Evaluating Simple Node-Fu and Write-up Node-Fu:

The Simple Node-Fu (SNF) and the Write-up Node-Fu (WNF) are both based on calculating an average of the mean of a given dataset. In the SNF calculation, this dataset is the accumulated XP and as Pike already pointed out, this also includes XP collected through voting.

Indeed, in order to evaluate your node-writing ability, it may be better to evaluate the accumulated reputation of all the write-ups. At first, it seems fair to evaluate the reputation by calculating the average of the mean:

Mean reputation = Σr / NC

Where Σr is the sum of all the write-up reputations, and NC is the total node count.

However, examination of the Range (defined as Highest Rep - Lowest Rep) of the write-up reputations shows that there is generally a big gap between the highest and lowest valued write-up. In my case it is currently 29, but more extreme examples are plentiful. Since the write-up reputations are so widely spread around the mean, the mean reputation is not the correct measure for a person's node writing ability.

More definitive evidence on the wide spread of the node reputations comes from calculating the standard deviation of Σr. The standard deviation describes how widely spread the sample reputations are from the mean. My write-ups have a mean reputation=4.0, with a (sample) standard deviation=4.6. This is a huge standard deviation, especially considering that the standard deviation is actually larger than the magnitude of the mean. No doubt other noders have similar statistics.

Since Pike's calculation of WNF is also based on a mean write-up reputation (with a correction for C!'s), this method incorporates the same inaccuracies that are introduced due to the wide spread of node reputation. Nodes with a high reputation have a dramatic influence on the accuracy of the WNF.

Median Node-Fu (MNF):

The problem of wide distributions around the mean is often encountered in statistics. In these cases, the median is a better measure of central tendency. The median is the midpoint of a distribution; half of the observations are below the median, and half are above it. For example: family income for a country or region is usually listed at the median, since families with very high or low income can have a large influence on the mean.

Since the median is less affected by extreme scores (very low-, or high-reputation write-ups), I propose the use of an alternative index, the Median Node-Fu (MNF). It is calculated as follows:

1. Arrange the nodes in order from smallest to largest node reputation.
2. Determine the node count (NC); the number of write-ups of a user.
3. If NC is odd, then the MNF is equal to the reputation of the (NC+1)/2 th write-up.
4. If NC is even, then the MNF is equal to the average (mean) reputation of the NC/2 th write-up and the 1+(NC/2)th write-up.

Example:

Let's take the Everything User Search output of Bob, who made 10 write-ups. Sort them by Lowest Reputation First:
```My favorite X  (thing)     full     -3  2000-10-05 20:05:02
Urk (place)                full      0  2000-11-07 21:34:45
John Doe    (person)       full C!   1  2000-07-28 14:28:53
tire (thing)               full      2  2000-09-04 17:45:23
Atari (thing)              full C!   3  2000-09-15 11:11:19
Eating out (thing)         full      4  2000-12-14 23:06:47
Senor Spielbergo (person)  full      5  2000-10-18 10:14:34
Phoebe Snow (person)       full      6  2000-10-05 15:48:51
Elm Street (place)         full C!  10  2000-11-07 18:23:12
Nude bagpiping (idea)      full C!  48  2000-10-09 21:52:16
```
Bob's SNF could be anything, since it is not based on reputation but on XP. His WNF is equal to (10 + 76 + 40)/10 = 12.6. Now Bob's MNF is (3 + 4)/2 = 3.5.

Calculating anyone's MNF

As opposed to WNF, it is easy to calculate the MNF of any user on Everything, at the price of one vote:
1. Find the user on Everything User Search
2. Find out the number of write-ups (NC) of this user
3. Display the write-ups, display by Lowest Reputation First
4. Page through until write-up (NC-1)/2, and display the write-up (1 is subtracted from NC, since the first write-up is 0)
5. Vote. The write-up reputation will be listed
6. Add or subtract one reputation point, depending on whether you upvoted or downvoted, respectively. This will give you the user's MNF.

Alternative Method:

Open in your browser:

Where {(NC-1)/2} is the median node count (e.g. it is 124 for a user with 250 write-ups), and username is the user you want to calculate the WNF for. Continue with steps 5 and 6.

Discussion:

MNF is low:

The Median Node-Fu will generally be lower than the SNF or WNF, simply because it is not affected by extreme write-up reputations.

Another interesting observation is that the accuracy of the MNF increases with increasing number of write-ups. Even though the range of write-up reputation can become very large, it has no effect on the MNF.

C!'s:

Unlike SNF and WNF, the MNF is independent of C!'s. The reason is that C!'ed write-ups are already rewarded through longer exposure on the front page. Good write-ups will receive all the votes they deserve.

"MNF never goes up"

The Median Node-Fu will certainly go up, but it requires a significant amount of high quality write-ups. On average, your new write-ups need to gain higher reputation than your MNF. Also, take a look at low-reputation write-ups and improve them.

Final Remarks:

Use this index only as a personal measure of your write-up quality, not as a measure to compare to others. The point is not to be better than someone else; it is to become better than you were. However, since an Everything's Best Users ranking is apparently part of the game, please see Median Node-Fu Product for a further analysis.