How I calculated the Probability:
First I made IV Tables in Excel (well OpenOffice Spreadsheet) with the Stat Formula:
HP uses a different Formula, however HP Stats are illrelevent for this article.
Then I grouped similar Natures (Mild/Rash)(Lonely/Naughty)(Neutral,+Speed,+Def) and then using http://www.calculator.net/probability-calculator.html started to find the probability of getting a runable squirtle when you get a Nature in one of the groups. For example: If you get a Mild/Rash Squirtle, there is a 49.21875% chance that that Squirtle is runnable.
After that I weighted each group of Natures according to how often you get them.
Finally I added each Group of Natures probability together to get a final probability of runnable squirtles.
Neutral Natures/Stats - 1x
10 Attack at level 5 requires IV to be 4 or greater. 28/32 IVs satisfy the requirement.
15 Sp. Attack at level 8 requires IV to be 25 or greater. 7/32 IVs satisfy the requirement.
10 Speed at level 6 requires IV to be 0 or greater. 32/32 IVs satisfy the requirement.
Boosted Natures/Stats - 1.1x
10 Attack at level 5 requires IV to be 0 or greater. 32/32 IVs satisfy the requirement.
13 Sp. Attack at level 6 requires IV to be 14 or greater. 18/32 IVs satisfy the requirement.
Hindered Natures/Stats - .9x
10 Speed at level 6 requires IV to be 16 or greater. 16/32 IVs satisfy the requirement.
I don't run Modest Squirtles but by going MEvRNGs Guide:
9 Attack at level 5 requires IV to be 4 or greater. 28/32 IVs satisfy the requirement.Accept any stats with 12 special but if they are truly garbage (like 8 speed or 9 attack) and you don't get a +2 to special attack at level 7 just bin it because it isn't worth it.
15 Sp. Attack at level 7 (+2 from level up) requires IV to be 24 or greater. 8/32 IVs satisfy the requirement.
Reasoning behind the Stat Requirements:
10 Attack at level 5.
-I haven't heard of any attack requirements besides 10 Attack at level 5. lol
15 Sp. Attack at level 8.
-This is a big one because if you have 14Sp. Attack at level 8 then you don't kill Pewter Gym's Geodudes in 1 Hit in Torrent, or Sandshew in 2. And then a lot of minor damage ranges later down the line.
10 Speed at level 6.
-The only way to have lower is with a -Speed Nature.
10 Attack at level 5.
-Same as before.
13 Sp. Attack at level 6.
-If you don't get this your Sp. Attack IV is less than 14 and thus is terrible, and your hindering another stat at the same time.
10 Speed at level 6.
-This is actually a huge deal. If you don't get this then Route 1 lvl 3-4 Ratattas have the opertunity of not letting you run away. In Viridian Forest if you run into a lvl 5 Pikachu then you'll actually have a chance to get away, at 9 speed your fucked. 12Speed at lvl8 is also noteworthy. If you get it you'll speed tie the Mankey at Nugget Bridge if your Wartortle is level 23. In Mt.Moon a lvl 16 Wartortle has a chance to speed tie the grunts Ratatta. After that Speed does not matter until Kangastan but -Speed means it's always faster. All other Speed problems lategame are solved with a X speed which you'll mostlikely be doing anyways.
1 in 25 chance - If your Squirtles Nature is Brave, you have a 10.9375% chance of having a runable Squirtle. .4375% of Squirtles overall.
1 in 25 chance - If your Squirtles Nature is Quiet, you have a 24.609375% chance of having a runable Squirtle. .984375% of Squirtles overall.
2 in 25 chance - If your Squirtles Nature is Mild/Rash, you have a 49.21875% chance of having a runable Squirtle. 3.9375% of Squirtles overall.
2 in 25 chance - If your Squirtles Nature is Lonely/Naughty, you have a 21.875% chance of having a runable Squirtle. 1.75% of Squirtles overall.
9 in 25 chance - If your Squirtles Nature is Neutral/+Speed/+Def, you have a 19.140635% of having a runnable Squirtle. 6.890625% of Squirtles overall.
1 in 25 chance - If your Squirtles Nature is Modest, you have a 12.3046875% chance of having a runnable Squirtle. .4921875% of Squirtles overall.
Now if we tally the numbers.
If you only run (Mild/Rash),(Lonely/Naughty),(Bashful/Docile/Hardy/Quirky/Serious/Hasty/Naive/Lax/Gentle) Squirtles, you have 12.578125% of getting a runable Squirtle. Approx. 1 in 8 Squirtles.
If you also add Quiet and Brave Squirtles, you have 14.003125% chance of getting a runnable Squirtle. Approx. 1 in 7 Squirtles.
Then if you also add Modest Squirtles, you have a 14.4953125% chance of getting a runnable Squirtle. Approx. 1 in 7 Squirtles.
Adding Quiet Squirtles to your list of Natures you run has the largest increase in runnable Squirtles; nearly a whopping 1%.
Adding both Brave and Modest Squirtles add almost another 1%.
Other things I Noticed
If you have a Neutral Sp. Attack and have 11 Sp. Attack at level 5 then at level 8 you're going to reset 42% of the time because you'll fail to get 15 Sp. Attack.
If you have a Neutral Sp. Attack then at level 13 you'll always have 21 Sp. Attack unless your Sp. Atk IV is 31 in which case you'll have 22 Sp. Attack.
EVs add a bunch of stats. However you barely get any Sp. Atk EVs, Almost all come from your Rivals Bulbasaur, the rest come from Pokemon Tower in Lavender Town and the E4. I haven't done a complete count but the EVs you get the most of are Defense/Speed.
Thanks for reading and I'll try to answer any questions/suggestions in a timely manner.