Introduction

The Honor Roll is an addition to Everything's Voting/Experience system designed to better accommodate a broad range of noding styles. Some noders focus mostly on quantity by adding short writeups. Other noders take a quality approach; they add well researched, in-depth writeups, and as a result produce fewer writeups. However for both extremes of noding styles, each writeup counts as one, not taking into account the amount of effort and time the noder has spent on creating it. The Honor Roll is a system that rewards noders that consistently write high quality writeups, by allowing them to level-up with fewer writeups.

Quality quantified: Merit and Level-Up Factor

The Honor Roll system introduces two concepts, namely merit and a Level-Up Factor (LF). The merit is a measure for your average writeup reputation, while LF is an index that determines how many writeups are required to Level-Up, compared to the regular requirements in the Voting/Experience system.

Merit is calculated by a statistical measure called the Interquartile Mean. It is similar to the scoring method used in sports that are evaluated by a panel of judges. The outliers, the highest and lowest marks are discarded, and an average is calculated of the remaining values. This system has the advantage that extreme outliers will not affect the value of the average. Merit is calculated as follows:

• Rank the writeup reputations lowest-to-highest
• Discard 25% of the data with the lowest reputations, and 25% of the data with the highest reputations.
• Calculate the average (arithmetic mean) of the remaining 50%.

A more detailed description and an example is given under Interquartile Mean.

The Level-Up Factor determines how many writeups are required to level up in the Honor Roll. Before going into the mathematical background of this parameter, this factor works as follows:

• Each day the average merit of all noders with 25 or more writeups is calculated
• All noders with a merit smaller than the average merit, or with fewer than 25 writeups are not eligible for the Honor Roll, and have a Level-Up factor equal to 1.
• All noders with a merit greater than the average merit and 25 or more writeups enter the Honor Roll and have a Level-Up factor between 0.5 and 1. The LF becomes smaller with increasing merit.
• Multiply the LF with the regular number of writeups required to reach a level (see Voting/Experience System).

In formula:

(Honor Roll WUs required) = (LF) × (Level WUs required)

For instance, a noder with LF=0.7 would need 0.7 × 150 = 105 writeups to reach Level 4 (thus, 45 writeups less). A noder with LF =0.5 would need 0.5 × 700 = 350 writeups to reach Level 8 (and consequently level-up twice as fast compared to the regular requirements).

Qualitatively, the Level-Up factor begins at 1, and drops gradually to 0.5 as merit is increased. Thus, the lower LF, the fewer writeups are required to level-up.

How is LF calculated?

Following is a quantitative description of how the Level-Up Factor is calculated. A knowledge of basic statistical terms is helpful for understanding this section.

The merit of noders with 25 or more writeups can be approximated by using the Normal Distribution. Thus, if we count noders with a merit ranging from 1-2, from 2-3,..., the observed frequencies resemble a traditional bell-curve that can be modeled using the Normal Distribution.

```
0.16 ++-+------+------+------+-----**-----+------+------+------+-++
|  +      +      +      +    *  *    +      +      +      +  |
|                           *    *                           |
|                          *      *                          |
0.14 ++                        *        *                        ++
|                         *        *                         |
|                        *          *                        |
|                        *          *                        |
|                        *          *                        |
0.12 ++                      *            *                      ++
|                       *             *                      |
|                      *              *                      |
|                      *              *                      |
0.1 ++                     *               *                    ++
|                     *                *                     |
|                     *                *                     |
|                     *                 *                    |
|                    *                  *                    |
0.08 ++                   *                   *                  ++
|                   *                    *                   |
|                   *                    *                   |
|                  *                      *                  |
Fraction  0.06 ++                 *                       *                ++
in             |                 *                        *                 |
Class          |                 *                        *                 |
|                *                          *                |
|                *                          *                |
0.04 ++               *                          *               ++
|               *                            *               |
|              *                              *              |
|             **                              **             |
0.02 ++            *                                *            ++
|           **                                  **           |
|          **                                    **          |
|        **                                        **        |
|  +  ****+      +      +      +     +      +      +****  +  |
0 *******---+------+------+------+-----+------+------+---*******
-2      0      2      4      6     8     10     12     14

Reputation

```

This type of distribution is easily characterized by two parameters:

1. The mean of the distribution μ, which is the value corresponding to the maximum of the bell curve.
2. The standard deviation of the distribution σ, which is a measure of the broadness of the curve.

Both the mean and standard deviation are calculated daily for the merit of noders with 25 or more writeups. The probability density function for this distribution is now given by:

f(x) = e(-(x-μ)2/2σ2) / (σ√(2π))

It is important to note that the maximum of this curve occurs at x=μ, and that the curve approaches zero at both ends of the curve, at -∞, and +∞.

The maximum of the Normal curve can be made equal to unity by multiplying it with σ√(2π):

g(x) = e(-(x-μ)2/2σ2)

Values for g(x) range from 0 at the extremes, to 1 at the mean. We are only considering the upper half of the distribution. The equation is modified, so that noders with merit at the mean will have a Level-Up factor equal to 1, and LF decreases for increasing merit. The minimum LF is set at 0.5, thus at best half of the regular number of writeups are required to level-up. An appropriate function for this is:

LF(x) = 1/(2-g(x))
LF(x) = 1/(2-e(-(x-μ)2/2σ2))

LF(x) describes how the level-up factor is a function of merit, the average merit and standard deviation of the sample population. For LF < μ, LF is set equal to 1. Note that in theory, the minimum value for LF can only be achieved for infinitely high merit values. However, due to rounding, LF values equal to 0.5000 may occur.
```
1 +**********-------+------------+-----------+-----------+----++
|          **     +            +           +           +     |
|            **                                              |
|              *                                             |
0.95 ++              **                                          ++
|                **                                          |
|                 **                                         |
0.9 ++                  *                                       ++
|                   **                                       |
|                     *                                      |
|                     **                                     |
0.85 ++                     **                                   ++
|                        *                                   |
|                        **                                  |
0.8 ++                        *                                 ++
|                          **                                |
|                           *                                |
|                            **                              |
LF     0.75 ++                            **                            ++
|                              *                             |
|                               **                           |
|                                **                          |
0.7 ++                                 *                        ++
|                                   *                        |
|                                    **                      |
0.65 ++                                    **                    ++
|                                       **                   |
|                                        ***                 |
|                                          **                |
0.6 ++                                           **             ++
|                                              ***           |
|                                                ***         |
0.55 ++                                                  ***     ++
|                                                      ***** |
|                                                          ***
|     +           +            +           +           +     |
0.5 ++----+-----------+------------+-----------+-----------+----++
6           8           10          12          14

Merit

```

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