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: 65 wild shinies from ~19330 encounters (rate: 297.4) + 102 event/community day shinies = 167 total since 16nov18 mali: 64 wild shinies from ~19330 encounters (rate: 302.0) + 72 event/community day shinies = 136 total since 16nov18 cumulative rate is one wild shiny for every 299.7 encounters 16nov18 0 0 26190 17nov18 63 63 26253 18nov18 208 145 26398 20nov18 284 76 26474 21nov18 379 95 26569 22nov18 535 156 26725 23nov18 572 37 26762 25nov18 730 158 26920 27nov18 784 54 26974 28nov18 829 45 27019 30nov18 877 48 27067 03dec18 1459 582 27649 06dec18 1533 74 27723 12dec18 1679 146 27869 15dec18 1740 61 27930 19dec18 1899 159 28089 26dec18 2169 270 28359 27dec18 2239 70 28429 03jan19 2474 235 28664 11jan19 2622 148 28812 16jan19 2738 116 28928 22jan19 3091 353 29281 27jan19 3283 192 29473 28jan19 3393 110 29583 30jan19 3470 77 29660 04feb19 3619 149 29809 07feb19 3702 83 29892 11feb19 3860 158 30050 17feb19 4092 232 30282 20feb19 4168 76 30358 23feb19 4482 314 30672 28feb19 4658 176 30848 05mar19 4877 219 31067 11mar19 5190 313 31380 20mar19 5572 382 31762 26mar19 5789 217 31979 05apr19 6316 527 32506 11apr19 6497 181 32687 13apr19 6594 97 32784 21apr19 7023 429 33213 22apr19 7247 224 33437 28apr19 7423 176 33613 02may19 7643 220 33833 18may19 8379 736 34569 21may19 8516 137 34706 11jun19 9467 951 35657 15jun19 10348 881 36538 29jun19 10811 463 37001 05jul19 11462 651 37652 13jul19 11743 281 37933 26jul19 12166 423 38356 28jul19 12568 402 38758 12aug19 13433 865 39623 29aug19 14286 853 40476 10sep19 14808 522 40998 19sep19 15392 584 41582 03oct19 16388 996 42578 01nov19 18098 1710 44288 03dec19 19330 1232 45520 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 0 1 | 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 s 19aug19 1 0 0 0 maya: bons s 27aug19 1 0 0 0 maya: barb s 29aug19 1 0 0 0 maya: barb s 31aug19 0 1 0 0 mali: meow-a s 01sep19 0 0 1 0 | maya: rayq s 02sep19 1 0 0 0 maya: sent s 06sep19 0 2 0 0 mali: sent & grim-a s 13sep19 0 2 0 0 mali: farf & houn s 15sep19 0 0 4 1 | maya: turt x 4 & mali: turt - turtwig community day s 18sep19 0 1 0 0 mali: patr s 19sep19 1 1 0 0 maya: mank & mali: grim-a s 20sep19 0 1 0 0 mali: taur s 21sep19 1 0 0 0 maya: yanm s 22sep19 0 1 0 0 mali: nidf s 23sep19 1 0 0 0 maya: bron s 25sep19 0 0 1 2 | maya: gira & mali gira x 2 s 05oct19 2 0 0 0 maya: wyna & lill s 08oct19 0 0 1 0 | mali: mewt s 12oct19 0 0 4 2 | maya: trap x 4 & mali: trap x 2 - trapinch community tday s 17oct19 0 1 0 0 mali: turt s 18oct19 1 1 0 0 maya: vulp & mali: plus s 23oct19 0 1 0 0 mali: ratt s 26oct19 1 0 0 0 maya: natu s 27oct19 1 1 0 0 maya: clef & mali: grow s 28oct19 0 1 0 0 mali: pika-e s 30oct19 1 0 0 0 maya: snea s 02nov19 0 0 2 0 | maya: rste + rice s 04nov19 0 1 0 0 mali: skar s 08nov19 1 0 0 0 maya: iggl s 13nov19 0 1 0 0 mali: maku s 14nov19 0 1 0 0 mali: ekan s 16nov19 0 1 8 4 mali: vulp | maya: chim x 8 & mali chim x 4 - chimchar community day s 21nov19 0 1 0 0 mali: magb s 26nov19 1 0 0 0 maya: nidf s 30nov19 2 0 0 0 maya: grim-a skar s 02dec19 0 1 0 0 mali: patr s 05dec19 1 0 0 0 maya: yanm s 07dec19 2 0 0 0 maya: hors + sciz s 09dec19 1 0 0 0 maya: burm-p-m
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: 4391 | Total: 2081 | Luckies: 112 | Average: 18.58 0-10 39 11-20 31 21-30 17 31-40 17 41-50 3 51-60 2 61- 3 11 1 8 12 5 35 5 3 4 9 4 8 4 4 4 29 4 19 3 7 3 32 3 21 3 20 3 2 3 18 3 16 3 15 3 14 2 6 2 5 2 39 2 38