Originally Posted by 2020dad:
Numbers are a wonderful thing. You can make them say whatever you want sometimes. Lets just use.the numbers provided by that sporting news article. And the article said 'less' than a .001% chance. If you may indulge me here lets just use .001 shall we. Those numbers were based on 'any given pitch'. So if you threw 100 pitches then the chance would be .1 correct? Now 30 games a year would that be 3% now? 10 years pitching... 30%? I am not entirely sure how probability and statistics work but if we were dealing with just one pitch and that was all you were ever going to throw then I guess you're good to go. If there is anyone out there with an actual probability and statistics background would be interesting for you to chime in based upon the given number of .001% of pitches hit pitchers in the head.
The article mentions a "less than" 1 in 100,000 chance, but doesn't get more precise than that, which makes it somewhat suspect.
This article mentions that Bryan Mitchell was the 7th pitcher hit by a line drive since 2013. I can't speak to the veracity of that number, or even take an educated guess at the economic value of the injuries incurred on those 7 occasions, but that implies about a 1 in 300,000 pitches chance given that there are around 700K pitches a year in MLB. Oh, and that's just line drives to the head.
Of course, those are the best athletes in the world, and pitching talent is matched well to hitting talent, and they're not swinging metal bats, etc, etc. I'm not sure there's an easy comparison to be had to the risks at other levels, and I really don't want to spend the time trolling the web for injuries to youth players over time to find a more useful basis from which to draw a conclusion. If someone else wants to do it, the math for the odds is relatively straightforward, depending on the assumptions you want to make.
FWIW, given the large odds involved and relatively small number of pitches thrown by a given pitcher, it's a decent approximation to use pitches thrown/incidence odds as a proxy of the chances of getting hit. The more pitches you throw over a career though, the less useful that approximation will be. Given, for instance, Greg Maddux' MLB career, and incidence of more like 1/300,000, there's about a 19% chance that he should expect to take a line drive off the head at least once.
That seems high on it's face to me, but I don't have nearly enough data about the incidence rate to really feel confident about it. That same incidence rate suggests that there should only be about a 10% chance of making it through an MLB season without someone getting cracked in the skull, and that we ought to expect about 2 per season, which is actually pretty close to where we've been recently based on the Forbes article, though.