Real value of Player Rater numbers

As we're all aware -- much as we might like to ignore it -- fantasy basketball is a cold game of numbers. The players on your team accumulate statistical data, and when that data all gets mashed together, you get to see how it looks in comparison to the data accumulated by other teams. Looking at it this way allows you to make roster decisions that can help your team, even if they make no sense in the context of real basketball. Blake Griffin, for example, is better than Nicolas Batum at basketball, but if you have Batum in a fantasy league, and someone offers you Blake Griffin for him straight up, you're probably shrugging and saying you just can't do it.

Ultimately, we probably do end up making these decisions with whatever strange combination of head and heart feels most right to us in the moment; that's OK, and it's what makes fantasy basketball more fun than pure math (unless you really like math, in which case, you're probably reading something other than this column). With this conundrum in mind, though, this week I wanted to point out one of the weaknesses of the Player Rater (a weakness, hopefully, that you can use to your advantage).

A ranking system is helpful because it neatly arranges players in order of their value according to a common set of criteria, and because of this, it tells us things we might not be able to see with just our eyes (i.e. Nicolas Batum looks like he's pretty good at basketball, but you might not intuitively imagine that he's a top-10 fantasy player just from watching him play). Unfortunately, looking at a list like the Player Rater, it's easy to forget that the distance between one player and the next in the rankings is not always uniform.

We have a great example of this right at the top of the list. Kevin Durant's total Player Rater value, if we rank players based on per-game stats rather than total stats, is 18.12. We arrive at that number by looking at how many standard deviations better than the average he is in each category, and adding those values together. 18.12 is a ridiculous number. You can tell it's a ridiculous number because the difference between 18.12 and Kobe Bryant's second-place 13.78 is roughly equivalent to the difference between Kobe and David Lee's 14th-place 9.26. This is all a complicated way of saying that Kevin Durant is way, way more valuable than everyone else. In a vacuum, having Kevin Durant and David Lee (first and 14th on the Player Rater, respectively), would be more valuable than having Kobe Bryant and LeBron James (second and third, respectively). Of course, you always have to account for the particularities of the players you already have on your roster, but remembering that the difference between first and second might not be the same as the difference between second and third is an important (if overly simple) principle in assessing value in fantasy leagues.

Based on this line of reason, the major takeaway here is that it is usually worth overspending to get a great player (one of the ways in which fantasy basketball is, happily, a lot like real basketball). You have a limited number of roster spots on your team, and a plethora of players with whom you might consider filling those spots. Ideally, you want to plug the best possible players into as many of those spots as possible and fill in the spaces around them. Let's say the person who owns LeBron James in your league is a little worried that James seems to be content scoring fewer points this season and has also slipped in steals and free throw percentage at the same time. All of a sudden, an elite player is available. How much can you offer up for LeBron without destroying your own team? The answer might be more than you think.

Take, for example, an offer of Deron Williams, Kevin Garnett and Gerald Wallace. LeBron's Player Rater value is 13.40. Williams' is 6.64, KG's is 5.44 and Wallace's is 3.95, which comes to 16.03. In this trade, you're giving up more total value, but LeBron's total value carries more weight because it is contained in just one roster spot. So in addition to the 13.40, let's say you move a couple of guys you've been leaving on your bench into your starting lineup. LeBron takes Wallace's spot at small forward, so you plug in Amir Johnson as your center and Eric Bledsoe as your point guard. The values for Johnson and Bledsoe, respectively, are 2.31 and 3.40. So now you're actually getting at total value of 19.11 for the 16.03 you traded away, just by moving spare parts into your starting lineup. Even subbing in players you could have added off the waiver wire -- say Kosta Koufos and J.J. Barea instead of Johnson and Bledsoe -- you're coming out ahead in the deal, and there's the fringe benefit of having the freedom to add and drop players in order to take a chance on someone getting more minutes or a bigger opportunity after a trade or roster shake-up. By having more of your team's total value wrapped up in one roster spot, you've given yourself the flexibility to go make your team better (though it comes with the risk of that player getting hurt).

It's true, of course, that Player Rater values do not guide you when it comes to roster fit and balance. These values exist in a vacuum, and the Player Rater is not aware that you already have, for example, Larry Sanders, Serge Ibaka and Roy Hibbert on your team and can probably sacrifice some blocks without giving up any ground in the standings. The Player Rater doesn't know that you've punted free throw percentage because you're carrying Dwight Howard, Blake Griffin and a surprisingly disappointing Al Horford on your roster.

Fortunately, the Player Rater does present you with values in each individual category, and these values are a key to understanding why certain players seem to move the needle more than others. Take, for example, the difference between points and assists. The biggest value in the points category -- again, based on per-game numbers -- is Kobe Bryant's 3.86. The biggest value in assists is Rajon Rondo's 5.48. The higher value in assists -- a high standard deviation -- means the values in that category are spread out over a larger range relative to the average. If you think about it intuitively, this makes sense. Everyone scores points in basketball, especially guys who are also in the subset of players commonly owned in fantasy leagues; even guys who are out there for nothing but defense make a basket once in a while. Assists, on the other hand, tend to be more specialized. Even a player who is acknowledged to be a great passer might only rarely pick up an assist; Kevin Garnett, for example, averages just 1.9 per game.

Chuck Hayes, this season, is averaging 1.8 assists per game, which gives him a value of 0.00 on the Player Rater. LeBron James is averaging 6.9 assists for a value of 2.76 on the Player Rater. Linas Kleiza is averaging 7.9 points per game this season for a value of 0.00 on the Player Rater. Kyrie Irving is averaging 22.8 points per game for a value of 2.61 on the Player Rater. Looking at these four facts together, it's clear that in fantasy basketball as it is most commonly played, Kyrie Irving's 22.8 points is actually of slightly less value than LeBron James' 6.9 assists. This isn't how we generally look at basketball. A player who averages 22.8 points per game is generally thought of as an All-Star-level talent in most cases, whereas a player who averages 6.9 assists per game could very well be considered a complementary piece (Greivis Vasquez is averaging 8.7 assists this season).

Using the values on the Player Rater as they are intended -- as a tool to help you in the context of what you are seeing as a fan -- is a great way to take advantage of these sorts of perceptions. By offering multiple complementary pieces for superstar-level talent, and by filling in with high values in categories where you need help, you can shoot up the standings in your league over the coming weeks.