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Cracking the math, Pt. 1

I've noticed this sort of thing before, but hadn't found a great example until now. I've noticed that sometimes a change in incoming value doesn't always correspond to a similar change in outgoing value. You would assume that more in equals more out, all else being equal. Obviously, something is not equal:

Inc. LinksOut. LinksValueOut. Link ValueMarket Share
12:51 31 Jul 20081135B$51,143,195.71B$5,581,796.100.000093766 %
10:48 30 Jul 20081135B$50,068,599.21B$5,594,348.580.000134516 %
15:21 28 Jul 20081135B$51,296,168.99B$6,075,437.080.000147697 %
14:56 27 Jul 20081135B$50,460,461.54B$6,181,589.980.000101717 %
11:17 26 Jul 20081135B$53,450,325.98B$6,787,356.810.000107811 %

Note that in each case, the incoming and outgoing link totals are the same. From the 26th to the 27th, incoming value dropped, and we saw a drop in outgoing value. On the 28th incoming value rose, but outgoing dropped again. On the 30th, incoming dropped, and outgoing dropped even more than before. On the 31st, incoming rose to a similar level as the 28th, but outgoing fell again by a small amount.

Does outgoing depend on a trend of past outgoing values, or is there some other factor at work?

Let's take a look at the data again, this time with the multiplier in the table instead of Market Share (which isn't a terribly useful value anyway). Multiplier calculated as follows: (Outgoing Value * Outgoing Links) / Incoming Value

Inc. LinksOut. LinksValueOut. Link ValueMultiplier
12:51 31 Jul 20081135B$51,143,195.71B$5,581,796.103.8199189704
10:48 30 Jul 20081135B$50,068,599.21B$5,594,348.583.9106786167
15:21 28 Jul 20081135B$51,296,168.99B$6,075,437.084.1453446132
14:56 27 Jul 20081135B$50,460,461.54B$6,181,589.984.2876272372
11:17 26 Jul 20081135B$53,450,325.98B$6,787,356.814.4444534995

Now, let's take a look at a different blog, with very different numbers, picking reindex values for those same dates:

Inc. LinksOut. LinksValueOut. Link ValueMultiplier
17:43 31 Jul 200853144B$211,393,946.77B$5,607,684.383.8199133091
15:16 30 Jul 200853143B$193,656,051.20B$5,295,982.223.9106728283
10:21 28 Jul 200848136B$168,688,822.41B$5,141,708.474.1453389853
10:20 27 Jul 200847106B$158,365,825.61B$1,494,018.171.000000634
10:18 26 Jul 200845107B$138,897,093.41B$5,769,354.794.4444483853

Here we can definitely see a pattern, the multiplier vales are identical to several decimal places, and there may be extra precision (more than two decimal places) being tracked by B$ that isn't displayed here which would result in rounding errors, so for our purposes this is close enough to being exact.

Some last values I was able to pull from B$ for several others, with a few more prior dates:

Inc. LinksOut. LinksValueOut. Link ValueMultiplier
09:50 25 Jul 200874213B$209,360,891.00B$4,534,365.424.6131817163
14:51 24 Jul 200818125B$61,231,437.13B$2,346,429.324.7900829827
13:59 23 Jul 200819125B$53,939,375.58B$2,144,683.074.9701239747
23:05 23 Jul 2008981191B$19,236,094.28B$80,273.84.9701239747
22:51 21 Jul 200819125B$43,392,824.41B$1,844,410.105.3131195223
16:03 19 Jul 2008340931B$24,044,713.57B$144,114.045.5800278448
11:11 15 Jul 2008100347B$11,395,325.89B$186,029.825.6648092528
02:41 07 Jul 2008971202B$4,206,465.44B$15,553.954.4445504585
22:10 02 Jul 2008971212B$3,129,347.06B$9,675.743.819979751
13:11 24 Jun 2008991211B$5,474,202.35B$17,267.833.74742611
23:16 23 Jun 200895346B$5,894,777.90B$65,080.673.8199762912
22:52 14 Jun 2008851052B$5,512,945.09B$26,972.855.147056199
219:02 04 Jun 200899349B$8,823,377.67B$134,326.855.3131660463

Note that I have two entries for July 23, the very large number of outgoing compared to incoming (12x!) seemed very interesting, but since it fit the multiplier pattern I added the entry for that date mainly as a proof, reindex values for that blog appear later in the chart for June. Going back a month, we can see the values for the multiplier increase, then start falling going back to July 7, bottoming out on June 24.

We have multipliers of 3.8199 on June 23, July 2, and July 31. Since values were lower between June 23 and July 2, the June 23 value was on the downward slope, as is the value on July 31, this puts the cycle of the multiplier at about 38 days. We also see a multiplier of 5.313 on both June 4 and July 21, but I believe that the June 4 value was still on the rise, but may have been close to peaking. We know that the cycle bottomed out between June 23 and July 2, a period of 9 days, so going back to the topmost table, outgoing values will continue to have a lesser multiplier for the next 4-5 days before the cycle hits an upswing again.

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This page contains a single entry from the blog posted on July 31, 2008 7:52 PM.

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