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Research talk:Modeling monthly active editors/Work log/2014-06-26

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Baselines

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Rates are means over the last 11 months and counts are taken from April, 2014.

Monthly active editors (MAE)
1206
Registrations (REG)
32005
New active editors (NAE)
1004
New activation rate (NAR)
0.02591
Surviving new active editors (SNAE)
77
Surviving new activation rate (SNAR)
0.08641
Recurring old active editors (ROAE)
124
Recurring old activation rate (ROAR)
0.2740
Reactivated active editors (RAE)
201

Equation

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Basic
MAE = REG * NAR + NAE * SNAR + (SNAE + RAE + ROAE) * ROAR + RAE
Expanion
NAE = REG * NAR
SNAE = REG * NAR * SNAR
ROAE = (SNAE + RAE + ROAE) * ROAR
     = ((REG * NAR * SNAR) + RAE + ROAE) * ROAR
     
MAE = REG * NAR + REG * NAR * SNAR + (REG * NAR * SNAR + RAE + (REG * NAR * SNAR + RAE + ROAE) * ROAR) * ROAR + RAE

Goal

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MAE + 2500 = 3706

Registrations

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     MAE = REG * NAR     + REG * NAR     * SNAR    + (REG * NAR     * SNAR    + RAE + (REG * NAR     * SNAR    + RAE + ROAE) * ROAR)   * ROAR   + RAE
    3706 = X   * 0.02591 + X   * 0.02591 * 0.08641 + (X   * 0.02591 * 0.08641 + 201 + (X   * 0.02591 * 0.08641 + 201 + 124)  * 0.2740) * 0.2740 + 201
(3706 - 201)                                                                                                                                  ( - 201)
    3505 = X   * 0.02591 + X   * 0.02591 * 0.08641 + (X   * 0.02591 * 0.08641 + 201 + (X   * 0.02591 * 0.08641 + 201 + 124)  * 0.2740) * 0.2740
(3505 / 0.2740)                                                                                                                      ( / 0.2740)
          (0.02591 / 0.2740)
                          (0.02591 * 0.08641 / 0.2740)
12791.97 = X   * 0.09456 + X   * 0.00817           + X   * 0.02591 * 0.08641  + 201 + (X   * 0.02591 * 0.08641 + 201 + 124)  * 0.2740
(12791.97 - 201)                                                            ( - 201)
12590.97 = X   * 0.09456 + X   * 0.00817           + X   * 0.02591 * 0.08641  + (X   * 0.02591 * 0.08641 + 201 + 124)  * 0.2740
                                                          (0.02591 * 0.08641)         (0.02591 * 0.08641)
         = X   * 0.09456 + X   * 0.00817           + X   * 0.00224            + (X   * 0.00224           + 201 + 124)  * 0.2740
(12590.97 / 0.2740)                                                                                                  ( / 0.2740)
           (0.09456 / 0.2740)
                           (0.00817 / 0.2740)         (0.00224 / 0.2740)
45952.45 = X   * 0.34511 + X   * 0.02982           + X * 0.00818              + X   * 0.00224           + 201 + 124
                                                                                                         (201 + 124)
         = X   * 0.34511 + X   * 0.02982           + X * 0.00818              + X   * 0.00224           + 325
(45952.45 - 325)                                                                                      ( - 325)
45627.45 = X   * 0.34511 + X   * 0.02982           + X * 0.00818              + X   * 0.00224
         = X * (0.34511 + 0.02982 + 0.00818 + 0.00224)
         = X * 0.38535
(45627.45 / 0.38535)
118405.2 = X
Baseline
32005
Desired
118405.2
Delta
118405.2 - 32005 = 86400.2
Proportional
86400.2/32005 = 270%

New activation rate

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Because NAR and REG are part of the same term, we can do some simple math using results above as a input. 

X = (118405.2 / 32005) * 0.02591
X = 0.09586
Baseline
0.02591
Desired
0.09586
Delta
0.09586 - 0.02591 = 0.06995
Proportional
0.06995 / 0.02591 = 270%

Surviving new activation rate

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     MAE = REG   * NAR     + REG * NAR     * X       + (REG * NAR     * X    + RAE + (REG * NAR     * X    + RAE + ROAE) * ROAR)   * ROAR   + RAE
     
     ...a little re-ordering to make X leftmost...
     
     MAE = REG   * NAR     + X   * REG   * NAR     + (X   * REG   * NAR     + RAE    + (X   * REG     * NAR     + RAE + ROAE) * ROAR)   * ROAR   + RAE
    3706 = 32005 * 0.02591 + X   * 32005 * 0.02591 + (X   * 32005 * 0.02591 + 201    + (X   * 32005   * 0.02591 + 201 + 124)  * 0.2740) * 0.2740 + 201
          (32005 * 0.02591)       (32005 * 0.02591)        (32005 * 0.02591)              (32005   * 0.02591) (201 + 124)
         = 829.2495        + X   * 829.2495        + (X   * 829.2495        + 201    + (X   * 829.2495          + 325)        * 0.2740) * 0.2740 + 201
                                                     (829.2495 * 0.2740)  (201 * 0.2740)                                   (0.2740 * 0.2740)
         = 829.2495        + X   * 829.2495        +  X   * 227.2144        + 55.074 + (X   * 829.2495          + 325)        * 0.07508          + 201
(3706 - 201)                                                                                                                                   ( - 201)
    3505 = 829.2495        + X   * 829.2495        +  X   * 227.2144        + 55.074 + (X   * 829.2495          + 325)        * 0.07508
                                                                                       (829.2495 * 0.07508)   (325 * 0.07508)
         = 829.2495        + X   * 829.2495        +  X   * 227.2144        + 55.074 + 62.26005                 + 24.401
                                                                             (55.074 + 62.26005                 + 24.401)
         = 829.2495        + X   * 829.2495        +  X   * 227.2144        + 141.7351
    (829.2495 + 141.7351)
         = 970.9846        + X   * 829.2495        +  X   * 227.2144
(3505 - 970.9846)
2534.015 =                   X   * 829.2495        +  X   * 227.2144
         = X * (829.2495 + 227.2144)
         = X * 1056.464
(2534.015 / 1056.464)
 2.39858 = X
Baseline
0.08641
Desired
2.39858
Delta
2.39858 - 0.08641 = 2.31217
Proportional
2.31217/0.02591 = 8924%
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