This article is part of our Numbers Game series.
Welcome to a new column that will focus on decoding the math that underpins fantasy basketball. Alex Rikleen is a certified math teacher who decided that the field of education pays too well, so he left it for writing.
To make for easier reading, more detailed explanation of methodology will be put at the end of the article.
What does the average fantasy starter produce?
Answering this question is one way of approaching the fantasy offseason's most critical task -- building a team that produces more than all of your opponents' teams. Once the average starter profile is determined, you have a specific goal to aim for as you build your team.
Since "average" has a specific mathematical meaning, to avoid confusion I will now use the term "benchmark starter" when I'm not referring explicitly to the mathematical term.
During the draft, you can refer to the benchmark starter to see how valuable a player is. Early in your draft, you want a player who outperforms the benchmark in as many categories as possible (or by as much as possible in certain categories, if you are punting). Later on, you want a player who can either A) beat the benchmark in the specific categories you need, or B) develop into someone who performs at or near benchmark levels. (I'll go into more specifics about how to use the benchmark later.)
Can anyone know what players will produce ahead of time?
No one can predict with certainty any individual outcome. However,
Welcome to a new column that will focus on decoding the math that underpins fantasy basketball. Alex Rikleen is a certified math teacher who decided that the field of education pays too well, so he left it for writing.
To make for easier reading, more detailed explanation of methodology will be put at the end of the article.
What does the average fantasy starter produce?
Answering this question is one way of approaching the fantasy offseason's most critical task -- building a team that produces more than all of your opponents' teams. Once the average starter profile is determined, you have a specific goal to aim for as you build your team.
Since "average" has a specific mathematical meaning, to avoid confusion I will now use the term "benchmark starter" when I'm not referring explicitly to the mathematical term.
During the draft, you can refer to the benchmark starter to see how valuable a player is. Early in your draft, you want a player who outperforms the benchmark in as many categories as possible (or by as much as possible in certain categories, if you are punting). Later on, you want a player who can either A) beat the benchmark in the specific categories you need, or B) develop into someone who performs at or near benchmark levels. (I'll go into more specifics about how to use the benchmark later.)
Can anyone know what players will produce ahead of time?
No one can predict with certainty any individual outcome. However, looking at population as a whole -- in this case, the NBA players -- there is enough data that the averages should be predictable.
I looked at the last three years of fantasy basketball, and focused on the top per-game performers. I used per-game performance as a stand-in for fantasy ownership -- in a mathematically perfect world, the 130 players owned on standard league rosters would be the top 130 per-game producers. If the production values were consistent from year to year, then it would be fair to project similar results for the 2016-17 season. If there were differences, then I'd use the differences to project the trend one year further.
As it turned out, for most categories, the three years of data showed almost identical results. The only difference was that, in shallower leagues, the benchmark fantasy starter has been slowly improving his three-pointer and his shot-blocking.
What does the benchmark starter look like?
For standard 10-team leagues, our benchmark starter is a slightly-worse version of Rudy Gay, with more assists. This finding makes a lot of sense -- Rudy Gay rated as last season's 44th best per-game producer, and we are looking at the top 90 player pool. Compare Gay's line to our top 90 benchmark:
Rudy Gay: 17.2 points, 1.1 threes, 6.5 rebounds, 1.7 assists, 1.4 steals, 0.7 blocks, 46% FG, 78% FT
Top 90 Benchmark: 16.4 points, 1.3 threes, 6.0 rebounds, 3.6 assists, 1.1 steals, 0.8 blocks, ~46% FG, ~79% FT
It's logical that a versatile wing scorer matches the archetype of the benchmark player. The benchmark player is good, but not great at everything, possessing a balance of the strengths and the weaknesses of big bruisers and small ball handlers.
As you look down the chart at larger leagues, the benchmark player continues to resemble lower-ranked wings like Tobias Harris and Will Barton.
See the table below to find the stats of the appropriate benchmark player for your league size and settings:
Why do the percentage categories have little squiggles?
Because the percentage categories are a combination of several different statistics -- shots made and shots attempted, and ratio of shots made to shots attempted. As a result, the percentages listed are approximate values, while the other categories were based on concrete averages.
Why is the benchmark player so good?
You may have noticed that the benchmark player is no slouch. In fact, the benchmarks here should be, generally speaking, higher than the actual production levels you've experienced in your own league. There are a few reasons for this, explained in greater depth at the bottom of the article. The reasons boil down to the differences between human error and computer models. The model can't account for managers who make poor substitutions, such as ineffective replacements during an injury, or starting a player who just didn't pan out.
The benchmark is a goal, not a minimum requirement. Any team that can match the benchmark with their average production should be one of the best in their league.
How do I use this if I want to punt some categories?
Fear not, I've got benchmarks for you too.
The benchmarks above are for players trying to build a balanced roster. If you are trying to punt some categories, then you are going to need to dominate some categories as well. For example, there's not much reason to punt assists if doing so doesn't let you dominate rebounds.
Again, these benchmarks are goals, not requirements, and they err on the side of over-performing. If you hit these levels, you should be comfortably in the top two or three teams in that category. For every category you want to confidently dominate, these should be your targets. For the categories you just want to remain competitive in, try to hit the balanced benchmarks in the table above.
Sorry for those of you looking to lock down either percentage category – my data gets too muddled in those categories to provide trustworthy insight.
How can I use the benchmark player data during my draft?
Early in the draft, you want players who will obviously and handily defeat the benchmark player in head-to-head combat. Or in fantasy production. The more balanced a player's production profile, the more categories they should beat the benchmark in. Players with unbalanced profiles -- most centers, for example -- should build up significant margins over the benchmark in their areas of expertise, while remaining close to the benchmark in as many categories as possible.
In every subsequent round, your pick will fall closer and closer to the benchmarks.
By the late middle of the draft, roughly the seventh or eighth round, the benchmark should be better than the players left available (if you think there is someone left equal or better than the benchmark, then you have found your next selection). This is OK -- it's what is supposed to happen. The benchmark is the average starter, and you are filling in the below-average starting spots on your roster. Whoever you take, they should beat the benchmark in some area you need, and they shouldn't get blown out by the benchmark in more than a few categories.
In later rounds, remember: it's not enough to identify that a player is underrated. If his production never competes with the benchmark starter, then underrated or not, he still won't be good enough to help your fantasy team. Put differently, I think RotoWire has Buddy Hield underrated at 188 (in eight-category ESPN roto leagues). But if he ends up as fantasy's 131st best player, while I was correct that he was underrated, he still wasn't worth owning in my 10-team league (where 130 players are rostered). Applying that same concept to the benchmarks give you specific category goals to consider. Before drafting Hield, I consider his performance against the benchmark. I think Hield can beat the benchmark in points, three-pointers, and free-throw percentage, while not losing too badly in rebounds, assists, or steals. If I'm right, that's great work for one of my last draft picks.
Did you notice anything else interesting while you were figuring all this out?
As a matter of fact, yes, I did.
1) Democratization of three-pointers, assists, and free-throw percentage. I'll use an example to explain. Amongst fantasy starters – the top 90, 108, etc. -- the total number of made three-point shots has remained effectively constant year to year. But during that time, the league-wide average-player has made more three-pointers. This means there are more waiver -wire players who can provide some help in that category. This trend is seen in three-pointers, assists, and free throws. Two caveats apply: first, many of those players available on waivers may not be worth starting due to deficiencies in other categories, but if you are focusing on just one category at a time, the options here are improving; second, the democratization in assists has been small enough that it might be more coincidence than anything meaningful.
2) Centralization of rebounds, blocks, and field-goal percentage. This is the exact opposite of the trend described in Point 1. It means that there are fewer waiver-wire players who can provide some help in these categories. Similar to the trend with assists, the rebound trend is very slight, and could possibly be a matter of coincidence.
Why are you looking at the average starter, and not team total production?
Every league has its own settings with its own twists and quirks. Do you have a weekly games max of 30 games? A roto league with nine starting positions and 82 games per position? Can you start as many players as you can fit into your starting lineup each day? Whatever your league's settings, the average starter's production is only one step removed from your weekly or seasonal goal. Therefore, it is the most universally useful benchmark, regardless of settings.
Addressing the three types of leagues just mentioned: for the first, multiply the benchmark player by 30 to get your weekly goal; for the second, multiply by 738 (since 9 x 82 = 738) for a season-long objective; for the third, estimate how many games per week you can fit in, and multiply by that (you should be able to fill your starting lineup on Wednesdays, Fridays, and Saturdays; you should be able to start half your roster Sunday and Monday; and one third of your roster Tuesday and Thursday; for a standard nine-starter/13-man roster, that works out to a touch less than 50 games per week).
How did you determine the benchmark's production?
I figured out the benchmark using two different methods. For both methods, I started by limiting the player pool to the top 90, top 108, top 130, top 156, and top 182 overall fantasy players, according to per game production. By limiting the pool this way, I'm figuring out the average among only the owned players in the league. We aren't interested in the league-wide averages, since not every player in the NBA is used in fantasy.
For the first method, for each year, I figured out the per-game average (basic mean) production of a player in the top 90, top 108, top 130, top 156, and top 182. For the second, I started with league-wide standard deviation. Then I determined the average standard deviations across each of the same player lists (top 90, etc.).
The two methods lead to effectively identical per-game raw totals – i.e., both show that the average top-90 player records between 3.8 and 3.9 assists per game. That's not a surprise with a data set of this size, but it is also not necessarily a given. Among other advantages, using two approaches, rather than one, ensured a more reliable conclusion.
Why those particular thresholds? (90, 108, etc.)
Each one represents the number of starting spots or roster spots in 10-, 12-, or 14-team leagues.
Top 90: nine starters, 10-team league
Top 108: nine starters, 12-team league
Top 130: 13 roster spots, 10-team league (also an approximation of the top 126, for nine starters, 14-team league)
Top 156: 13 roster spots, 12-team league
Top 182: 13 roster spots, 14-team league
Why is the benchmark player so good? (Expanded answer)
There are several factors working in the benchmark player's favor.
1) I'm working backwards, looking at the players who already showed they were the most productive. Actual managers don't have the benefit of hindsight, and will frequently play unproductive players, for a wide variety of reasons. And they typically will do so for many games at a time.
2) I'm working with the mathematically determined top players. But humans, not computers, play fantasy. Some of these players aren't actually used in most fantasy leagues. For example, Manu Ginobili earned a spot inside my top 130. Mathematically speaking, he wasn't really painful in any category. Most real live humans, however, were turned off by his paltry 9.6 points and 20 minutes per game. Further, due to his age, his health, and his team situation, Ginobili offered no optimism that his production would get better. Most managers opted for players who produced slightly less overall, but had more potential to improve.
3) I can't properly account for missed games. In real life, someone far worse than Anthony Davis replaces Davis in fantasy lineups for roughly 15 games each season. This brings down the average level of real-life fantasy production significantly. I've adjusted my model to attempt to compensate, but as managers know, balancing missed games in real life is rarely elegant. In a computer model, on the other hand, Player 91 seamlessly transitions in for any missed game amongst the top 90; once all of Player 91's games are used, then Player 92 comes in, and so on and so forth.
I have only come up with one significant factor working against the benchmark player: the benchmark is based on year-long average production by individual players. Last season, after a largely irrelevant first two months, Devin Booker broke out and became a fantasy mainstay. However, the breakout came late enough that Booker remained outside of the top 130 for the season overall. In real fantasy, Booker replaced someone mildly productive on fantasy teams. But this model does not allow for a first half of the season of middling Player X combined with Booker's second half.
