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: 118 wild shinies from ~39907 encounters (rate: 338.2) + 160 event/community day shinies = 278 total since 16nov18 mali: 104 wild shinies from ~39907 encounters (rate: 383.7) + 102 event/community day shinies = 206 total since 16nov18 cumulative rate is one wild shiny for every 359.5 encounters 16nov18 0 0 29776 17nov18 63 63 29839 18nov18 208 145 29984 20nov18 284 76 30060 21nov18 379 95 30155 22nov18 535 156 30311 23nov18 572 37 30348 25nov18 730 158 30506 27nov18 784 54 30560 28nov18 829 45 30605 30nov18 877 48 30653 03dec18 1459 582 31235 06dec18 1533 74 31309 12dec18 1679 146 31455 15dec18 1740 61 31516 19dec18 1899 159 31675 26dec18 2169 270 31945 27dec18 2239 70 32015 03jan19 2474 235 32250 11jan19 2622 148 32398 16jan19 2738 116 32514 22jan19 3091 353 32867 27jan19 3283 192 33059 28jan19 3393 110 33169 30jan19 3470 77 33246 04feb19 3619 149 33395 07feb19 3702 83 33478 11feb19 3860 158 33636 17feb19 4092 232 33868 20feb19 4168 76 33944 23feb19 4482 314 34258 28feb19 4658 176 34434 05mar19 4877 219 34653 11mar19 5190 313 34966 20mar19 5572 382 35348 26mar19 5789 217 35565 05apr19 6316 527 36092 11apr19 6497 181 36273 13apr19 6594 97 36370 21apr19 7023 429 36799 22apr19 7247 224 37023 28apr19 7423 176 37199 02may19 7643 220 37419 18may19 8379 736 38155 21may19 8516 137 38292 11jun19 9467 951 39243 15jun19 10348 881 40124 29jun19 10811 463 40587 05jul19 11462 651 41238 13jul19 11743 281 41519 26jul19 12166 423 41942 28jul19 12568 402 42344 12aug19 13433 865 43209 29aug19 14286 853 44062 10sep19 14808 522 44584 19sep19 15396 588 45172 03oct19 16396 1000 46172 01nov19 18110 1714 47886 03dec19 19346 1236 49122 02jan20 20717 1371 50493 01feb20 22062 1345 51838 01mar20 23386 1324 53162 01apr20 26514 3128 56290 01may20 30879 4365 60655 01jun20 37762 6883 67538 01jul20 39907 2145 69683 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 11jun20 1 0 0 0 maya: koff
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: 5199 | Total: 2889 | Luckies: 149 | Average: 19.39 0-10 52 11-20 40 21-30 22 31-40 21 41-50 6 51-60 3 61- 5 14 1 8 3 8 12 7 19 6 4 5 8 5 7 5 35 5 29 4 9 4 20 4 2 4 18 4 15 3 5 3 44 3 32 3 28 3 24 3 21 3 16 3 14