AeroMaestro

Yes

Thanks for your question, /u/vagabond9.
You're partially correct. Most of the work I do happens before the concert. How much organizing and teaching I do depends on the orchestra. A professional orchestra has other staff who do the organizing -- planning out venues, distributing sheet music, contracting musicians, etc.

If I'm working with an inexperienced orchestra, then most of what I do with them is teaching -- how to make a great sound together, how to produce an appropriate style to the composers' music we're working on, etc.

If I'm working with a professional orchestra, my job is a little different. My job is more of a "decision maker." Sheet music isn't always 100% precise. Sometimes somebody needs to make a decision. How loud is forte? How fast is Allegro con brio, ma non troppo? How long should we hold this fermata? Orchestras can make some of these decisions democratically without a conductor, but it's so much more efficient to have a conductor who plans all that stuff out and helps coordinate it with the orchestra in rehearsal.

When it comes to the actual performance, my job is to give the musicians the information they need to be at their best, but also to manage the whole show. Think about when you're driving a car -- you already know the roads to take, and when to turn left or right. But you also need to check in every once in a while with the speed limit signs, the traffic lights, and the stop signs. That's me in the show. I'm giving the musicians what they need to keep themselves organized. But I'm also in a privileged position relative to the orchestra. I'm able to hear what they're all doing and I can help them do it together in a way that leads to the best possible performance. While I'm conducting, I'm thinking about what the orchestra is playing right now, and how it sounds and how it's going. And I'm also thinking about what's coming up next and how to best help the ensemble navigate the turns and changes. And I'm also thinking about the whole piece --- is this the strongest point of the piece? How much louder, or faster, or whatever do we need to be playing to get to the most important place at exactly the right volume or speed or emotion? I'm working on pacing out the movement, the piece, the whole concert all at once.

Lots of audience members like to share this cartoon with me:
https://i.pinimg.com/564x/9e/98/ff/9e98ffb6278ba99161fa0f2e73c646b3--music-jokes-music-humor.jpg

Only once did this happen to me. I was conducting a new piece (that I'll admit probably wasn't all that great) and it had so many repeated measures that I lost track at the very end of how many measures we had left. So I just stood up straight and kept a steady beat until the ensemble stopped. I was personally embarrassed, and felt like I'd failed, but I doubt anybody else had noticed.

I've never fallen off the podium. Or, at least, I've never fallen off the back of the podium. At lot of time I conduct from memory, and sometimes I take away the music stand in front of me. A few times I've nearly stepped off the front of the podium. Now, when I'm conducting from memory, I usually leave the stand there in front of me for two reasons.
1. When the orchestra sees a conductor isn't using a music stand, it sometimes causes them stress, because they feel like the conductor's showing off. 2. I like to have that physical barrier in front of me to prevent me from walking off the front of the podium in my desire to get closer to the musicians.

I've dropped my baton a few times, and always have a spare stick on the music stand for that reason. The best story was a concert I conducted in Washington DC about ten years ago. Somewhere in the middle of the first movement of Beethoven 7, I felt my baton clip the bottom of the music stand while my arm was on the way up, and the stick left my hand. I thought the baton had just fallen below my stand, so I grabbed my spare and kept going. But when I looked up to give a cue to the horns, I saw the principal horn looking aghast and staring up at the ceiling --- the baton had flipped out of my hand and was flying way high up in the rafters and it landed in the back of the orchestra by the horns. At the end of the first movement I had to stand and wait while they made a big show of passing it all the way back up to me. I didn't really feel embarrassed --- it was a lighthearted moment. It's little goofs like that that make live performance so much fun.

It really depends on the piece. Sometimes a composer will write something so complicated for 4 or 5 people that it really helps to have a conductor there who can manage things. Lots of contemporary orchestral music uses smaller ensembles but still needs a conductor. Here's one of my favorite new pieces for a small-ish ensemble, that still definitely needs a conductor.

The smallest ensemble I've conducted, in a situation that actually needed a conductor, was 4 musicians. The largest had well over 300.

But older pieces by Mozart, for example, are less likely to need a conductor. The rhythms are less complicated, and the orchestra plays more "homophonic" (everybody's playing the same rhythm) material.

Non traditional instruments and conductors depends on the instrument, of course. But a great example is the way Mason Bates uses a drum machine in "Mothership." He's actually got a drum machine player in the orchestra, who's working with the conductor just like all the other musicians.