It's not that MLB managers are necessarily managing in order to produce the statistic on purpose (although maybe some of them actually are, who knows), I think that the existence of the statistic itself is to give understandable, defined parameters to a number of different situations which would be considered mathematically relevant to assign your best reliever to. The statistic itself can indeed be a little hokey because of its inconsistency, as "not all saves are created equal" especially when some saves involve "the tying run being on-deck", every three-inning relief appearance resulting in a "save" regardless of whether a team's lead is 1 or 100, etc. The save statistic can definitely be artificially-manufactured, but the concept of a "closer" is relevant regardless of whether the save existed as a statistic or not.

"but the concept of a "closer" is relevant regardless of whether the save existed as a statistic or not."

Except that it's really not.

One study of boxscores by retrosheet.org researched the seasons 1930 to 2003 and found that the likelihood of a team winning when they enter the ninth inning with a lead has been virtually unchanged over the years, from before the "ninth inning closer" era to the present time (or at least, through 2003),  One-run leads entering the ninth inning are won 85% of the time, two-run lead are won 94% of the time, and three-run leads are won 96% of the time.  So in that respect, the "closer" provides little to no added value over a game ending without a designated closer.  That fact is blurred by the save as a statistic, because too many people tend to get mesmerized with guys who rack up large numbers of saves year after year and give them perhaps more credit than they really deserve.

Change the name of the role from "closer" (which implies that they are closing out the end of the game) back to the previous name of the role ("fireman", or "stopper"), and it takes on a completely different and much more relevant meaning.  Your best reliever is now brought in at the point where you need to get out a a jam, "put out the fire", or to stop the other team's rally.  This is more fitting for the example of getting the third out when the bases are loaded in the 6th or 7th inning, rather than getting the first out with the bases empty in the ninth inning.  That's where you want to leverage your best reliever, not to protect a three run lead in the ninth.

Additional research by the baseball "think tanks" such as Baseball Prospectus, estimates that teams could gain up to 3 or 4 more wins a season if they bring their best reliever in during critical pre-ninth inning situations rather than hold them back for the now all-too-common "ninth-inning save".

I think, in real sports, that there is a mentality that's required to do specific tasks.    In baseball, I'm pretty sure the "closer" has a different mindset than the 6th inning reliever.  Maybe I'm right, maybe not.   Either way, it doesn't exist in HBD.

In MLB, there theoretically is a mentality or mindset that is attributed to the closer.  However, the actual numbers don't seem to support that a closer makes much of a difference in the long run.

The "elite" closers, such as Mariano Rivera, might be the exception.  In reality, there have been very few elite closers in MLB.  But the psychological impact of a Rivera may be less on his part and more on the part of the hitters.

And as you pointed out, the closer rule is completely irrelevant in HBD, and is probably actually detrimental to a team.

Well, if you didn't do the job very well, you probably didn't have it very long.  And, if you were unable to "shake off" that three run bomb that cost you the game, you didn't have the mentality to do the job long-term.    That's why there have been few elite closers.   It's hard to "lose" the game on a couple of pitches and show up the next night with the same attitude.

Posted by MikeT23 on 1/23/2014 4:04:00 PM (view original):
I think, in real sports, that there is a mentality that's required to do specific tasks.    In baseball, I'm pretty sure the "closer" has a different mindset than the 6th inning reliever.  Maybe I'm right, maybe not.   Either way, it doesn't exist in HBD.

You employ/manage more people than I do, I'm guessing from previous posts.  My sense from limited experience as a manager is that people like to have their role be consistent from day to day-- but they are open to creative definitions of "roles"  So I think that, for example, Grant Balfour would be able to fire himself up to be just as effectively dickish in tec's "fireman" role as in the "closer" role.  The only thing that makes me doubt that is that saves get paid, so there's a financial motivation to want to "close--" but look at this year's FA market, the financial gap between closers and non-closers is shrinking (Jim Johnson notwithstanding).

And of course, you're right about its not existing in HBD.

Honestly, I actually liked most of mushashi's article.. except for the one part where the guy they interview says "let's just get this out and worry about the rest later." That's exactly the point that those who argue against the a closer's importance are missing. 

The biggest problem with using the #1 guy in the 6th or 7th inning to stop a rally or "get a key out" is 1) the other team still gets chances to bat and 2) your team still gets to bat.

a) In the next half inning (or innings if it's as early as the 6th) your hitters can and will score additional runs a statistically-definable percentage of the time, which therefore invalidates the importance of the spot in the previous inning. That uncertainty principle violates the overall importance of that spot over the course of the long-run.  Once again to make a blackjack analogy (because I dealt blackjack part-time for a year...doing something 20,000+ times allows for a different perspective on the frequency of outcomes amongst a sample size), let's say you had a trump card where you could play a 10 whenever you wanted and you're allowed to save the 10 for a key spot, but you're only allowed to play it once. In this analogy, the inning you are in relates to your total.  So if you have 10, you can play it now and get to 20 and that's pretty good, you definitely might win, and you especially might want to take it if you have a big bet and the dealer shows 10. However playing 10 on 10 can never be 100% perfect because you are not last to act, and because the dealer has a hidden card AND can still draw, the final outcome can never be known. There will be statistically-definable percentage of instances within this subset where you won by too many and a stastically-definable percentage of instances, no matter what the dealer's upcard (2, 6, 10, whatever) where the dealer will pull 21. Because your trump card is played without knowing the final outcome, it is inherently wrong. I'm sure you can relate the analogy to our bullpen example.

Purely from a numbers standpoint, baseball is broken up into defined units (outs) broken up into equal segments (innings). Outs are of limited commodity, and become more and more limited as the game goes by.  At the beginning of the 7th inning, the next out is 11% of an opponent's remaining outs, the next inning 33% of a team's innings. At the beginning of the 9th inning, the next out is 33% of a team's remaining outs and 100% of a team's remaining innings, so therefore one out in the 9th is worth the entire 7th inning. This dynamism of baseball relates to some of David Sklansky's game theory regarding poker tournaments. As a player's chip-stack decreases relative to the stacks of other players, the value of one individual chip for that person is much higher relative to the value of one chip belonging to the largest stack. Most players do not realize this important mathematical oddity, especially towards the end of a tournament, and this is why short-stack players virtually always short-change the value of their stack as part of deals at the end of tournaments.  Players assess value of their chips in a vacuum.  Similarly, the relative importance of outs increase at the end of baseball games. These ideas can be and have been proven to be fact and cannot be debated; these are not my opinion. Sklansky and his associates went to MIT and reproduced their findings time after time; he probably knows what he's talking about compared to you or me or Baseball Prospectus or any of us.

Subsequently, the value of an out in a 7th inning bases loaded 1-run jam can be weighted relative to a 9th inning spot with the bases-empty and 2 outs (or at the beginning of the 9th with the bases empty.) You can weight the value of that 7th inning spot to argue that it is a very important spot and may end up being the most important spot from a results-oriented perspective, but via the uncertainty principle, the best reliever should not come in unless his success or failure will in fact absolutely define the outcome. You may be able to define a 7th inning out as the key out of a game if and only if that definition is done in retrospective after the game is over.  Your spot may be best that one time, but over the course of thousands of thousands of equal trials, it is sub-optimal game theory.

So now let's do some algebra and say, as an example, over the course of a season, you use your best guy in 50 games for 100 innings (6th and 7th) and I use my guy 75 games for 75 innings (9th only and in "save" situations only), you can weight the value of your innings and I can weight the value of mine and my weighted value will be higher.

50 [full 6th-innings] x .25 [value of a full 6th inning] + 50 [full 7th-innings] x .33 [value of a full 7th inning] = 12.5 + 16.5 = 29.
50 [full 7th-innings] x .33 [7th value] + 50 [full 8ths] x 0.5 [full-8ths] = 16.5 + 25
75 [full 9th innings] x 1.0 [value of a full 9th inning] = 75.  
(also, every inning past the 9th has a progressively-higher value than 1.0 by extrapolating an inversely proportional factor of the values before the 9th inning ... )
You would have to complie all 150 innings for your total to be more valuable than my 75.

Because of this, my guy can actually have worse numbers in a vacuum yet still be more valuable because the conditions in which your guy obtained his stats (your innings) were less valuable; your innings would have been obtained under an element of future uncertainty that can (and sometimes do) invalidate your guy's success. Also, I spread my guy out over more appearances and allowed him to impact a larger volume of outcomes than your guy did.  Furthermore, saving the player isn't terrible; the closer's potential energy is just as valuable as his kinetic energy. 

To extend this even further, you could make a rebutal that this algebra de-values starting pitching because 1st innings are worth so little.  My rebuttal to that is that it precisely qualifies (and quantifies) the importance of "innings pitched" to a starting pitcher's overall value. The value of a guy like Justin Verlander or Clayton Kershaw is defined entirely by the volume of innings they pitch above & beyond the industry standard of 6.0 with 3 or fewer earned runs. JV and CK are constantly pitching into the 7th, 8th, and 9th innings with unbelievable efficiency, and that 7th,8th,9th inning gravy contains virtually all of their (nearly infinite) VORP.  33 games started x 6.0 = 198 innings pitched.  Last season Kershaw threw 236 innings.  Those 38 extra innings are not just 38 innings in a vacuum, they are 38 weighted innings of disproportionately (re: exponentially) higher value than the value of the first 198. This concept (among others) contributes to the all-time sabermetric value of, say,1997 Pedro Martinez relative to the industry standard.

Back to your guy, let's say your guy gets out of that jam like he is supposed to and then your team immediately extends the lead by 2-3 runs, is the plan to commit to his usage or to take him out because his next inning is not as valuable?  If the latter, then you've wasted a valuable asset. Who do you turn to if something goes wrong?  If you commit to your closer for the remainder, you win the sh*t out of this one particular outcome, but he will tire and may be unavailable tomorrow while he recovers and when you need him in a crucial spot (the uncertainty principle once again applies) you have a higher % of losing that outcome. Conversely, if you take him out, the opposition now has a better chance (albeit slight) of rallying relative to if you had just played your 2nd-best reliever in the key spot.

I want to point out that I'm not necessarily debating any of the numbers you've reproduced from retrosheet or whatever, I just want to point out the importance of 11%, 9%, and 4%, and 2%.  Those edges are statistically significant (re: blackjack !!), and in retrosheet's case, they are a subset of results that could have been derived from false pretenses and not necessarily those of optimal game theory. The statistics could have been arrived upon as a result of incorrect decision-making and are therefore not true.  Proper game theory could slant those numbers from the observed outcomes and widen your advantage.  Question everything.  Test your own hypotheses.  Prove your own solutions. 

Posted by MikeT23 on 1/23/2014 4:49:00 PM (view original):

Yes, and athletes are creatures of habit.   They'd like to show up at the park at 3, take BP at 4, rest for an hour or so, play the game.   Closers stretch in the 7th, loosen up in the 8th and pitch the 9th.   Telling Rivera to get loose in the 5th might wreck his entire routine and make him less effective.  So, yeah, that "I'm doing this tonight" plays into the mental part of it. 

That's more a function of the culture change of "the ninth inning closer" and "the eighth inning setup guy" of the closer era.  Thank Tony LaRussa for that.

Back in the 70's and early 80's, the firemen/stoppers (Lyle, Gossage, Sutter, Quisenberry, etc.) were able to come into the games in the 6th, 7th, 8th innings, whenever they were needed, and they were able to function effectively.

In response to pjfoster's book:

Based on everything in your post, if outs are somehow more valuable in later innings than in earlier innings, are runs also more valuable in later innings than they are in earlier innings?

Do not short-quote me. I'm sorry that your attention span is not enough to at least say hmm that's interesting.

The ML season can be more accurately compared to an amalgamation of single-table poker sit & gos rather than one six-month-long cash game where you tally up the score at the end and it's 900 to 800 or whatever. If an ML season was a six-month-long cash game, then an out in the 4th inning on May 5th would have the same value as an out in the 9th inning on September 25th.  But it's more similar to sit & gos where the decisions at the end are more important than those at the beginning.

In response to tec- Based on everything in your post, if outs are somehow more valuable in later innings than in earlier innings, are runs also more valuable in later innings than they are in earlier innings?

Yes, of course, that's why teams only do defensive replacements and pinch-hitting/pinch-running at the end. Nobody would argue otherwise about pinch runners so why would you argue otherwise about closers vs setup men it makes no sense

Answer the question.    If it's not too complicated.    Be brief.   You're not interesting enough for a long read.

Posted by pjfoster13 on 1/23/2014 7:59:00 PM (view original):
Do not short-quote me. I'm sorry that your attention span is not enough to at least say hmm that's interesting.

The ML season can be more accurately compared to an amalgamation of single-table poker sit & gos rather than one six-month-long cash game where you tally up the score at the end and it's 900 to 800 or whatever. If an ML season was a six-month-long cash game, then an out in the 4th inning on May 5th would have the same value as an out in the 9th inning on September 25th.  But it's more similar to sit & gos where the decisions at the end are more important than those at the beginning.

In response to tec- Based on everything in your post, if outs are somehow more valuable in later innings than in earlier innings, are runs also more valuable in later innings than they are in earlier innings?

Yes, of course, that's why teams only do defensive replacements and pinch-hitting/pinch-running at the end. Nobody would argue otherwise about pinch runners so why would you argue otherwise about closers vs setup men it makes no sense

First: stop comparing baseball to blackjack and poker.  Baseball is primarily a game of physical skill, with an element of chance mixed in.  Blackjack and poker are primarily games of chance, with elements of intellectual skill.  You can't compare the two, they are quite obviously dissimilar.

Second, I'll argue that runs are NOT more valuable in later innings that earlier innings.  If one team scores 2 runs in the top of the first, and the other team scores 2 runs in the bottom of the ninth . . . the game is tied.  Runs are runs, no matter when they are scored.  Preventing runs from being scored in the 6th or 7th inning should not be marginalized compared to preventing runs from being scored in the 8th or 9th inning.

Third, your examples of defensive replacements and pinch-hitting/pinch-running fail to back up your assertion.  Defensive replacements are done towards the end of the game when the team that's leading changes it's emphasis from scoring runs on offense to preventing runs on defense.  If you're leading 4-2 going into the bottom of the ninth, you likely are not going to have any further opportunities to score.  So instead, you take out your offensive players and put in the d-reps to minimize the likelihood of the other team scoring.  The potential for, or need of, generating additional offense at that point of the game has been minimized to the point of being negligible, so defense has far more relative value.  A similar argument can be made for PH/PR.