G-scores
It is well-understood that player value in category leagues is dependent on context. No single number, independent of circumstances around team, opposition, etc. can ever fully define a player's value. However, that has not stopped fantasy enthusiasts from designing and applying so-called 'static' ranking systems. Despite their limitations in theory, they are useful in practice because they are simple and convenient. One ought not let the perfect get in the way of the good.
The website uses G-scores as a measure of static value. G-scores are a variant of the traditional Z-score metric, as described in my first paper. See also the justification section of this page for a relatively simple explanation.
G-score table
During auctions and drafts, a tab will be available with the G-score table for available players. It includes the categorical components of G-scores as well.
Team table
The team table shows the G-scores of players already chosen for a team, and their totals. The totals show how the team is doing in general, though one should keep in mind that non-turnover categories tend to have high values during early rounds because only the strongest players are being taken.
Justification
Warning- math 
What are Z-scores?
Fantasy basketball has a standard way of quantifying player value across categories, called 'Z-scoring', and it is used to make objective rankings of players.
In a stats 101 class, Z-scores are what happens to a set of numbers after subtracting the mean (average) signified by \(\mu\) and dividing by the standard deviation (how “spread out” the distribution is) signified by \(\sigma\). Mathematically, \(Z(x) = \frac{x - \mu}{\sigma}\).
Z-scores in the fantasy context are essentially the same thing. They take a player's expected performance in a category, subtract out the average from the paper pool, and divide by the standard deviation.
One complication is that some categories are percentage-based, like free throw percent. See the paper for details on how the analysis is extended to them.
Justifying Z-scores
Consider this problem: Team one has \(N-1\) players randomly selected from a pool of players, and team two has \(N\) players chosen randomly from the same pool. Which final player should team one choose to optimize the expected value of categories won against team two, assuming all players perform at exactly their long term mean for a week?
The difference in category score between two teams indicates which team is winning the category and by how much. Randomly selecting the \(2N -1\) random players many times gives a sense of what team two's score minus team one's score will be before the last player is added. See this simulation being carried out for blocks below with \(N=12\)
You may notice that the result looks a lot like a Bell curve even though the raw block numbers look nothing like a Bell curve. This happens because of the surprising "Central Limit Theorem", which says that when adding a bunch of random numbers together, their sum always ends up looking a lot like a Bell curve.
The mean and standard deviation of the Bell curves for category differences can be calculated via probability theory. Including the unchosen player with category average \(m_p\) - The mean is \(m_\mu - m_p\) - The standard deviation is \(\sqrt{2N-1} * m_\sigma\) (The square root in the formula comes from the fact that \(STD(X + Y) = \sqrt{STD(X)^2 + STD(Y)^2}\) where \(STD(X)\) is the standard deviation of \(X\))
When the category difference is below zero, team one will win the category
The probability of this happening can be calculated using something called a cumulative distribution function. \(CDF(x) =\) the probability that a particular distribution will be less than or equal to \(x\). \(CDF(0)\), then, is the probability that the category difference is below zero and team one wins (ignoring ties).
The \(CDF\) of the Bell curve is well known. The details of how to apply it to this case are somewhat complicated, but we can cut to the chase and give an approximate formula
\(\mu\) and \(\sigma\) for the standard statistics are already known. Substituting them in yields
Hey look, that's the Z-score! this equation shows that an extra point of Z-score translates into an increased probability of winning the category in a consistent way.
Extending to G-scores
To justify Z-scores, it was assumed that each player would perform precisely at their long-term mean. But that was a bad assumption, because players don't perform consistently week-to-week. The question can be improved by assuming that players are chosen randomly and their performances are chosen randomly too.
Below, see how metrics for blocks change when weekly performance of the top \(156\) players are sampled, instead of just their averages
Although the mean remains the same, the standard deviation gets larger. This makes sense, because week-to-week "noise" adds more volatility, which is reflected in the additional \(m_\tau\) term. Note that the new standard deviation is \(\sqrt{m_\sigma^2 + m_\tau^2}\) rather than \(m_\sigma + m_\tau\) because of how standard deviation aggregates across multiple variables, as discussed previously
Also keep in mind that for Rotisserie, the uncertainty is in season-long performance, rather than week-by-week variance.
Substituting the new standard deviation into the Z-score equation creates G-scores. they are
Calculation logic
The definitions of Z-score and G-score are based off a highly idealized version of fantasy basketball, and some thought is needed to calculate them appropriately for a real league.
One of the inputs needed for the scoring process is a player pool. Using the entire pool of NBA players is a sensible starting point, but significantly flawed because most NBA players do not produce enough to be fantasy relevant. The approach of the website is to calculate scores based on the entire playing pool, then use the top players from that calculation as the player pool for the scores it ultimately calculates. This ensures that parameters like \(m_\sigma\) are calculated based on players that are somewhat likely to be in real leagues.
Based on the proxy for the real pool of players and forecasts for their performances, it is easy to calculate player-to-player variance. Week-to-week variance cannot be inferred from forecasts, and instead has to be calculated historically. The website uses historical conversion factors from player-to-player variance to week-to-week variance.
Limitations
G-scores are fundamentally limited because they do not adapt to drafting circumstances. Drafting based purely on total G-score, or any static metric, is a flawed approach.
With that said, it is worth listing out some of their limitations explicitly
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Total G-scores have no mechanism for balancing out teams across categories. Drafting purely by G-score can lead to teams which dominate in a small number of categories, and struggle with the rest
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G-scores cannot encode dynamic strategies like "punting" weak categories
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G-scores do not account for positional needs. Drafting purely by G-score can lead to teams which are imlabanced across positions
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G-scores are defined based on a projected set of relevant players, which may be inaccurate
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There are some small assumptions used in the papers to align the G-score definition with the traditional definition of Z-scores. Relaxing these assumptions would lead to slightly different results