l thought delta, I had entered a dec27th expiring put broken wing butterfly on 16 Dec13, SPY 179.5p, 177.5p, 174.5p at -.04 (credit), three days had past and underlying moved in opp direction, SPY increased almost 2 points from 179.13 when I had entered the trade, to 181.06 when exited, on 19 December 13 at 0.25, delta surely wasnt the most influential here, if the primary factor was vega / volatility, what should I of seen in these numbers? Is there an explanation for this profit in this trade?
The title of your post is a bit misleading. What you have isn't "an option", but rather a bunch of options. For a bunch of options, you could have all sorts of greeks, with all sorts of different relative significance.
Usually the greek with the highest value in portfolio. Regarding your posiiton, skew, vol of vol, stickiness etc. will affect it and these things arent always clear from looking just at the greeks.
Directional strategies are very responsive to delta, overwhelming all the other greeks. For Neutral Strategies, gamma becomes more critical as you get closer to expiration assuming your still watching delta and your strategy is still neutral. Nonetheless, you should be watching all at the same time. Though, I think theta has an overstated "fear and greed" effect that overweights itself in your psyche.