...I started to worry that statistics would prove my number was up...
You may already realize this, but that's not how statistics work, and is a good example of the "Gambler's Fallacy".
https://en.wikipedia.org/wiki/Gambler's_fallacy
Not losing your skis on 1 or 10 or 100 flights doesn't make you more or less likely to lose them on your next flight. Of course, that doesn't change the fact that it might
feel like you must be due... which is why the fallacy exists and is common.
...I think the odds of misplaced or lost luggage go up exponentially with the number of transfers you make...
That one I agree with, but I have no data to back it up. According to this article :
https://traveltips.usatoday.com/odds-losing-luggage-109295.html
The odds of losing a bag are about 0.3% as of 2012. Some Googling for reasons, or prevention of lost luggage gets a lot of hits - but after looking at several lists I don't see number of connections as a problem on most of them. One airline (SITA in Spain) is quoted as saying that half of their lost luggage is due to a transfer/connection. And another article said to avoid short layovers that would increase the chances of not having time to transfer your bags.
I know that the only time a bag didn't show up for me was when I literally had to run through the airport to make a connection. My bag showed up at my hotel later that night - luckily there was one more flight coming in that day.
All-in-all, airlines have gotten very good at not losing bags. I had an interesting experience in how good they sometimes are at handling bags. Due to some quirky flights and airlines (SATA out of Portugal is the worst, and Orbitz wasn't helping the problem), I had a situation where my bag did not get checked through to my final destination. Instead, after checking in, I realized that I'd have to pick it up in Boston, and recheck it to the Azores. American Airlines was handling that leg, and the woman at the desk was great - she said they'd track down my bag and get it prioritized to make sure it was in Boston in time.
I then took a flight an hour earlier than mine (the flights were hourly all day between DC and Boston), and my bag was STILL there waiting for me when I got there, with big striped priority tags on it. They found it and retagged it, and then sent it on the flight 2 hours before the one I had originally booked. I rechecked it in plenty of time to make my connection.