Not many.
Games v the 'big six':
Brighton: P2 W0 D0 L2 F0 A4 Pts 0
0-2 v City (H)
0-2 v Arsenal (A)
Bournemouth: P4 W0 D0 L4 F1 A7 Pts 0
1-2 v City (H)
0-3 v Arsenal (A)
0-1 v Spurs (A)
0-1 v Chelsea (H)
West Brom: P2 W0 D0 L2 F2 A5 Pts 0
0-2 v Arsenal (A)
2-3 v City (H)
West Ham: P2 W0 D0...
One more than 18th. The rest of your post is fluff and conjecture.
The actual figure is not the issue - one more point than the team who finished in 17th would have seen them safe. Obviously.