Another Segment of "Guess This Team's Record"

[JUMA]

Playing in Ebbetts:

SP: Lemon, Dean, Pollett, Nolan

C: Cochrane
1: Cooper
2: Fox
ss: Peckinpaugh
3: Mathews
lf: Keller (came in trade for Valentine at game 92)
cf: D. Dimaggio
rf: Alou
reserves: G. Burns, P. Fox, Chalk, Koenig, T. Pena

Team is 6th in runs scored & 1st in least runs allowed. Scoring differential is +109. Fielding % is .982 (3rd in league.) Closer's save % is .789 (4th in league.)
Season is still underway & at the 120 game mark. There are 2 teams in my division with losing records; the division leader is 12 games above .500.
Care to hazard a guess at my record?

[JCHansen]

.500 (60-60)? Stats seem to support a better W/L, but the question seems designed to surprise...

[JUMA]

They're now 63-60. Underwhelming.