This is the output of my wild shiny eligible encounter log script since November 16, 2018, as well as a record of all shinies encountered since that date. The first three lines are the summaries for two accounts labelled "maya" and "mali". I've only kept careful track of the encounters for "maya" but it's a reasonable assumption that second account (used by my daughter) is nearly identical.
The second group of lines are the counts of shiny eligible encounters at different dates (first column) followed by the cumulative count of encounters since start date (second column), count since last date (third column), and the total number of encounters of the shiny eligible species (fourth column). This fourth column of course is not very useful and primarily serves as a sanity check.
The third group of lines is shinies actually encountered. The prefix "s" followed by the date of the encounter(s), followed by four columns of counts (wild shinies-maya, wild shinies-mali, other shinies-maya, other shinies-mali) and then the identities of the shinies. The wild shinies come first and then other shinies (events, community days, shiny meltan, etc.) come after the "|" symbol.
I also have all the raw counts for each shiny eligible species which was processed to generate the data below which I can make available upon request or will put it up at some point.
maya: 33 wild shinies from ~10348 encounters (rate: 313.6) + 66 event/community day shinies = 99 total since 16nov18 mali: 28 wild shinies from ~10348 encounters (rate: 369.6) + 49 event/community day shinies = 77 total since 16nov18 cumulative rate is one wild shiny for every 339.3 encounters 16nov18 0 0 21563 17nov18 63 63 21626 18nov18 208 145 21771 20nov18 284 76 21847 21nov18 379 95 21942 22nov18 535 156 22098 23nov18 572 37 22135 25nov18 730 158 22293 27nov18 784 54 22347 28nov18 829 45 22392 30nov18 877 48 22440 03dec18 1459 582 23022 06dec18 1533 74 23096 12dec18 1679 146 23242 15dec18 1740 61 23303 19dec18 1899 159 23462 26dec18 2169 270 23732 27dec18 2239 70 23802 03jan19 2474 235 24037 11jan19 2622 148 24185 16jan19 2738 116 24301 22jan19 3091 353 24654 27jan19 3283 192 24846 28jan19 3393 110 24956 30jan19 3470 77 25033 04feb19 3619 149 25182 07feb19 3702 83 25265 11feb19 3860 158 25423 17feb19 4092 232 25655 20feb19 4168 76 25731 23feb19 4482 314 26045 28feb19 4658 176 26221 05mar19 4877 219 26440 11mar19 5190 313 26753 20mar19 5572 382 27135 26mar19 5789 217 27352 05apr19 6316 527 27879 11apr19 6497 181 28060 13apr19 6594 97 28157 21apr19 7023 429 28586 22apr19 7247 224 28810 28apr19 7423 176 28986 02may19 7643 220 29206 18may19 8379 736 29942 21may19 8516 137 30079 11jun19 9467 951 31030 15jun19 10348 881 31911 s 16nov18 1 0 0 0 maya: bulb s 21nov18 2 1 0 0 maya: eeve x 2 | mali: natu s 23nov18 0 1 0 0 mali: cubo s 03dec18 0 1 15 8 mali: pine | maya: bulb x 2 + char x 2 + squi + pika x 4 + mare x 5 + drat & mali: char x 2 + squi + pika + larv x 3 + beld - community weekend event s 15dec18 1 0 0 0 maya: cate s 16dec18 0 2 0 0 mali: pine + magb s 27dec18 1 1 0 0 maya: snor & mali: snor s 10jan19 0 1 0 0 mali: magb s 12jan19 0 1 8 3 mali: murk | maya: toto x 8 & mali: toto x 3 - community day event s 19jan19 0 0 3 1 maya: minu | maya: feeb x 3 & mali: feeb - feebas event s 21jan19 0 1 0 0 mali: minu s 27jan19 2 1 0 0 maya: psyd + zigz & mali: psyd s 07feb19 0 1 0 0 mali: murk s 08feb19 0 0 0 1 | mali: melt - event s 11feb19 0 0 0 1 | mali: melt - event s 16feb19 0 0 7 7 | maya: swin x 7 & mali swin x 7 - community day s 20feb19 1 0 0 0 maya: pine s 23feb19 0 1 3 7 mali: pine | maya: clam x 3 & mali: clam x 6 + latias s 28feb19 1 0 0 0 maya: eevee s 10mar19 0 1 0 0 mali: cate s 20mar19 0 1 0 0 mali: solr s 23mar19 0 0 3 3 | maya: tree x 3 & mali: tree x 3 s 26mar19 0 1 0 0 mali: aero s 30mar19 0 0 5 7 | maya: lota x 4 + cast x 1 & mali: lota x 3 + cast x 4 - weather-focussed event s 05apr19 1 0 0 0 maya: cate s 11apr19 2 0 0 0 maya: snub + shup s 13apr19 1 0 5 3 maya: murk | maya: bago x 5 & mali: bago x 3 s 14apr19 1 0 0 0 maya: shel s 20apr19 0 1 0 0 mali: shuc s 21apr19 2 1 0 0 maya: bune + shuc & mali: shuc s 28apr19 1 0 0 0 maya: tree s 29apr19 0 1 0 0 mali: digl s 30apr19 0 0 1 1 | maya: melt & mali: melt s 01may19 4 1 2 0 maya: digl x 3 + sunk x 1 & mali: digl | maya: lugi + grou s 02may19 1 0 0 0 maya: digl s 03may19 0 0 0 2 | mali: melt x 2 s 07may19 0 1 0 0 mali: pich s 10may19 0 1 0 0 mali: psyd s 19may19 0 0 5 2 | maya: torc x 5 & mali: torc x 2 s 21may19 1 0 0 0 maya: sunk s 22may19 1 0 0 0 maya: elek s 25may19 0 0 2 1 | maya: lapr x 2 & maki: lapr - lapras event s 07jun19 0 1 0 0 mali: anor s 08jun19 0 0 6 2 | maya: slak x 6 & mali: slak x 2 s 11jun19 1 1 0 0 maya: anor & mali: onix s 12jun19 0 0 1 0 | mali: cres s 14jun19 7 5 0 0 maya: wail + swab + lota + mach + bron + sand + gast & mali: drif + dusk + larv + bude + swin | go fest s 18jun19 1 0 0 0 maya: sunk
This reports the distribution (histogram) of lucky trades since I started keeping track of them. The first line below gives the start trade, the end trade, the total trades made, the number of luckies encountered, and the average number of trades made to obtain a lucky trade.
The second group of lines gives the histogram values. The first column is the range when the lucky trade occurred and the second is count. For instance, the number of luckies encountered between 0-10 trades is given in first line, between 11-20 trades in the second line, and so on. The one thing I got out of this is that if you don't encounter a lucky by the 20th trade or so, it might not happen for a while (as many as 100 trades, which is when I decided to start keeping track, but easily 30+ and sometimes more). Most of the luckies happen before the 20th trade (which is natural given the odds) but if it doesn't, best to keep trading throwaways until you encounter the lucky. This is especially relevant for the timing of legendary/special trades.
The third group twenty lines shows the frequency of when the trade becomes lucky. First column is count and second is the number of trades made when the lucky happened. In other words, a trade became lucky after [second column] number of trades [first column] times.
Start: 2310 | End: 3901 | Total: 1591 | Luckies: 84 | Average: 18.94 0-10 29 11-20 24 21-30 10 31-40 13 41-50 3 51-60 2 61- 3 8 1 7 12 5 3 4 8 4 35 3 7 3 21 3 18 3 16 3 14 2 9 2 6 2 4 2 39 2 34 2 32 2 31 2 29 2 20 2 2 2 19 2 15