How I calculated the Probability:

First I made IV Tables in Excel (well OpenOffice Spreadsheet) with the Stat Formula:

(((((IV+(2xBase)+(EV/4))*level)/100)+5)*Nature)

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.

Stat Requirements:

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.

SPECIAL

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:

Neutral Natures

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.

Boosted Natures

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.

Hindered Natures

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.

THE RESULTS

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.

Summary

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.