The beauty of fantasy basketball is that no matter how many spreadsheets you make, no matter how many games you watch, there is never a ‘correct’ way to design a winning team. Head-to-head leagues encourage owners to punt categories. Roto owners must take a more holistic view of a player’s value. Dynasty leagues force owners to balance immediate success against future returns. Some leagues count free throw percentages, some only count free throws made. And no matter which approach you take toward your team, a few quick trades and injuries can decide your season.
This article is a follow up to last week’s The Numbers Game, which covered statistical means and medians for the 2012-13 season, the concept of ‘Fantasy Points’ and relative statistical values, and scarcity. Read that before diving into what follows. There are tools to help build a winning team, but there is no blueprint to a championship.
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What are Standard Deviations?
The standard deviation of a data set measures how narrowly or widely dispersed data are around the mean. Do most NBA players score roughly the same amount of points with only a few outliers? Is there a ‘regular’ distribution resembling a bell curve around the mean? Or are players far-flung between zero points per game and Carmelo Anthony’s league leading 28.7 per game?
By looking at standard deviation (SD) we can answer those questions and more. It can be summarized as ‘predictable dispersion’, and once we calculate the SD of a given data set (e.g. how many points the top-170 players averaged last season) we can gauge how those players were arranged around the mean, via the formula: σ=√((∑(x-x ̅ )^2 )/N
This looks and sounds far more complicated than it is. Figuring out how to type the equation above (and get it to show on the web) took me longer than it did to compute the SDs themselves. Thanks to the magic of computer software, these equations can be calculated in milliseconds by anyone with a basic familiarity with Excel (or Open Office, EditGrid, Tables, and so forth). If you have spreadsheets with appropriate data, you can find the means, variances and SDs of your data within five minutes even if you have never before heard of a Standard Deviation. I mean that literally – follow this link for a YouTube video which explains the process in 4:35.
Before diving into slightly more advanced numbers, here is a quick reminder about the medians and means from the 2012-13 season. As usual, this only accounts for the top-170 players.
Points – 13.3 (i.e. the player directly in the ‘middle’ of the top-170, ranked No. 85, averaged 13.3 points per game)
Three-pointers – 1.3
Rebounds – 5.0
Assists – 2.6
Steals – 1.0
Blocks – 0.5
Field goal percentage – 45.9 percent*
Free throw percentage – 79.5 percent*
Minutes per game – 30.5
(Note: For the purposes of this article, the FG and FT percentages are not weighted by volume of attempts)
Points – 13.7 (i.e. on average, the players in the top-170 averaged 13.74 points per game)
Three-pointers – 0.9
Rebounds – 5.4
Assists – 3.2
Steals – 1.0
Blocks – 0.7
Field goal percentage – 46.6
Free throw percentage – 77.1
Minutes per game – 30.3
Thus informed, we can easily calculate the Standard Deviations for each category.
Standard Deviation (SD)
Points = 4.30 (i.e. 68.3 percent of the top-170 players scored within +/- 4.3 points of the mean 13.7 points per game)
3-pointers = 0.83
Rebounds = 2.70
Assists = 2.17
Steals = 0.42
Blocks = 0.58
FG percentage = 5.1 percent
FT percentage = 9.1 percent
The SD approach is particularly useful for gauging the positive and negative contributions of an individual player across categories, and the intensity of the effect on that category. J.J. Redick’s 30.5 minutes per game nearly mirror the top-170 mean, so we’ll use him as our example. Last season, between the Magic and the Bucks, he averaged 14.1 points, 2.1 threes, 2.2 rebounds, 3.8 assists, 0.5 steals and 0.1 blocks. This puts him 1.4 SDs above the mean for per-game 3-pointers (0.93), which is an excellent result. His FT shooting is also positive, but he falls at least one SD below the mean in rebounds (1.2 below) and steals (1.3 below), while coming perilously close in blocks (0.96 below).
You would know by glancing at Redick’s boxscores and season averages that he’s sub-par in rebounds, steals and blocks— SDs simply provide a quick way to compare and quantify his individual variance from the mean in a given category with the expected variance across the population (in this case, the top-170 eight-cat players).
Here are 15 players with the highest cumulative SDs across eight-cat leagues last season (FG and FT percentages are included but unweighted). The names will look familiar:
Kevin Durant = 10.26 SDs
LeBron James = 10.09
Stephen Curry = 8.08
James Harden = 7.40
Chris Paul = 7.25
Kobe Bryant = 6.30
Russell Westbrook = 5.27
Tim Duncan = 5.11
Kyrie Irving = 5.00
Paul George = 4.83
Carmelo Anthony = 4.81
Dwyane Wade = 4.43
Nicolas Batum = 3.92
Joakim Noah = 3.85
Dwight Howard = 3.82
Notice the precipitous drop-off from Durant/LeBron to the next group of guys, after which the slope of the decline levels off. (For those interested…of the top-170 players, the bottom 10 in cumulative SD last season were, in descending order, Elton Brand, Jordan Crawford, Steve Blake, Brandan Wright, Kirk Hinrich, Jason Richardson, Lance Stephenson, Gerald Wallace, Emeka Okafor and Andrew Bogut.) This list is based upon cumulative SD but you can also look at component categories (rebounds, FTs made, etc.) to find the intensity of different players’ contributions. You could also change it from per-game values to cumulative games-played totals. You could merge the numbers with the 2011-12 season and develop an even larger, perhaps more reliable data set. The only real limits are your league settings and imagination.
Relative Standard Deviation (RSD)
So what else can we use these numbers for, other than a simple and effective means to rank player values? You may have already noticed that the SD for 3-pointers (0.83) is nearly 90 percent as large as our mean for that category (0.93). This is a concept known as relative standard deviation or ‘standard deviation as a percentage of the mean’, and the takeaway is simple—an individual player has a strong tendency to either make 3-pointers (think Vince Carter) or not make 3-pointers (think Marcin Gortat). I will abbreviate this idea as ‘RSD’ for relative standard deviation.
As you may have guessed if you read last week’s article, or simply stopped to think about it, blocks (88 percent RSD) and assists (68 percent RSD) also qualify as boom-or-bust categories when gauged by RSDs. On the other hand, scoring, FG percentages and FT percentages show relatively small deviations from the mean.
The graph below shows RSDs for key top-170 statistics, revealing the amount of variability in a given category.
For the purposes of this graph I’ve included games played, minutes per game and FG and FT percentages, as well as FGs and FTs attempted. The variance in games played and minutes per game have a profound effect on overall value, something I intend to explore further in a future column. For now, it’s enough to say that the higher the percent of relative standard deviation, the wilder the swings will be in that category from player to player:
This is essentially another way of thinking about scarcity. Last week I discussed how certain stats (particularly assists and blocks) are concentrated in a relatively small number of players, and how the top-50 players have particularly high concentrations of assists, points, blocks and steals. Just how concentrated the numbers are becomes clearer when we add relative SDs to the mix, and if you take the time to plot the individual categories you can see exactly where they are concentrated.
SDs also provide an easy way to gauge the value of punting a category, and to determine which players to target if you do choose to punt. This is a topic which I hope to explore next week, but I’ll conclude with a brief preview to set up next week’s column and provide another example of the usefulness of SDs.
For breaking player news and occasional stats/insights, follow me on Twitter @Knaus_RW.
Ignoring steals primarily benefits big men, and the 12 players who gain the most are all PF/Cs. In descending order, they are Jonas Valanciunas (jumping a cumulative 1.9 SDs), Spencer Hawes, Amare Stoudemire, Jermaine O’Neal, Serge Ibaka, JaVale McGee, Robin Lopez, Brandan Wright, Carl Landry, Patrick Patterson, Brook Lopez and Chris Kaman.
J.J. Redick interrupts the streak of big men, gaining 1.3 SDs when steals are excluded. The only other guards to make the top-50 are Jordan Crawford, Steve Nash, Arron Afflalo, Joe Johnson, C.J. Miles, Steve Blake, Jarrett Jack, Brandon Knight, and Ramon Sessions.
And here are some potential SFs who make the list: Mike Dunleavy, Tobias Harris, Jeff Green, Martell Webster, Michael Kidd-Gilchrist, Carmelo Anthony, and Dorell Wright.
Overall, there are 94 players who benefit from punting steals vs. 76 players who lose value. Accordingly, steals among the top-170 are concentrated in a relatively small group of players. This section about punting steals, as stated, was a previews...for a full breakdown of punting strategies, in general and with the use of SDs, check back next week.
That concludes this edition of The Numbers Game. I used my premium account at BasketballMonster.com to obtain raw averages for 2012-13, which I then manipulated to arrive at the information above, as well as the content of a few columns I’ll roll out over the next few weeks. I can’t recommend BBall Monster highly enough, and they belong on your list of ‘go-to’ fantasy sites. They also came out with a site this year called RotoMonster.com, which bills itself quite simply as a “fantasy basketball stats archive.” As noted last week, I am not a statistician and I don't particularly enjoy math, but I do enjoy the clarity math can bring to obscure problems. Email me at KnausRotoworld@gmail.com if you have a keen eye for z-scores and spreadsheets, further insights, a bone to pick, or for any other reason your heart desires.
My final thought is that I’m hosting a live chat on Thursday Oct. 24 at 3pm which is exclusive to Draft Guide members, so if you have any questions about SDs, punting or anything else, you should check it out. Thanks for reading.