Jud,
Growing up my grandmother had a saying, and I honestly don't know why, that there were Liars, Damned Liars and Statisticians.
Not that you're a liar, but I must disagree with your statement, "It's statistics 101 Jason. If a guy is a lifetime .300 hitter then regardless of whether he's 0 for his last 25 or it's the bottom of the ninth with 2 outs, the winning run's on second and he's got a 20 game hit streak going, the odds of him getting a hit are exactly 3 in 10...."
Built into that lifetime .300 average is the facts that in 150 plate appearances with two out and two men on the batter got 75 hits while over his career he he batted just .055 while striking out 83% of the time in the first inning. In other words, each at bat has a whole series of individual aspects that can change both the actual average and statistical likelihopod of the batter getting a hit. How many runners are on base? Is one of them a pinch runner? How HEALTHY has he been leading up to the game? How OLD is he? How many years has he played in the majors? Is the pitcher throwing from the Stretch? Is the pitcher the number one reliever or is the starter who has now gone almost 9 complete innings and thrown 134 pitches. Is it a middle reliever brought in because the closer has thrown too often as of late? What is the temperature? What time of year...
There are simply TOO MANY variables that will directly effect the ACTUAL outcome to make a true statistical prediction?