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: 44 wild shinies from ~13533 encounters (rate: 307.6) + 82 event/community day shinies = 126 total since 16nov18 mali: 44 wild shinies from ~13533 encounters (rate: 307.6) + 62 event/community day shinies = 106 total since 16nov18 cumulative rate is one wild shiny for every 307.6 encounters 16nov18 0 0 22839 17nov18 63 63 22902 18nov18 208 145 23047 20nov18 284 76 23123 21nov18 379 95 23218 22nov18 535 156 23374 23nov18 572 37 23411 25nov18 730 158 23569 27nov18 784 54 23623 28nov18 829 45 23668 30nov18 877 48 23716 03dec18 1459 582 24298 06dec18 1533 74 24372 12dec18 1679 146 24518 15dec18 1740 61 24579 19dec18 1899 159 24738 26dec18 2169 270 25008 27dec18 2239 70 25078 03jan19 2474 235 25313 11jan19 2622 148 25461 16jan19 2738 116 25577 22jan19 3091 353 25930 27jan19 3283 192 26122 28jan19 3393 110 26232 30jan19 3470 77 26309 04feb19 3619 149 26458 07feb19 3702 83 26541 11feb19 3860 158 26699 17feb19 4092 232 26931 20feb19 4168 76 27007 23feb19 4482 314 27321 28feb19 4658 176 27497 05mar19 4877 219 27716 11mar19 5190 313 28029 20mar19 5572 382 28411 26mar19 5789 217 28628 05apr19 6316 527 29155 11apr19 6497 181 29336 13apr19 6594 97 29433 21apr19 7023 429 29862 22apr19 7247 224 30086 28apr19 7423 176 30262 02may19 7643 220 30482 18may19 8379 736 31218 21may19 8516 137 31355 11jun19 9467 951 32306 15jun19 10348 881 33187 29jun19 10811 463 33650 05jul19 11462 651 34301 13jul19 11743 281 34582 26jul19 12166 423 35005 28jul19 12568 402 35407 12aug19 13533 965 36372 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 s 25jun19 0 1 0 0 mali: magb s 26jun19 0 0 1 0 maya: kyog s 29jun19 1 1 2 2 maya: nidf & mali: digl | maya: raik x 2 & mali raik x 2 - raikou raid day s 03jul19 2 0 0 0 maya: ratt-a & magb s 05jul19 1 1 0 0 maya: toto & mali: elek s 11jul19 0 1 0 0 mali: ratt-a s 12jul19 1 0 0 0 maya: ratt s 14jul19 0 0 2 1 | maya: ente x 2 & mali ente - entei raid day s 18jul19 0 1 0 0 mali: toge s 21jul19 0 0 4 4 | maya: mudk x 4 & mali mudk x 4 s 22jul19 0 1 0 0 mali: meow-a s 24jul19 1 0 0 0 maya: eeve s 26jul19 0 1 0 0 mali: koff s 28jul19 1 2 0 0 maya: pins & mali: ekan + wail s 29jul19 0 1 0 0 mali: koff s 02aug19 1 0 0 0 maya: sunk s 03aug19 0 0 6 5 | maya: 6 x ralt & mali 5 x ralt - ralts community day s 04aug19 1 0 0 0 maya: pidg s 07aug19 0 1 0 0 mali: meow-a s 12aug19 1 1 0 0 maya: poli & mali: anor s 14aug19 0 1 0 0 mali: ekan s 15aug19 0 3 0 0 mali: elek + murk + smoo s 17aug19 0 0 1 1 | maya: suic & mali: suic - suic raid day s 18aug19 1 0 0 0 maya: iggl
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: 4000 | Total: 1690 | Luckies: 91 | Average: 18.57 0-10 32 11-20 26 21-30 11 31-40 14 41-50 3 51-60 2 61- 3 9 1 7 12 5 35 5 3 4 8 3 7 3 4 3 21 3 2 3 19 3 18 3 16 3 14 2 9 2 6 2 39 2 34 2 32 2 31 2 29 2 20 2 15