As promised, here is the script that I had prepared for going over Gotoh's streak. I hit most of the talking points in the podcast discussion
with Gibson-san, but we ran out of time before I could get to the end. Hopefully this will clear up any lingering questions about the research.
Mitsutaka Gotoh has been up and down in batting average over his career, hitting just .255 in 2007, and .295 in 2010. He's shown that he can hit well over the years, 2007 being an exception rather than the norm. So, let's pull a number out of the air and call Gotoh a “true” .280 hitter this season. That's a little below his average of .289 when his streak ended, but well above his .262 average before the streak began. It also matches well to his career .279 batting average (as of the end of play on September 15).
What does it mean to be a “true” .280 hitter? Basically that, in the long run, he'll get a hit for 28% of his at bats. But there may be sequences where he doesn't hit quite to that level, such as going 83 for his first 317 at bats of the season for a .262 average; or going 42 for 108 (a .389 pace) during this 26 game hitting streak.
So, if Gotoh is a “true” .280 hitter and he gets 4 at bats in a game, what is the chance that he'll go 1 for 4?
Based on 281 games where Gotoh had 4 at bats, he had 1 hit 44% of the time, no hits 28%, 2 hits 22%, 3 hits 5%, and he went 4 for 4 one time for a .36% of those at bats. That's 72% of his games where he got 1 or more hits.
Now, if you look at his numbers over 525 games where the number of at bats is not taken into account, he went hitless 30.2% of the time, had 1 hit 41.5%, 2 hits 21.5%, 3 hits 5.9%, and had 4 hits just 4 time for .76%. So he had at least one hit almost 70% of the time.
OK. Stop rolling your eyes at these numbers. This is just to set the foundation. What happens when Gotoh only gets 3 at bats? Well, he has had no hits 34 out of 105 such games, 32% of the time. He's had 1 hit 53%, 2 hits 12%, and gone 3 for 3 twice, 1.9% of the time. So, with only 3 at bats, he generally goes hitless a third of the time. During this hitting streak, Gotoh only had three at bat games 3 times, having 2, 1, then 3 hits in those three games respectively. September 16 saw his fourth 3 at bat game during the stretch, and he went 0 for 3 (with a walk) against Lotte to end the streak.
Some would say “the numbers caught up with him,” ending Gotoh's streak. While there is some truth to that, when the numbers will catch up is not so easily predicted. He had an equal chance of getting at least one hit in that 27th game on the 16th as he had in the previous 26 games. That 42 hits all got lumped together in 26 games is coincidence. Or, if he's a “true” .280 hitter who was hitting .259 to that point, a result of the numbers catching up with him.
Now, wouldn't you say that playing with numbers is great fun?"
Research included in this article: "Curve Ball" by Jim Albert and Hat Bennett; ISBN 0-387-00193-X - Chapter 5: Streakiness