"Some Maths and probability figures about Ditto from Spearow"

#PokemonGO: I really liked a recent thread here by /u/DeweyIsOverrated pledging a year of Reddit Gold to the person providing him with a screenshot of a spearow turning into a ditto. This got me thinking to apply some Maths to investigate the problem. Let’s start with some data. I wrote down some numbers early December to get a better idea of the ditto drop rate. All of this data is for caught and you can easily get it from your Pokedex yourself. Today I wrote down the values again (haven’t caught anything yet). It isn’t perfect – I forgot Zubat – but I avoid them. So there should be less Zubat as Spearow.PidgeyRattataSpearowMagicarpDittoDate42444219120655th December 2016474485209315117th January 2017Reporting bias / memory:Some observations. I recall from memory that I got at least 1 ditto from each of the accepted 4 – Pidgey, rattata, magicarp and zubat. I only ever got a single one from zubat – most from pidgey and magicarp. I was under the impression that the chance in magicarp seemed higher as in any other species. Interestingly I caught double the number of magicarp compared to pidgey and rattata. The likely reason for that – I got a 100% CP23 magicarp that I evolved into a Bite/Hydro Pump Gyarados. That explains that I caught every single magicarp I saw in the last month while I left quite a few rattatas, pidgeys and expecially zubats untouched. But it is interesting for someone who praises himself on being good with numbers/trends to remember wrong and assume the chance is higher in magicarp. At least my data can’t support this.Now lets use the numbers. They leads to a calculated rate of around 3% (6/202). The sample isn’t large enough to give an exact value – but we can say it is likely in the 1% to 5% range as this is also backed up by a lot of earlier posts here.Now let us calculate how many spearows I need to be nearly certain to catch a ditto. We can calculate the chance to catch a ditto from spearow using p = 1 – (1-x)n with p being the chance to catch a ditto from a spearow, x the chance that a spearow is a ditto and n the number of spearows we catch. I have done the calculations already and display them in the second table. I start with an assumed rate of 1% - similar to the lowest rate I assume for the accepted four pokemon. 1% is the same as 1 ditto out of 100 spearow. I then assume we catch 500 spearows. I use 500 because that gives me a chance just above 99% to get a ditto.% occurringoccurringassumed catcheschanceassumed catches in prespective1%1 out of 10050099.3%half a Spearow for each upvote (DewleysOverated Article)0.50%1 out of 200100099.3%One Spearow for each upvote (DewleysOverated Article)0.10%1 out of 1000500099.3%Five Spearows for each upvote (DewleysOverated Article)0.005%1 out of 2000010000099.3%half a Spearow for each Silph Road subscriber0.0001%1 out of 1 million500000099.3%five Spearows for each Silph Road subscriberWe can now interpret each row. So all it takes would be half a spearow for every reader who upvoted DewleyOverated’s article. Surely if it would be that common then he would have paid out gold already. So we half the chance – after all – do we know the chance is the same for all accepted species. This still doesn’t help as we now need 1 spearow caught for each upvote of the article.Row three now drops the chance to one tenths of the other pokemon. Still only 5 pokemon need to be caught by each person upvoting. You might notice the chance is always the same. Halfing the chance of occurrence and doubling the number of assumed catches will give me the same value back. So even at a chance of 1 in 1000 we should see proof very quickly. This is still in the realms of possibility of just 3 or 4 dedicated players hunting for the reward. After all they don’t need a 99% chance – they likely will stop earlier.Okay – now we go for really rare – what about a chance 1 in 20000 or even 1 in a million? We have 200000 SilphRoad subscribers. I don’t know how many players read/contribute but don’t subscribe (I don’t subscribe myself but I’m pretty active).So even with a 1 in a million chance proof of a screenshot should be forthcoming – especially if it is connected to a reward. Also keep in mind - even if you don't do the screenshot yourself - you might get a friend to make it if you find something so rare. I guess around half my dittos were caught by 1 or more other players who I notified me/whom I notified. So if this doesn’t happen then we have to face 2 options:The chance is very, very low – 1 in 1 million might just be possibgle, but then it's more likely 1 in 10 or 1 in 100 million (take your pick)The chance is zero via /r/TheSilphRoad http://ift.tt/2i5PWCP