The Numbers Game
Last year, in one of my ‘Saturday Dose’ columns, I wrote briefly about the idea of statistical scarcity as pertains to fantasy basketball. The concept is fundamental to the successful management of any team, so this column will revisit the idea of scarcity by diving into stats from the 2012-13 season.
Note: All lists of players are given in descending order. The “top-170” refers to the top-170 fantasy players (eight-cat) from the 2012-13 season. It’s the sub-set I’m using for baseline statistics, and although it’s not the entire ‘population’ of data (i.e. the stats from every player in the 2012-13 season) it is the ‘population’ of interest for my purposes. I used my premium account at BasketballMonster.com as a shortcut to getting spreadsheets of raw averages, which I then manipulated to arrive at the information below, 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.”
My final introductory thought is that anyone who hasn’t subscribed to Rotoworld’s NBA Draft Guide for 2013-14 is doing themselves a disservice. Steve Alexander’s schedule grid and schedule breakdown columns are worth the $14.99 price of admission. Every year I print out the grid and keep it near my desk as a handy reference tool. You also get early-bird access to Aaron Bruski’s minute-projections columns and the Bruski 150, dynasty tips from Mike Gallagher, and my own columns about this year’s rookie class and the summer’s top trades and free agent signings.
2012-13 Medians and Means
A 14-team league with 12 players per team requires 168 players to be drafted. Even 12-team leagues must account for players who flit in and out of value throughout the season, so I will focus on the top 170 players in eight-cat leagues, on a per-game basis. Owners in nine-cat leagues should simply keep in mind that this discussion doesn’t account for turnovers. It’s easy enough to plug TOs into the equation. Send me an email if you have any questions.
If you isolate the top 170 eight-cat players in the 2012-13 season, the median statistical line was 13.3 points, 1.0 three-pointers, 5.0 rebounds, 2.6 assists, 1.0 steals, and 0.5 blocks in 30.5 minutes per game. The median shooting percentages were 45.9 percent FGs and 79.5 percent FTs.
As a curiosity, the ‘median’ player in terms of fantasy value, i.e. the guy ranked No. 85 out of 170, is none other than Carlos Boozer. He averaged 16.2 points, 9.8 rebounds, 2.3 assists, 0.8 steals and 0.4 blocks per game, while shooting 47.7 percent from the field and 73.1 percent from the FT line. He also earned $15 million last year, and he’s owed another $32.1 million over the next two seasons.
Getting back to the top-170 cohort from the 2012-13 season, the mean statistical line was 13.74 points, 0.93 threes, 5.44 rebounds, 3.20 assists, 1.04 steals and 0.66 blocks. The mean percentages were 46.6 percent FGs and 77.1 percent FTs.
Fantasy Point Values
We can use the means above to develop ‘fantasy point’ values for an individual statistic. The ‘FP’ values (something I’m making up on the fly) indicate the absolute value of a given statistic in eight-cat fantasy leagues, enabling apples-to-apples comparison between stats. Note that this simple arithmetic assumes each category is weighted equally, which won't be the case depending upon your format/team/strategy. Shooting percentages are excluded and will be dealt with separately (though not in this column).
1 point = 0.07 FP
1 three-pointer = 1.08 FP
1 rebound = 0.18 FP
1 assist = 0.31 FP
1 steal = 0.96 FP
1 block = 1.52 FP
Accordingly, to equal the fantasy value of a single blocked shot (worth 1.5 FP) a player would have had to score 21.7 points (also 1.5 FP).
By this measure, last year’s fantasy MVP Kevin Durant averaged:
Points = 1.97 FP
3-pointers = 1.84 FP
Rebounds = 1.42 FP
Assists = 1.43 FP
Steals = 1.34 FP
Blocks = 1.98 FP (Durant averaged a career-high 1.3 blocks last year, greater than LeBron's 0.9 per game)
Relative Statistical Values
The numbers above have another easy, useful and interesting application. The table below displays the relative values of a given stat as compared to the other primary fantasy stats (again, shooting percentages are excluded). Read across the rows.
Let’s take Serge Ibaka as a case study. He averaged 13.2 points, 0.3 threes, 7.7 rebounds, 0.5 assists and 0.4 steals last season, with rebounds the only one of those categories in which he exceeded the top-170 mean. He also made a terrific 57.3 percent of his FGs, but his elite fantasy value was grounded in a league-leading 3.0 blocks per game (4.56 FPs). It’s easy to see why such gaudy shot-blocking has massive fantasy appeal, but just for fun here are the fantasy-equivalent averages if you converted Ibaka’s 3.0 blocks per game into other statistical categories:
Points = 65.1
3-pointers = 4.2
Rebounds = 25.3
Assists = 14.7
Steals = 4.7
Nobody in the NBA came close to averaging any of those numbers last season, with the vague exceptions of Rajon Rondo (11.1 assists) and Steph Curry (3.5 triples per game, en route to a new NBA record). In other words, Ibaka didn’t merely lead the league in blocks per game – he lead the league in total FP value for any of the six statistical categories under consideration. I’m avoiding commentary on specific players in this column, which is focused on ways to measure player values, but it’s worth saying that Ibaka is poised for a massive season. He’ll finally average more than last year’s career-high 31 minutes per game, he’s worked hard to improve his already-solid offensive game, and he’ll play a featured role all season (and especially while Russell Westbrook is out). But there’s still another reason why Ibaka’s shot-blocking has outsized value in fantasy leagues — statistical scarcity.
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Scarcity
In addition to being rare as regards league-wide stat totals, blocks are also concentrated in a handful of (mostly) PFs and Cs. To be more explicit, there were 79 players who exceeded the mean 13.7 points per game last season, but only 52 players exceeded the mean 0.7 blocks per game.
Below is a list showing how many of the top-170 players raised the statistical mean in a given category last season — the lower the number, the harder it is to find value-added players (i.e. the scarcer the category). Note: the numbers for FG percentage and FT percentage do NOT account for the fundamentally important volume of shots attempted, and should only be viewed as a rough approximation of the properly-adjusted numbers.
Points = 79
3-pointers = 86
Rebounds = 71
Assists = 66
Steals = 72
Blocks = 52
FG percentage = 70
FT percentage = 100
This confirms what most fantasy owners already know, or at least suspect, which is that blocks and assists are the two ‘scarcest’ categories. Being heavily reliant upon PF/Cs and PGs, respectively, they are more top-heavy than the other categories.
Does this mean that you should hunt for blocks and assists during the early rounds? By isolating the top-50 players from last year, we find useful spreads between the ‘top-50 means’ and the ‘top-170 means’ (FP values in parentheses).
Points = +4.21 (0.30 FP) In other words, the top-50 players, on average, scored 4.21 more points (or 0.3 FP) than the overall mean for the top-170.
3-pointers = +0.04 (0.04 FP)
Rebounds = +1.01 (0.18 FP)
Assists = +1.51 (0.47 FP)
Steals = +0.26 (0.25 FP)
Blocks = +0.18 (0.27 FP)
The numbers above suggest that assists are indeed the statistic most heavily concentrated in the top-50 fantasy players, and will therefore be more difficult to find as the draft progresses into later rounds. The next most top-heavy categories are scoring, blocks and steals. Rebounds are somewhat more evenly dispersed throughout the top-170, and there is barely any concentration of 3-point shooting. As usual, absolute FG percentages and FT percentages are misleading since, by themselves, they don’t account for volume of attempts. These results should simply be kept in mind on draft day.
The broader point is that it’s easy to make a few spreadsheets and dig up the type of numbers referenced throughout this column, and as many more as you can dream up. Doing so confers an advantage to fantasy owners, even if it only provides a few pieces of the puzzle that is a player’s value. When you begin constructing an entire roster, or drafting according to a specific strategy, the need for orderly statistics and objective information becomes paramount.
In my next column I will address the critical notion of standard deviations. That will be followed by columns about the importance and value of games played, the relative merit of ‘punting’ categories, and maybe a few other columns which I haven’t yet sketched out. I am not a statistician, a mathematician, nor even a person who particularly enjoys math. I do, however, enjoy the clarity which math can bring to thorny and complex 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. Thanks for reading.
