This is a religious topic on Talkbass but I always enjoy the debate.
The truth of it is that you should do whatever makes you comfortable.
If you want to be anal and analytical about it - I don't have a large dataset beyond my own 30 years of playing gigs. But I'm confident that any of the following are far more likely to fail on a given gig than your bass is:
- A cable
- A power cord
- A battery
- The amp head
- The cabinet
- Your car
So if your only argument is "it might fail, so I bring a backup" you're being inconsistent if you don't also keep a backup car in the garage to get you to your gig if yours won't start.
But, you say, it would be way too expensive to have a backup car. Which brings up the subject of grey area around probability of failure, cost of failure versus cost to de-risk, and time to remediate the failure.
Having an extra car to ensure you can drive to your gig is probably an absurd idea given the cost. So where do you personally draw the line of absurdity?
The most probable "failure" of a bass on a gig would be a broken string, followed perhaps by a dead battery and then a bad output jack. Many of us would be able to get to the end of the set down one string, then replace the broken one on the set break. If you carry an extra bass only to avoid that particular calamity, it might be too much cost and schlep. On the battery, some basses can go passive with the pull of a knob, others would require between 45 seconds and perhaps 3 minutes to swap a dead battery. Doable mid-set.
Output jacks are a little tougher. If one of those fails, the set is over and you may or may not have a soldering iron and the skill to quickly fix the jack.
But in my estimation the probability of an output jack failing during a gig lags way, way behind the probability of a broken string. And any other catastrophic failure of a bass guitar would come in way, way behind that.
Then you do have to factor in the added risk of the backup bass. Some of the places I play, there's really not room on the stage for an extra bass, so it would have to stay in its case in the corner or even in the car, where the chances of it being stolen are perhaps not trivial.
I realize this is overanalysis. But I don't usually take a backup bass. Unless I have two basses and I want to play them both on the gig.