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: 180 wild shinies from ~65322 encounters (rate: 362.9) + 265 event/community day shinies = 445 total since 16nov18 mali: 154 wild shinies from ~65322 encounters (rate: 424.2) + 196 event/community day shinies = 350 total since 16nov18 cumulative rate is one wild shiny for every 391.1 encounters 16nov18 0 0 34812 17nov18 63 63 34875 18nov18 208 145 35020 20nov18 284 76 35096 21nov18 379 95 35191 22nov18 535 156 35347 23nov18 572 37 35384 25nov18 730 158 35542 27nov18 784 54 35596 28nov18 829 45 35641 30nov18 877 48 35689 03dec18 1459 582 36271 06dec18 1533 74 36345 12dec18 1679 146 36491 15dec18 1740 61 36552 19dec18 1899 159 36711 26dec18 2169 270 36981 27dec18 2239 70 37051 03jan19 2474 235 37286 11jan19 2622 148 37434 16jan19 2738 116 37550 22jan19 3091 353 37903 27jan19 3283 192 38095 28jan19 3393 110 38205 30jan19 3470 77 38282 04feb19 3619 149 38431 07feb19 3702 83 38514 11feb19 3860 158 38672 17feb19 4092 232 38904 20feb19 4168 76 38980 23feb19 4482 314 39294 28feb19 4658 176 39470 05mar19 4877 219 39689 11mar19 5190 313 40002 20mar19 5572 382 40384 26mar19 5789 217 40601 05apr19 6316 527 41128 11apr19 6497 181 41309 13apr19 6594 97 41406 21apr19 7023 429 41835 22apr19 7247 224 42059 28apr19 7423 176 42235 02may19 7643 220 42455 18may19 8379 736 43191 21may19 8516 137 43328 11jun19 9467 951 44279 15jun19 10348 881 45160 29jun19 10811 463 45623 05jul19 11462 651 46274 13jul19 11743 281 46555 26jul19 12166 423 46978 28jul19 12568 402 47380 12aug19 13433 865 48245 29aug19 14286 853 49098 10sep19 14808 522 49620 19sep19 15396 588 50208 03oct19 16396 1000 51208 01nov19 18110 1714 52922 03dec19 19354 1244 54166 02jan20 20745 1391 55557 01feb20 22100 1355 56912 01mar20 23434 1334 58246 01apr20 26572 3138 61384 01may20 30947 4375 65759 01jun20 37840 6893 72652 01jul20 39995 2155 74807 01aug20 43324 3329 78136 01sep20 46441 3117 81253 01oct20 47461 1020 82273 01nov20 49557 2096 84369 01dec20 51142 1585 85954 01jan21 55347 4205 90159 01feb21 58207 2860 93019 01mar21 61629 3422 96441 02apr21 65322 3693 100134 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 + scyt s 09dec19 1 2 0 0 maya: burm-p-m & mali: onix + snor s 10dec19 2 0 0 0 maya: glig + snea s 12dec19 1 0 0 0 maya: scyt s 22dec19 0 1 0 0 mali: elek s 01jan20 0 1 0 0 mali: snea s 10jan20 1 0 0 0 maya: pins s 15jan20 2 0 0 0 maya: snub & oddi s 19jan20 0 1 0 0 mali: bude | maya: pipl x 3 & mali pipl x 4 s 22jan20 0 0 0 1 | mali: heat s 26jan20 0 0 2 0 | maya: latios and latias s 29jan20 0 0 1 0 | maya: heat s 01feb20 1 0 0 0 maya: magi s 02feb20 0 1 4 2 mali: nidm | maya: minc x 4 & mali: minc x 2 s 10feb20 0 1 0 0 mali: ratt-a s 11feb20 1 0 0 0 maya: seel s 12feb20 1 0 0 0 maya: drow s 15feb20 1 0 1 2 maya: yanm | maya: lick & mali: lick x 2 s 22feb20 1 0 4 3 maya: oddi | maya rhyh x 4 & mali rhyh x 3 s 29feb20 0 1 0 0 mali: eevee-partyhat s 07mar20 1 0 0 1 maya: zigz | mali: dark s 09mar20 1 0 0 0 maya: aero s 14mar20 1 0 0 0 maya: medi s 15mar20 0 1 0 0 mali: maku s 19mar20 0 1 0 0 mali: aero s 20mar20 0 2 0 0 mali: snea + ninc s 21mar20 1 0 0 0 maya: grow s 23mar20 2 0 0 0 maya: magn + snor s 24mar20 0 1 0 0 mali: ratt s 30mar20 1 1 0 0 mali: drow & maya natu s 01apr20 2 0 0 0 maya: pooc + tail s 04apr20 0 2 0 0 mali: sent + shel s 05apr20 3 0 0 0 maya: nido-f + croa + aipo s 13apr20 1 0 0 0 maya: exeg s 15apr20 1 1 0 0 maya: pika-e & mali: pika-e s 19apr20 0 0 13 5 | maya: anor + carv x 2 + chin + hors + krab + lile x 2 + mudk + pika-e + poli x 3 + tent & mali: chin x 3 + hors + tent - safari zone liverpool s 22apr20 1 0 0 0 maya: illu s 23apr20 0 1 0 0 mali: illu s 24apr20 1 0 0 0 maya: volb s 25apr20 0 1 7 4 mali: lill | maya: abra x 7 & mali: abra x 4 s 27apr20 0 1 0 0 mali: feeb s 30apr20 0 1 0 0 mali: feeb s 01may20 0 3 0 0 mali: chan + seel + poli s 02may20 2 1 0 0 maya: char + nido-m & mali: tent s 03may20 1 0 0 0 maya: pika-e s 05may20 1 1 0 0 maya: hors & mali: hors s 06may20 1 0 0 0 maya: exeg s 09may20 0 0 14 2 | maya: bron + glig + krab + medi + mrmi + sand x 3 + seel + volt x 2 + yanm + zang x 2 & mali: volt + poli - safari zone philadelphia s 14may20 1 1 0 0 mali: mach & maya: misd s 16may20 1 1 0 0 mali: carv & maya: plus s 17may20 2 1 0 0 maya: abso + pooc & mali: medi s 20may20 2 0 0 0 maya: barb + wurm s 22may20 2 0 0 0 maya: pika-e x 2 s 23may20 1 2 0 0 maya: snov & mali: croa + glam s 24may20 0 1 4 5 mali: glam | maya: seed x 4 & mali: seed x 5 - seedot community day s 25may20 1 0 0 0 maya: snov s 27may20 0 1 0 0 mali: drif s 29may20 1 0 0 0 maya: drif s 30may20 1 0 0 0 maya: ratt s 31may20 1 0 0 0 maya: veno s 04jun20 0 1 0 0 mali: aero s 20jun20 0 0 8 5 | maya: weed x 8 & mali weed x 5 - weedle community day s 21jun20 0 1 0 0 mali: magm s 22jun20 1 0 0 0 maya: clefairy s 23jun20 1 0 0 0 maya: snea s 27jun20 2 2 0 0 maya: ninc x 2 & mali: ninc x 2 s 28jun20 1 0 0 0 maya: wurm s 29jun20 0 1 0 0 mali: shuc s 30jun20 0 1 0 0 mali: grim-a s 04jul20 0 1 0 0 mali: pika-e s 05jul20 1 0 0 0 maya: hors s 08jul20 1 0 0 0 maya: zuba s 11jul20 1 0 0 0 maya: koff s 17jul20 0 1 0 0 mali: wurm s 19jul20 0 0 5 7 | maya: gast x 5 & mali gast x 5 - gastly community day s 23jul20 0 1 0 0 mali: lill s 25jul20 0 0 5 3 | maya: unoG + unoO + exeg-a + exeg + croa & mali: bude + qwil + mari s 26jul20 0 0 14 7 | maya: bulb-pikahat x 2 + dura + magi + maro + heat x 2 + qwil x 2 + sabl + swab + tang x 2 + woob & mali: bulb-pikahat + carv + gibl + maro + seve + tang + zang s 02aug20 0 0 0 1 | maya: rayq s 08aug20 1 0 14 16 maya: misd | maya: magi x 14 & mali: deox-n & magi x 15 event s 10aug20 1 0 0 0 maya: star s 11aug20 0 1 0 0 mali: sabl s 12aug20 0 1 0 0 mali: solr | maya: deox s 14aug20 0 2 0 0 mali: star & balt s 15aug20 0 0 0 2 | mali: gene x 2 s 16aug20 0 0 0 1 | mali: rose - go fest makeup s 17aug20 0 0 2 0 | maya: gene x 2 s 21aug20 0 1 0 0 mali: misd s 23aug20 1 0 0 0 maya: turt s 31aug20 1 0 0 0 maya: turt s 01sep20 0 1 0 0 mali: lota s 02sep20 1 1 0 0 maya: magn & mali: tedd s 09sep20 0 1 0 0 mali: zuba s 13sep20 0 1 0 0 mali: dusk s 14sep20 1 0 0 0 maya: scyt s 16sep20 0 1 0 0 mali: veno s 20sep20 0 1 0 0 mali: pido | maya: pory x 9 & mali: pory x 2 event s 22sep20 1 0 0 0 maya: duns s 23sep20 1 0 0 0 maya: duns s 25sep20 0 1 0 0 mali: wail s 28sep20 0 1 0 0 mali: exeg-a s 03oct20 2 0 0 0 maya: kric & skit s 07oct20 1 0 0 0 maya: croa-h s 08oct20 0 1 0 0 mali: kric s 13oct20 0 0 1 0 | maya: gira-o s 15oct20 1 0 0 0 maya: houn s 17oct20 1 0 0 0 maya: vulp s 19oct20 1 0 0 0 maya: ekan s 20oct20 1 0 0 0 maya: houndoom s 23oct20 1 0 0 0 maya: bulb s 25oct20 1 3 0 0 maya: spir & mali: drif x 3 s 30oct20 1 0 0 0 maya: shup s 18nov20 0 0 1 1 | maya: viri & mali: terr s 19nov20 1 0 0 0 maya: drow-shadow s 26nov20 1 0 0 0 maya: gold s 28nov20 0 0 1 2 | maya: nido-m & mali nido-f x 2 - nidoran event s 29nov20 0 1 0 0 mali: gold s 01dec20 1 0 0 0 maya: pidg s 03dec20 0 1 0 0 mali: woob s 04dec20 0 1 0 0 mali: lapr s 07dec20 0 1 0 0 mali: pidg s 10dec20 1 1 0 0 maya: woop & mali: woop s 12dec20 0 0 1 1 | maya: elec & mali: regirock - community day year end/regirock raid weekend event s 13dec20 0 0 0 1 | mali: regirock s 14dec20 0 1 0 0 mali: woob s 18dec20 1 0 0 0 mali: wobb s 19dec20 2 0 0 0 maya: cubc + vulp-a s 20dec20 0 1 0 0 mali: pika-explorer s 21dec20 1 0 0 0 maya: cubc s 23dec20 1 1 0 0 maya: jigg & mali: cubc-e s 26dec20 0 1 1 0 mali: stan-e | maya: regice - weekend event s 17dec20 0 1 0 0 mali: deli-e s 29dec20 2 0 0 0 maya: vulp-a + deli-e s 30dec20 1 0 0 0 maya: pika-e s 31dec20 1 0 0 0 maya: cubc-e s 01jan21 0 1 0 0 mali: slow-e s 02jan21 2 0 0 0 maya: pidg + gold s 12jan21 1 0 0 0 maya: pins-shadow s 13jan21 0 1 0 0 mali: glam s 15jan21 1 0 0 0 maya: buiz s 16jan21 0 0 20 20 | maya: mach x 20 & mali: mach x 20 - machamp community day s 22jan21 1 0 0 0 maya: medi s 23jan21 1 0 0 0 maya: aron s 26jan21 0 1 0 0 mali: grim s 27jan21 1 0 0 0 maya: aipo s 30jan21 0 0 3 3 | maya: snea x 3 & mali snea x 3 - sneasel event s 03feb21 1 0 0 0 maya: skor s 04feb21 1 0 0 0 maya: grim s 05feb21 0 1 0 0 mali: murk s 07feb21 0 0 9 9 | maya: rose x 9 & mali rose x 9 - roselia community day s 09feb21 0 1 0 0 mali: milt s 13feb21 0 0 1 0 | maya: latios s 15feb21 1 1 0 0 maya: snor & mali: nidf s 16feb21 1 0 0 0 maya: illu s 20feb21 0 0 8 8 | maya: mank + drat + oddi + eeve x 2 + ditt + gast & mali: eeve x 2 + hitm + mach + drat + ditt + squi + bulb s 22feb21 0 1 0 0 mali: oman s 23feb21 2 1 0 0 maya: char + oman & mali: geod s 24feb21 0 1 0 0 mali: pidg s 25feb21 1 1 0 0 maya: char & mali: drat s 27feb21 0 1 0 0 mali: krab s 28feb21 0 0 1 0 maya: arti x 2 s 01mar21 0 0 1 0 | maya: land-i s 05mar21 1 0 0 0 maya: drow s 06mar21 0 0 8 8 | maya: flet x 8 & mali: flet x 8 - fletchling community day s 08mar21 1 0 0 0 maya: glam s 09mar21 1 0 0 0 maya: spoi s 10mar21 4 0 1 0 maya: aron + geod-a + geod + beld | maya: torn-i s 11mar21 2 0 0 0 maya: geod + rogg s 12mar21 1 1 1 0 maya: rogg & mali: geod | mali: thun-i s 14mar21 1 2 0 0 maya: magn & mali: ralt + beld s 21mar21 1 1 0 0 maya: elec & mali: elec s 27mar21 0 0 2 0 | maya: rayq x 2 s 31mar21 0 2 0 0 mali: shup & spoi s 02apr21 1 0 0 0 maya: wurm s 03apr21 1 0 0 0 maya: wurm s 06apr21 1 1 0 0 maya: bunn & mali: exeg s 08apr21 1 0 0 0 maya: bunn s 09apr21 0 2 0 0 mali: wurm x 2 s 10apr21 0 1 0 0 mali: bunn s 11apr21 0 0 5 4 | maya: sniv x 4 & mali: sniv x 5 - snivy community day s 12apr21 1 0 0 0 maya: illu
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: 6629 | Total: 4319 | Luckies: 235 | Average: 18.38 0-10 90 11-20 64 21-30 30 31-40 29 41-50 10 51-60 5 61- 7 24 1 12 3 10 5 10 11 9 16 9 12 8 9 8 19 8 15 7 7 7 4 7 2 6 8 6 6 6 35 6 18 5 29 5 21 5 20 4 44 4 39 4 25