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: 126 wild shinies from ~46443 encounters (rate: 368.6) + 200 event/community day shinies = 326 total since 16nov18 mali: 117 wild shinies from ~46443 encounters (rate: 396.9) + 139 event/community day shinies = 256 total since 16nov18 cumulative rate is one wild shiny for every 382.2 encounters 16nov18 0 0 31150 17nov18 63 63 31213 18nov18 208 145 31358 20nov18 284 76 31434 21nov18 379 95 31529 22nov18 535 156 31685 23nov18 572 37 31722 25nov18 730 158 31880 27nov18 784 54 31934 28nov18 829 45 31979 30nov18 877 48 32027 03dec18 1459 582 32609 06dec18 1533 74 32683 12dec18 1679 146 32829 15dec18 1740 61 32890 19dec18 1899 159 33049 26dec18 2169 270 33319 27dec18 2239 70 33389 03jan19 2474 235 33624 11jan19 2622 148 33772 16jan19 2738 116 33888 22jan19 3091 353 34241 27jan19 3283 192 34433 28jan19 3393 110 34543 30jan19 3470 77 34620 04feb19 3619 149 34769 07feb19 3702 83 34852 11feb19 3860 158 35010 17feb19 4092 232 35242 20feb19 4168 76 35318 23feb19 4482 314 35632 28feb19 4658 176 35808 05mar19 4877 219 36027 11mar19 5190 313 36340 20mar19 5572 382 36722 26mar19 5789 217 36939 05apr19 6316 527 37466 11apr19 6497 181 37647 13apr19 6594 97 37744 21apr19 7023 429 38173 22apr19 7247 224 38397 28apr19 7423 176 38573 02may19 7643 220 38793 18may19 8379 736 39529 21may19 8516 137 39666 11jun19 9467 951 40617 15jun19 10348 881 41498 29jun19 10811 463 41961 05jul19 11462 651 42612 13jul19 11743 281 42893 26jul19 12166 423 43316 28jul19 12568 402 43718 12aug19 13433 865 44583 29aug19 14286 853 45436 10sep19 14808 522 45958 19sep19 15396 588 46546 03oct19 16396 1000 47546 01nov19 18110 1714 49260 03dec19 19354 1244 50504 02jan20 20745 1391 51895 01feb20 22100 1355 53250 01mar20 23434 1334 54584 01apr20 26572 3138 57722 01may20 30947 4375 62097 01jun20 37840 6893 68990 01jul20 39995 2155 71145 01aug20 43324 3329 74474 01sep20 46443 3119 77593 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 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 s 22sep20 1 0 0 0 maya: duns s 23sep20 1 0 0 0 maya: duns
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: 5517 | Total: 3207 | Luckies: 162 | Average: 19.80 0-10 53 11-20 46 21-30 25 31-40 23 41-50 6 51-60 3 61- 6 14 1 8 3 8 12 7 19 6 4 6 16 5 8 5 7 5 35 5 29 5 18 5 11 4 9 4 20 4 2 4 15 3 6 3 5 3 44 3 38 3 37 3 32