Loading scores...
The Numbers Game

Stats: Scarcity and Volatility

by Ryan Knaus
Updated On: October 4, 2018, 4:09 pm ET

This week's column deals primarily with the statistical scarcity and volatility of fantasy categories. Before explaining those ideas and diving into the numbers, let’s take a quick look back at some conclusions drawn over the past three weeks.


In last week’s column, Values and Trends, it was shown that points and weighted FT percentage were highly concentrated early in fantasy drafts for 2013-14. Steals, rebounds and assists all showed a predictable and steady drop-off across the top-100 players, but value-added players could still be found in these categories throughout the middle rounds and (occasionally) beyond the top-150. Three-point shooters were readily available in the middle-to-late rounds, as were players capable of raising your fantasy team’s FG percentage. Blocks were primarily concentrated in the first few rounds, though eight outliers offered at least +1 standard deviation between picks 100-150.


The week before that, in Busts and Values, guards were found to comprise the majority of the season’s premier ‘value picks’ (e.g. Lance Stephenson, Isaiah Thomas, Jodie Meeks) while forwards and centers dominated the list of the biggest ‘busts’ (e.g. Omer Asik, J.J. Hickson, Ersan Ilyasova). The top-216 players, similarly, included slightly more guards than forwards, with centers predictably scarce in leagues that require two Cs on each active roster. A few rookies broke through for substantial value, such as Michael Carter-Williams and Ryan Kelly, but the vast majority was worthless for fantasy purposes. It was also found that the middle rounds of fantasy drafts, rounds 5-7, were riddled with ‘busts’ and under-performing fantasy picks, whereas rounds 8-12 provided more reliable value relative to Average Draft Positions.


Most of the above conclusions were derived from my overall top-216 rankings, which showed a tendency for SFs to provide late-round value in nine-cat leagues, where their low turnovers are an underrated asset. A close examination of those rankings shows interesting splits between each player’s eight-cat and nine-cat rankings, and you can peruse them at your leisure.


There are more interesting takeaways, but let’s jump ahead to the focus of today’s column—statistical scarcity and volatility. Back in October I identified 3-pointers, blocks and assists as the categories with the greatest 'scarcity', which is to say they were concentrated in a relatively small group of players and/or showed wide variations from player to player. That analysis was based on a small sample size early in the season, however, so I’ve decided to revisit the concept to determine if my original conclusions held up throughout the season.


Number of Players Exceeding the Mean


The title of this section explains a simple way to understand the concentration of statistics across fantasy players, in this case the top-170 nine-cat options from 2013-14. Before looking at how many players raised the mean in a given category, let’s quickly look at what those means were for the relevant top-170 population:


Points: 14.04

3-pointers: 1.04

Rebounds: 5.46

Assists: 3.16

Steals: 1.02

Blocks: 0.58

FG Percentage: 46.30%

FG Attempts: 11.29

FT Percentage: 76.80%

FT Attempts: 3.34

Turnovers: 1.88


The chart below excludes FG and FT figures. It also lists the number of players below the mean for turnovers, which is the only category in which more than half of the top-170 players ‘improved’ upon the mean. The second-most readily available category was 3-pointers, in which nearly half of the population (83 players) raised the mean. The number of value-added players dwindles as you read the categories from left to right, and once again shot-blocking proves to be the category concentrated among the fewest number of players.


Image and video hosting by TinyPic


This highlights the appeal and rarity of players who average 1+ blocks per game, guys whose defensive contributions are easy to overlook such as Terrence Jones, Amir Johnson or Pau Gasol. It also suggests that a turnover machine like Russell Westbrook or John Wall can be compensated for as the draft progresses, since there are tons of guys who average below the mean 1.88 turnovers per game. Three-point shooters may also be less of a priority early in drafts considering the number of viable options averaging at least 1.04 triples per game. Although this is an easy way to visualize the hunt for value-added players across fantasy categories, it is an incomplete analysis. Knowing that a player raised the mean only tells us so much – it suggests the amount of statistical concentration and scarcity but doesn’t capture the degree to which players raised the mean. This is where standard deviations (SD) come in.


Standard Deviations as a % of the Mean


Let’s use assists as a quick case study to explain the concepts behind the following chart, which I’ll dub a ‘volatility index’. The SD for assists among this season’s top-170 players was 2.15. The mean for the category, as noted above, was 3.16 assists per game. By referencing the normal distribution for SDs, therefore, we know that 68.2 percent of the top-170 players handed out between 5.31 and 1.01 assists per game (that’s 3.16 assists +/- the standard deviation). A player cannot hand out negative assists, of course, but approximately 27.2 percent more players either averaged under 1.01 assists per game or they exceeded 5.31 – in fact, there were 14 players below and 31 players above.


By relying on SDs you can assign comparable ‘standardized scores’ to players across different fantasy categories, as I did for my columns regarding top-216 rankings, values and busts, and trends across categories. For instance, Chris Paul’s 2.48 steals per game give him a standardized score of 3.82 in that category, but his 0.06 blocks per game result in a -0.93.


The next step, which I consider in the chart below, regards the relative size of SDs compared to a category’s mean.  Points prove to be a relatively stable category, with approximately 68.2 percent of players averaging between 18.8 or 9.3 points per game. Blocks, on the other hand, is a more volatile category since the range of a single SD goes from a healthy 1.1 blocks per game to nearly zero (0.05). As I wrote in October, "The higher the percentage ... the wilder the swings will be in that category from player to player."



Image and video hosting by TinyPic


As alluded to above, categories like points, weighted FG percentage and steals show relatively low percentages in the chart, implying that most players contribute something in these categories. The notion that points and weighted FG percentage would be placid doesn’t strike me as odd, but I’m surprised to find that steals are both relatively easy to find and relatively stable throughout the top-170 players.


Blocks, 3-pointers and assists, however, are more ‘specialized’ categories in that players typically either do or do not contribute –such categories can be rightly called ‘boom or bust.’ Blocks once again prove to be both the most concentrated category (the fewest players raising the mean) and the most volatile (players do or don’t contribute). You’ll either need to snag a premier shot-blocker early in your draft, target one of the handful of mid-round specialist big men (see above), or in head-to-head leagues you might choose to punt the category and focus your draft strategy elsewhere. The severe volatility of 3-point shooting is less worrisome, since as we’ve seen above there are far more 3-point shooters available among the top-170 players.


Weighted free throw percentage is an interesting case. Last week’s column showed a stark concentration in the first few rounds, where players such as Kevin Durant and James Harden simply dominate the category, but it’s primarily about volume of attempts as opposed to percentages. Durant averaged a whopping 9.9 free throws per game and Harden averaged 9.1, which magnified their stellar percentages at the stripe (87.3% and 86.6%, respectively). The same logic holds in reverse, of course, for guys like Dwight Howard (54.7% on 9.0 attempts) and DeAndre Jordan (42.8% on 4.6 attempts).


On the other hand, you could have drafted a player like Andrew Bogut, who shot an abysmal 34.4% at the line (!) but didn’t hurt fantasy owners very much since he attempted a mere 0.96 freebies per game. Kendall Marshall is another great example – as a point guard his 52.8% FT shooting should have been unforgivable, but he only went to the line 0.7 times per game. On the flip side, we find players like Kyle Korver. While Korver’s 92.6 percent FT shooting is undeniably stellar and would have ranked second in the NBA behind Brian Roberts, he didn’t qualify as a league leader because he took just 1.3 attempts per game. Other high-percentage FT shooters who negated their fantasy value with low-volume include J.J. Redick, Ray Allen, Trey Burke, Reggie Jackson and D.J. Augustin. The moral is to not be blinded by percentages alone.


I'll end today’s column on that note. Check back next Monday for another Numbers Game column, the topic of which I’ve yet to decide. If you have any requests or recommendations, drop me a line via email or on Twitter.

Ryan Knaus
Despite residing in Portland, Maine, Ryan Knaus remains a heartbroken Sonics fan who longs for the days of Shawn Kemp and Xavier McDaniel. He has written for Rotoworld.com since 2007. You can follow him on Twitter.