bit longer than that.

And similar to what Christian Belt of WoW Insider said about mages, the "...real purpose -- the only role we play that really matters -- is that of DPS. We destroy things, and we do it as quickly and efficiently as possible. And if we can't provide that service, our raid will replace us with someone who can."

It's simple really: destroy things efficiently or get replaced like a punk, which leads to the importance of Effective Damage Per Second.

Effective Damage Per Second

Effective Damage Per Second (eDPS) is the damage a character does divided by all of the minutes the encounter is active, so it rewards you for finding ways to stay involved when the encounter gets tricky and you can't do your number one favorite thing repeatedly. In short, eDPS is a measure of how reliably you can actually deliver your DPS; in terms of the video above, it answers the question, how good are you over the course of the whole encounter as opposed to just when you can make contact with the boss giant?

The simplified calculation for eDPS is damage done divided by the number of seconds the player is actually engaged in the fight. I will defer to Shannon for further explanation:

Things that influence eDPS in the video above are the fight mechanics where you see 1) the red crystal pop up (if you watch the red crystal, you will see players explode outward from it), 2) the big stomp the giant does, and most importantly, 3) the black poisonous gas ooze the boss puts out every couple of minutes where the players have to run and hide behind some rocks (or you die).

Ideally, even though you can't maintain physical contact with the boss giant at that time, you want to continue to do as much damage as possible, so you load the boss up with damage over time with spells and figure out ways to maximize your uptime. You'll notice in the video after the second dark phase, the player we are following charges into the black cloud before it fully clears. The player is anticipating that (s)he can take that much of the (poison) contact but still score.

The Supreme Commander wiki describes eDPS as important, "...because missed shots have a large impact on the outcome of battles, and damage to units not targeted is also very significant." And that's a pretty good segueway to basketball.

World of Basketball

It's important to note that the WoW terminology is only an indirect analogy to basketball: it's useful conceptually (and visually) to describe the value of VCR but the math is different (and apparently differs by the RPG as well).

But VCR is not exactly an intuitive metric, so leveraging the MMORPG for a conceptual foundation is helpful.

Production vs. efficiency vs. tempo-free metrics

In basketball, damage would be anything that somehow hurts an opponent's chances of winning. Obviously, scoring points hurts the other team as does rebounding or blocking a shot. Similarly, a turnover, missed shot, or foul is like self-harm in that it hurts one's own team's chances of winning.

Reggie Miller offers an example of a high-DPS performance, especially if credited with a "steal" instead of a "foul".

But before understanding the value of VCR, it helps to understand the distinction between different types of stats that measure basketball "damage". In basketball terms, DPS is similar to a per minute stat (e.g. rebounds per 36 minutes) that people use as a measure of efficiency. Unlike in WoW, in the World of Basketball (WoB) there's evidence that a player can sustain a per minute rate in more minutes. Nevertheless, there are ways in which per minute stats can be misleading in certain circumstances, which is part of what makes tempo-free statistics valuable (click here for an example of that that using rebounding as the most obvious way to differentiate between production, per minute rates and tempo-free rates).

Production vs. efficiency vs. value

In short, per game averages are production stats that count how much "damage" a player does per game. But the efficiency rates (per minute) do significantly more to tell us how good a player is at inflicting a particular type of "damage". Tempo-free rates go a step further in telling us how good a player is at a particular type of "damage" independent of their team's tempo. In most instances, using a per minute stat is as useful as using a tempo free stat; the question is the level of precision you desire in pinpointing exactly how good a player is at a given thing and for that I favor tempo-free statistics.

But similar to WoW, it's also helpful in the WoB to have overall player ratings (like DPS) to assess the totality of the "damage" that a player inflicts within the game (i.e. combining points, rebounds, assists, etc). I like using Sparks' player ratings for one very simple reason: it's one constellation of statistics that fits together really well to help us understand a team from the player to team to game to season level, which really helps in developing a stable understanding of the game over time and who contributes what.

Sparks essentially has three types of player ratings: a productivity metric called Model-Estimated Value (which you could look at on a per game or per minute level), an efficiency metric called VCR, and a value metric called Marginal Victories Produced. I've used all of these countless times, so I won't describe all of them here, but VCR is essentially eDPS adapted for basketball - in short, it accounts for the total damage a player contributes to the team's effort relative to the proportion of the team's minutes a player played. More specifically, it's the ratio of the percentage of valuable contributions to the team's overall production relative to the percentage of team minutes a player played.

Valuable Contributions Ratio

The formula for VCR is described in depth here, but breaks down most simply to the following:

player percentage of valuable contributions to the team (PVC) / player percentage of possible minutes played

The important thing to know about VCR (and MEV or MVP) is that those individual forms of "damage" are weighted based upon their importance to the team. Most important is that unlike some other basketball metrics, it penalizes scorers who put up a lot of points by shooting (and missing) a lot of shots by weighting missed field goals and free throws. Perhaps whether that should be done might be a matter of debate - there is also the theory that just the act of creating a shot is valuable, especially in women's basketball, and should essentially be ignored - but Sparks addresses that elsewhere. But the point is that each action in the box score is weighted to account for what it contributes to the team's effort to win the game.

Although the VCR is not constructed the same way as eDPS - if for no other reason because it's per minute instead of per second - it's conceptually similar: it rewards players who make the most of the minutes they play by finding ways to contribute as much as they can when they're on the floor, even if their basic productivity numbers aren't that high. Even if a player isn't putting up points on the board or aren't playing big minutes, are they finding ways to contribute to the team's effort to win when they're actually on the floor?

The bottom line for VCR: the more minutes a player plays, the greater contribution they should make to the team.

It not only "levels the playing field" in terms of comparing the floor impact of players who play different minutes but also consistently "penalizes" players who put up a) gaudy statistics b) inefficiently in c) big minutes. The negative consequence of VCR's primary claim is that a player playing big minutes with a low VCR is probably playing too many minutes. But the upside of VCR is what makes it useful.

The use-value of VCR

Conceptually, that's a weird metric, if only because it's rather elaborate. But the payoff is pretty huge in terms of better evaluating the structure of a team.

For reference, the WNBA league average VCR is generally somewhere between 0.75-0.85 with the high never being more than 2 during the course of 34 games yet the low possibly dipping into negative numbers (meaning that a player made a negative contribution to the team, which gave them a negative PVC).

However, a player that has the best VCR in the league does not necessarily mean she is the "best" player - the value metric (MVP) is better for determining player quality. What a high VCR means is that a player is good at filling the role they played on their team in terms of the minutes they consumed. Another way of saying that is that it measures whether a player is offering their team "quality minutes". But just to get a sense for what VCR looks like, here are the top 10 VCRs from 2011:

Player Name


Fowles, Sylvia


Parker, Candace


Cambage, Elizabeth


Langhorne, Crystal


Catchings, Tamika


Taylor, Penny


McCoughtry, Angel


Charles, Tina


Jackson, Tiffany


Whalen, Lindsay


Top 10 VCRs from the 2011 WNBA season.

Sparks describes VCR as useful to measure the value of bench players, rookies, and players who missed games due to injury. The following is a description of how VCR can be used to help understand end of season awards as well as two additional things that Sparks didn't mention.

Most Improved Player award: This is probably the greatest value of VCR. Every year there are players who improve their productivity and by extension their value simply because they got more minutes. However, the best way to define "improvement" is by looking at whether a player did more with the minutes they got - did they actually demonstrate improvement in terms of contributing more in the minutes they got or did they just contribute at exactly the same rate in more minutes?

The 2011 MIP race provides an example of this dynamic. In 2011 Tiffany Jackson did a lot for the Tulsa Shock in the minutes she got, but she was also a very efficient contributor in 2010: despite an impressive + 0.32 change in her VCR between 2010 and 2011, she was already a well above average contributor on the floor in 2011. Meanwhile, both Ashley Robinson and Kia Vaughn were examples of players who didn't make the top 10 in VCR standings, but improved their contributions on the floor to the extent that they went from well below average contributors to above average contributors, with Vaughn seeing a league-high + 0.82 change in her VCR between 2010-2011.

Although Jackson was indeed a solid candidate for MIP last season, both Robinson and Vaughn were stronger candidates and VCR reflects what many people could tell just by watching them play.

Rookie rankings/projections: Rookie of the Year should probably be determined by value, to some extent. But there's also reason to include an assessment of potential for growth and VCR is very helpful for that as well.

Rookies often receive erratic minutes in changing roles as they adjust to the pro ranks. VCR helps to illustrate which rookies are doing the most with their minutes as they adjust to the league and thus the rookies that might have potential to continue contributing quality minutes if their minutes increase because we already know that they're capable of finding ways to make an impact on the floor.

In other words, a player with a high efficiency (VCR) in limited minutes can very likely be more productive (MEV or per game averages) in more minutes on the floor and thus become a more valuable contributor to the team (MVP).

However, as a player's minutes go up, there's also more time on the floor to not be doing any "damage" - assuming the player does not improve, minutes per game and VCR generally have an inverse relationship season to season (otherwise, they become a MIP candidate because they've actually improved their ratio of PVC to the proportion of minutes they play). At the point when a player's minutes increase to the point that their VCR drops to the of league average, we've probably found the maximum number of quality minutes they're able to offer.

So it probably comes as a surprise to nobody that Los Angeles Sparks rookie forward Nneka Ogwumike has the top VCR among rookies thus far in 2011. But who's in second? Undrafted Phoenix Mercury post Avery Warley, whose VCR is at 1.44 (elite) in her 15 minutes per game. Although their might be some question about how many more minutes she can play, there's little question that she's probably earned her place in the league as a rotation player.

Free agent value: That inverse relationship between minutes per game and VCR is also valuable on the free agent market. Although productivity is obviously important, when free agents change teams, their role - and, therefore, often their minutes - are likely to change. What VCR can help us project - especially for veterans that teams tout as bringing in "experience" - is how many quality minutes a player can really offer when they switch teams by comparing their VCR to the average VCR given their style of play and/or position.

Internal growth of a team: Consistent with using VCR for rookie and free agent value, VCR is a good metric to use for looking at how much room for growth a roster has and could help to pinpoint how to juggle minutes to maximize the talents on the roster.

This is more than enough for now, but hopefully it's clearer why VCR is useful for looking at player efficiency, development, and team building.

Huge props to Shannon for all the WoW info and this opportunity to combine two forms of blatant geekery. Follow her on Twitter to talk more WoW or WoB.

Naturally, this will remain in our "statgeekery" section as well as linked from the Swish Appeal statistics glossary. Got questions? Leave them in the comments.