It seems a little odd that the first piece on the site following felzzy's passing is all about the numbers. Adam wasn't one for the numbers of baseball as much as he was about the poetry of the game. He poked fun at me, more than once, for getting lost in numbers and theory and missing the game happening in front of me. But his jabs were never mean spirited. There was a child-like joy to his writing that reminded me a little of Mel Brooks at his best.
Those were hardly the only differences. We had different taste in music. Adam listened to the Replacements while I will do my work to Blackmore's Night. Different jobs: copywriter vs. graduate student. Different opinions on a great deal of things outside of baseball.
Yet, we shared a love of the Cubs. Everything both of us have ever written for this site has been motivated by the same desire: to see the Cubs play great baseball day-in and day-out to win a World Series. I'll miss you, my friend, and try to remember that there's a forest out there above the trees. Onwards.
Having said that, I'd like to take some time to focus on the trees. Today, those particular trees are about probabilities and why high OBP up and down the lineup can make a big difference to the offense.
The goal of the game, obviously, is to score runs. I'll make a simple assumption that having at least three guys reach base in an inning will generate one or more runs for the offense. (It's obviously flawed, but for my purposes it will do.)
As another simplifying assumption, I assume that everyone in the lineup has the same OBP (I'll ease that a bit at the end). Those assumptions give me enough to calculate probabilities.
Skip to the next bold if you don't like math. You've been warned.
I calculate this using "complementary probabilities." I can do this because I have two mutually exclusive events (0,1, or 2 runners reach base or 3 or more runners reach base) which are also "collectively exhaustive." That is simply statisticians deciding to use big words to confuse everyone. It simply means that one event or the other must occur but that both cannot happen together.
Complementary probabilities means that, instead of calculating every event for which a team can get three or more runners to reach, I simply calculate the probability that a team gets 0, 1, 2 or runners and base (Hereafter, "P012"). Since the sum of all events has to be 100%, I calculate 100% - P012 to get the probability that 3 or more runners score (P3+).
This is complicated but the easiest way to get what I want in this case. There is, theoretically, a way a team could place infinite runners on base. Although the likelihood of it happening is essentially zero (statisticians would say "infinitely small"), consider an inning where nobody makes an out and the inning simply goes on forever. That is bad enough, but unfortunately there are infinite ways in which an inning can go on forever. The first batter could make the only out. Or the second batter could make the only out. Or the third batter could make the only out. etc.
Boring math ends here
The odds of placing three or more runners on base in a given inning, with a lineup filled with guys who have a given OBP, are shown in the chart below.
The endpoints of the line are extreme cases unlikely to be relevant to major league teams. As bad as a team may be, no team has 9 hitters all of whom have a .200 OBP over a significant stretch of time. Similarly, a .400 OBP is exceptional. To have 9 hitters with an OBP of .400 is unrealistic. However, the middle range gives some valuable data. For example, consider a team with a .300 OBP. This would be extremely low for a professional team. With OBPs this poor, you could expect to get 3 or more baserunners only 16.3% of the time. Moving up to a more reasonable number, consider a team where everyone has a .330 OBP. In this situation, you could expect 3 or more baserunners 20.5% of the time. So, roughly once every five innings, your team will rally for a run. A team made up of guys with a .354 OBP (the Cubs' league-leading team OBP in 2008), you can expect 3 or more baserunners 24.1% of the time. Once every four innings -- twice a game -- you rally for one or more runs.
As the numbers attest, very slight differences in team OBP can result in a big difference in runs scored.
But what if we break from the idea above, and the "bad" team -- the one with a .300 OBP -- has two options to improve itself. It can either add one superstar with an OBP of .400 in the 3 hole or it can boost the first, second, and third hitter to .350. Which path should they choose? (For simplicity, we'll assume that they start at the top of the lineup each inning.) Taking the superstar makes the likelihood of getting 3 or more baserunners 19.0%. Taking 3 guys with an OBP of .350 increases the likelihood to 20.5%. Over a full season of 9 inning games, that increased 1.5% leads to 22 more innings where the team scores at least one run (277 vs. 299).
This underscores an important point in lineup construction: a good lineup needs to be balanced top to bottom. The high likelihood of even the best players making an out in a given at bat combined with need to string hits together to score a run (or to log a big inning in the case of a home run) means that the impact of one great player isn't as high as a bunch of good players. So when development guys obsess over getting a player to take walks, this is why.
Next: some ruminations on the other half of OPS, slugging percentage.
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