Saturday, January 25, 2014

Fantasy Basketball Manifesto Part II: Rarity Scoring

Ranking fantasy basketball players, and determining how valuable the players are in general, is not as easy as it seems due to the number of categories head-to-head and rotisserie leagues compete in. As I discussed in part I, Standard Scoring is the mainstream method used by big players in fantasy sports such as ESPN and Yahoo sports. Rarity scoring is a simpler method of ranking players, giving value to stats based on how rare they are. As I will discuss in part III, this is a much superior method than Standard Scoring.

Rarity Scoring Basics

The premise is simple - every category matters as much as another. If there are 1,000 points scored and 500 rebounds total, then each rebound will be twice as valuable as each point. As an illustrative example, I'll look at Yahoo's current (January 25th) top 12 players over this season's average stats.

The "population" of our league has 12 players. The most common statistic is points scored, so we will put all the other statistics in terms of points scored. Since no category is more important than another, we normalize each category so the total "fantasy points" are equal.

We just have to divide total points scored (286.5) by the total amounts of the rest of the categories and then we get a coefficient we can use to normalize all the categories. In this example, the coefficients are in the "value" column at the bottom. For blocks, the value coefficient is roughly 30 points. This means it is just as valuable for your player to score 1 block as it is to score 30 points.

Now we will use these coefficients to see how we rank and value the 12 players in our population. The coefficients and ranks won't work in any league with more than 12 players and 6 categories, but the concepts are the same.

(click image to expand)

Normalizing Percentages

Free throw and field goal percentages should be equally important as the other categories in fantasy basketball. In part I of this series, I went over FTOP and FGOP - my method of turning percentages into simple countable statistics. But even after making field goal percentage and free throw percentage countable, normalizing FGOP and FTOP is more difficult than the other categories, since half the scores are negative.

To account for how much more the worst shooters affect your team than the best shooters, I only normalize the positive shooting to points scored. The statistics FTOP and FGOP already ensure that there is equal value above and below the average shooter. The total effect of FGOP and FTOP coefficients is the same as the other categories, even though half of the effect is negative.

Ranking Players with Rarity Scoring

1. Determine the size of your league (your population).
2. Nominally rank all NBA players - we will have to re-rank players over and over again, so the way we rank them the first time doesn't matter. It helps to use a logical ranking so it takes fewer iterations though.
3. Assign nominal coefficients to all of the categories in your league. Again, the more logical your starting point the faster the process finds your solution.
4. Find the sums of all the countable statistics of players that would be owned in your league (a 13 player, 10 team league you would sum the top 130 players - your "population"), then determine the coefficients to normalize those scores back to points.
5. Using the new coefficients you just calculated, find the total fantasy production of each player in the NBA, then re-rank the players.

Since every time you re-rank your players, it will change the totals of all the players in your population, you have to re-calculate the coefficients and total values over and over again. Usually by 5 iterations, the ranks will have already stabilized and you have results. Please note that this whole process is a lot of work in excel, so before you try this make sure you have some time to invest. The last installment of this series will have a downloadable spreadsheet to calculate stats for your league if you want me to do the work for you!

Using average statistics for generating ranks and coefficients gives a lot better results - the number of games played or games missed will greatly affect results. In order to be more accurate, calculate the averages yourself using total stats and total games played - a spreadsheet carries a lot more decimal places than websites designed to be easy to read.

How to Use Rarity Scoring Coefficients

I am not posting results for most of the categories here because there is so much more to the Fantasy Basketball Manifesto that I haven't covered yet, but here are the coefficients. FTOP and FGOP are more difficult than posting a coefficient due to things we will discuss in part IV. Using these coefficients is easy - multiply a box score line by the coefficient below to see how valuable it is for fantasy.

Points: 1
Rebounds: 2.5
Assist: 4.5
3PM: 15
Steal: 10
Block: 20

These are rough estimates of the values using pure rarity scoring. A 30 point, 5 rebound game with no treys, blocks, steals, or assists doesn't help very much compared to a 12 points, 2 treys, 5 assist, 3 steal, and 1 block line, even though the first one has a better chance of getting you on SportsCenter!

Armed with this I hope you have better luck in your leagues trying to pick up new players or ripping off your friends in blockbuster trades! Keep looking here for the rest of the Fantasy Basketball Manifesto!


  1. Great write-up. I am doing something similar, but also incorporating the standard deviation and kurtosis in the statistical distribution of each category. I think this paints a better picture of the stat distribution, and how to valuate them (i.e. bulk of assists can be found in the top 5 PGs with a steep dropoff after).

    Best of luck!

  2. Thanks for reading, glad you enjoyed it. I'm not going to spoil the unposted articles, but most of the rest of the manifesto addresses a lot of the points you bring up, I hope you come back and let me know what you think.