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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LOL Moody you just put quantitative math into my drafting for the APBA league I am in. Except I uses chances to get on base as the target. So even before the cards come out (or the disk if I am in a BBW league) I am spending my prep time calculating on a player by player basis what the chances are of each of them getting on base verses 36 chances.

Richard, very nice to see you in an APBA league. I was in the Lame Duck league for many years but had to quit with family, church, work balance. I still play though and am working on an all Chicago season with great teams from Cubs and Sox history.

If you are interested in chatting with other APBA guys look up the group on Facebook.

https://www.facebook.com/groups/17354586764/

Sorry about adding a link on your John.

You should try the BBW 5.75 bleedblue. It is a great way to spend a few minutes to still play by yourself. I LOVE my 61 season. I have been trying to beat the Yankees for over a year. The closest I come is with Detroit. That team was STACKED.

I do have the BBW and love it. I have to admit a stronger tie to the dice but the BBW is excellent. I also use it to accompany some projects. I have done an 84 Cubs replay, and a 93 what if replay rolling the Cubs games and having the cpu play the league, of course I can jump in and manage some if I like/have time.

Great hobby and you can't beat the price vs. Hours of enjoyment!

Curious - haven't played any of the board games since before they were computer compatible/available. Is it possible to get old Cubs rosters pre-1983?

I would really love to try playing the 1969 and 1970 Cubs - and although I realize it would be an excercise in futility - my 'debut' Cubs season as a real fan c1974.

I too am a APBA player in a long running league (we use the disk and not the cards) and I too spend a lot of time looking at some of these types of numbers. Sometimes hard to compare real games vs. a disk game, but fundamentally it works.

I have a serious man crush on Dexter Fowler because of OBP verses his power. Really was ticked off when he went to Houston for spare parts.

You guys need to get ootp baseball. So much more than what apba has

I have heard that but I grew up with APBA.

I have heard that is a good game! I do play with many innovations so I don't play an out of the box basic game.

APBA--what a blast from the past. I had the 1976 season which wasn't too good. My brother had the 1972 season which was really good, and, of course, had a respectable Cubs team with a monster season from Billy Williams. My friend had the 1977 season which had great hitting.

I saved my money to buy the 1975 season--Bill Madlock, a great Reds team, and Fred Lynn and Jim Rice leading the Red Sox as rookies.

MOAR RUNS!!!

Nicely put - an oversimplification (of course) but begins to illustrate the point.

Dare I ask (I suppose I could easily go and dig the information up) what the current Cubs' team OBP is?

Next to last in the NL with a ...

... 0.297 OBP. Only San Diego is worse (0.274, if you can believe it. And considering their offense, yes, I can.)

Best is Pittsburgh at 0.333.

That .333 is stunningly low, BTW, historically speaking. It's another sign of the drop in offense the Cubs are trying to take advantage of.

Excellent point Mike. Also, why the move to power will be so important, as OBP decreases the value of a homer increases. Reminds me of Weaver and him looking for the three run homer with those great staffs he had in Baltimore.

For the season team OBP is 0.297,.... Down to a low of 0.277 for June, but has been 0.322 for July to date.

This is great stuff, Mike. Glad EconoBall is back. The left side of my brain needs the exercise.

OT but I noticed you guys are inching closer to 2000 likes on FB! People are finally figuring out where to go for their Cubs minor league info!!! Keep up the great work guys!!

Loaded question: So what's more important -- OBP or SLG?

Good question. The easy answer is both but let see if I can think of a way to test it.

I believe OBP is generally given a slight edge over SLG. A team only has a finite number of outs so every opportunity to decrease the chance of making an out is important.

To test which is better you could determine the chance of driving in a runner on 2nd base given for several different types of players. Give each player the same OPS but vary how the OBP and SLG are divided. My guess is you are likely going to end up with some sort of bell curve, where a mixture of OBP and SLG is best.

My best guess is OBP and SLG will cross like supply and demand. As you get OB less the value of doubles and triples increase, and especially homers since as Mike demonstrates with lower OB it is harder and harder to score. Homers become very important as OB shrinks. It makes the Cubs strategy of cornering power look all the better!

Just instinctively, what you're looking for is a balance. Home runs by themselves can be survived, but when they come with one or two guys on base, it makes life difficult for the opposing team. It's why the Cubs dream lineup is so scary, because with guys like Rizzo, Bryant, and Soler at the top, you're looking at guys who can either take you deep or take a walk to put the next guy in that much better a spot.

It could be a beautiful thing for sure!!

I would say obp.. because hitting a double,triple is obp.. so lets say a guy walks (obp) and the next guy hits a double/triple. that scores a run that wouldnt been there if it was just slugging

So to steal an argument from next week, think of it this way: two singles = no run scored. A double and a single, in any order, usually scores a run.

But with SLG, you're talking about immediately being in scoring position. Not only that, but you eliminate the possibility of double plays from wiping out your OB guys...

Of course the hits that are accounted for in SLG make up OBP, but isn't the point of OBP to weight some ways of getting on base (2B, 3B, HR) as more valuable/better than others (1B and BB)? I don't think the argument is that simple. If that was the case, there would have never been the need for SLG%.

It goes without saying that ultimately having high OPS is the goal. To move into analogy, I look at the OBP vs SLG argument like drafting strategies: would you rather have quantity (OBP) or quality (SLG) prospects?

I'd want to see if, statistically speaking, there is an increase (as I suppose) of chances of making one or multiple outs as the amount of runners on base increases.

And then looking at it from an opposite side, is it easier for a pitcher to escape from a lead off walk/single as opposed to a lead off double or triple? Or even with one out, what increases the pitcher's likelihood of giving up a run? A one out walk/single or a one out 2B/3B?

My intuition tells me that SLG is more valuable, assuming that you put 8 guys with high SLG in a lineup vs 8 guys with lower slug but higher OBP. Then again, I took statistics at a community college so I'm operating out of position of at least some ignorance.

When 'the boys' start trading excess quality everyday players One can bet obp will be a priority. Building a productive lineup isn't just about the best, but the best balance.

Mike, is there a way to value the way one gets on base? A .330 average from a team that gets all hits is different than .330 from all walks (the extreme examples) in their ability to score runs.

Excellent piece and demonstrates in a simple way how not making outs is critical to run scoring.

Yes. Tune in next week :)

WOBA (weighted on base avg) takes that into consideration. It seems to be a slightly better indicator of all-around offensive production than OPS which is simply a non-weighted total of on-base plus slugging. wOBA awards a hitter for reaching base with a double more than a walk or single, and so forth. It's not perfect, but it seems to address your area of concern.

I agree, good point

Really am happy this is back. Enjoyed the first few articles that got published awhile back about pitchers.

Interesting article, Mike. I especially like the way you reduce your undoubtedly complicated thinking about this to a simple thought process without losing all meaning. As a common recipient, by necessity, of ideas being "dumbed down", I have come to recognize the talent in those who do it well and without insult.

Separately, I have been on both a Replacements bender and a Rainbow spree on Spotify over the last month. There's room for both in my mostly empty head.

Richie wields one of the mightiest whammy bars in the history of rock'n'roll. Definately a unique style.

Ah yes, the numbers are important but for those who see poetry in the game and love taking a chance on a swipe of home or baseball strategy that goes beyond the numbers its where those who use numbers and those who watch baseball for sheer enjoyment meet.

Quick question. Your assumption that every inning starts at the top got me thinking. If you did have one .400+ OBP hitter, where would be the optimal place for him in the order? Obviously the other characteristics of that hitter matter but for example, the Reds have never really settled on where to put Joey Votto in the lineup. thanks

Every statistical lineup breakdown I have seen says the optimal lineup puts your best hitters 2nd and 4th.

I always put my best offensive force 3rd, so no matter what, my best hitter would bat in the first inning

The main reason you are supposed to bat your best hitter second is in the first inning there is a good chance that if you have your best hitter 3rd he is going to be coming to the plate with 2 out and nobody on. If you hit him 2nd, even if your leadoff guy makes an out, if your best hitter gets on base there is a much better chance of scoring a run with one out as opposed to two. Hitting your next best guy 4th means he is either going to be hitting in the 1st inning with a runner on (unless a run has already been scored) or leading off the second where hopefully he can start a rally. Its not like the 3rd spot is a bad spot to put a good hitter, but 2nd and 4th are just slightly more statistically significant.

Remarkably, if JUST considering OBP, it's 1st in the lineup because he gets the most plate appearances. If you start considering OPS, that changes. I'd actually need to build a simulator to tell your for sure, which is something I plan on doing, but haven't, yet.

there has been one made already..

Yeah, I want to do it a little different than that. But thanks for the link.

For me if it is OBP that is walk driven (Choo) then that guy bats 1st. If it is OBP that is balanced (Tulo/Trout/McCutchen) then they bat 2nd. So say you have 2 hitters that have a .400 APB and one bats .330 and the other bats .280 you want the one that bats .330 to bat 2nd just because there is more of a chance of getting that runner to 3rd or scoring.

http://www.baseballmusings.com/cgi-bin/LineupAnalysis.py

had to find it

Another way to conceptualize this idea: Suppose you have 10 units of WAR to distribute between adjacent batters--what would be the most effective way to do this--0-10, 3-7, 5-5, or some other pair of values? To simplify, the outcome of two events both occurring is the multiplicative product of those individual events, so that for the above numbers, 0x10=0, 3x7=21, and 5x5=25 (the best). It can be shown mathematically that the highest product will always occur when the two numbers are equal. Similarly, this concept can be extended to any set of numbers that add up to a constant. For example, the highest product of 9 numbers (hitters) adding up to 18 (WAR) is 2x2x2x2x2x2x2x2x2=512. It can be shown mathematically that the product of any other distribution of 9 numbers adding up to 18 will be less than 512. And consider what happens when one of the hitters is a 0 (an out) -- the product is 0. This is not to suggest that 5 WAR hitters have limited value, but that successful offenses minimize outs more by avoiding low WAR hitters. The example above is greatly simplified mathematically, but I hope you get the basic idea -- successful offenses AVOID OUTS!

examples, bunting, getting caught stealing...

Kyuji Fujikawa Being moved up ti Iowa AAA

Good to hear.

Speaking of OBP checkout Schwarber's first 150 PA compared to Bryants. I can see why they are trying to fast track Schwarber by playing the OF.

OT, but in re a thread on a previous post, it seems the 11th pick will in fact be protected - per MLBTR:

"The Astros’ failure to sign Brady Aiken resulted in the team receiving a compensation pick (No. 2 overall) in the 2015 draft, and while we’ve seen problems caused by comp picks in the Top 10 under the new CBA (specifically heading into the 2013 season), MLBTR’s Tim Dierkes reports that a change has been made to the protected pick structuring (Twitter links). Previously, the CBA had called for the “Top 10″ picks to be protected, but changes have been made that will protect the picks of the teams with the 10 worst records, regardless of whether or not comp picks are inserted into the first 10 selections."

Good info, SK. Thanks for posting it. There certainly was some confusion over the details

Two interesting (and, especially for the first one, potentially worrisome) substitutions in the minors tonight.

First, Soler came out of the game after hitting in the sixth. He popped out, so not sure it came running (he just didn't come out for defense in the 7th).

Second, Malave started the Boise game at catcher and was removed at his first at bat for a pinch hitter. He had a passed ball and the starter got rocked in the first, but am not sure that these are related to his removal (which was in the third).

He is okay from what I understand.

I read elsewhere that it's part of his "program"

Thank you John and Mike....story sounds much better when "Soler 2-3,back over .400" isn't followed by "but he will miss the next [__] games due to injury".

While reading this, the scene popped in my head from the movie Moneyball that was derived from the book when Billy Beane and J.P. Richardi (it was Jonah Hill's character but they used a different name) were battling it out with the scouts on trying to replace Giambi and Damon. The question then was how to replace Giambi and his OBP and the decision was not to go after another superstar but to package the OBP increase in a couple of other players. Much like your example shows Mike, they did as well as the goal was to increase runs and the correlation that has with getting on base. To me, this was a revelation when I first read Moneyball more than a decade ago. While there have been several statistics that have come to light since, OBP has continued to be the one simply understood stat with the most correlation to Runs - which you need to score in order to win. With Baseball being the most statistically driven sport out there, it is always fascinating to be able to statistically break everything down to its base level.

It also connects to the ratio of runs scored not via a HR and runs scored via a HR. Having high OBP in front of HR hitters appears to be a good approach but a better one is to have OBP not only in front but also with a string of HR power, so the secret is to find both and concentrate them. Minors stat's

Castro ..326 OBP .433 SLG OPS =.760

Rizzo: .384 OBP/.522 SLG/OPS=.907

Vlabuena .331 OBP/ .408 SLG OPS=.739

Castillo .291 OBP/ .384 SLG OPS =.675

Alcantara.353OBP/.537 SLG/ OPS=.890

Russell 361 OBP/.453 SLG OPS=.814

Bryant .441 OBP/.705 SLG OPS=1.146

Soler .493 OBP 862 SLG, OPS=1.355

Schwarber .479 OBP/.707 SLG OPS=1.186

Baez .313/.473 SLG OPS=.785

Rademacher .383 OBP/.425 SLG /OPS=.808

Almora .306 OBP/.398 SLG /OPS=704

Lopez 385 OBP.402 SLG/OPS=.787

Zagunis 431 OBP/.473 SLG/OPS=.904

McKinney .338/.396/OPS=.733

Bruno .348/.405/OPS=.753

Think the Cubs will score more runs with these younger guys?

OT: Christian Villaneuva on defense (hat tip Brett Taylor)

https://www.facebook.com/photo.php?v=10152523169843559

On Junior Lake's value, trading him and whether he will ever be a viable every day player....most likely he won't be and we do have safer options in the minors, so getting value for him now would be beneficial.

That doesn't mean there isn't a potential downside of trading him. Here is Sammy Sosa's stats the two years (albeit his 22 and 23 year old years) with the White Sox before the Bell-Sosa deal (and I don't think the steroid argument is necessary applicable for the 1993 stats below):

1990 CWS -- 532 AB, .233 .282 .404 ., 26-10-15 (2B-3B-HR), 150 K, 32-48 in SB

1991 CWS 316 AB 203 .240 .335 10-1-10 (2B-3B-HR) 98K 13-19 SB

1993 (1992 only played 67 games) with Cubs:

598 AB, .261 .309 .485, 25-5-33 (2B-3B-HR), 135 K, 36-47 SB

Sosa is comparable, and why Lake is high risk/high reward.

OT Is today the day that TJS is scheduled for Cease?

Joe Posnaski has a great piece on the Royals hitting philosophy on his blog.. cant link it per its blocked at work, but reading it made me think of this article.. talks about the Royals hitting troubles and their philosophy compared to the Cubs/Epsteins hitting philosophy.. interesting read - google posnaski's blog