One of the most repeated bits of managerial wisdom by bloggers, play-by-play crews and fans in baseball has been common knowledge for a very long time: never walk the lead off batter, because it will come back to bite you.

Late last night (okay, really early this morning), a discussion on Twitter between my co-writer at “You Can’t Predict Baseball” @jordansmed and @richardiurilli on the subject emerged; most notably, they were looking for the actual number as to how many lead off walks actually do come around to score.

So, of course, I thought it’d be a good idea to go try.

Here’s the thing, though: Baseball Reference will tell you how many times a team walked to lead off an inning, and you can use the play index to find a list charting all of a team’s walks, including the date, game, inning, bases/outs situation, etc…but if you want to find out if that actual walk came around the bases to score, you have to go to the game log to look it up. It’s doable, but tedious.

Of course, I’m, uh, stupid inquisitive enough to do it anyway.

So. Here’s the criteria I used:

1) I looked at ONLY Yankee walks in 2010. I did not count walks by an opponent that came around to score.

2) Walks had to occur with no one on base and no one out in the inning (thus, a lead off walk). ONLY walks were counted–no HBP, no hits, no errors; just walks.

CAVEAT: I included ONLY walks that truly led off an inning, not walks that occurred with no one on and no one out after a lead off home run.

3) The runner that walked had to be the runner that scored. For example, if Teixeira walks and scores on a Canó double, that counts. If Teixeira walks, Canó grounds into a force at second and then Canó scores on a Granderslam, I didn’t count it because it wasn’t Teixeira that scored.

4) ONLY the batter that walked is counted; any subsequent runs are not counted.

5) All box scores and play-by-play can be found on Baseball Reference (as well as a host of other sites, but I used baseball reference). The Play Index’s chart of 2010 Yankee walks can be found here. You may need a subscription to access the entire thing, I’m not sure.

So, the Yankees, so far in 2010 have had a total of 95 walks that led off an inning.

Of those 95, 41–or 43%–came around to score, and this doesn’t include leadoff HBPs or innings in which the lead off walk was forced at second, but the next runner came around to score.

Forty-three percent is, of course, much less than the oft-cited 60%, but I would include two caveats:

1) It’s still a very significant number, and
2) These are just the Yankee numbers for 2010–across a whole host of seasons or different teams, the number might be different. That said, the 2010 Yankees have one of the best offenses in baseball (with 679 runs, they’ve scored more than any other team in the league), so take that as you will.

If you’d like to know which leadoff walks did, in fact, come around to score, I jotted them down below:

You can find individual game logs here/

So yeah, don’t walk the lead off hitter.

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I’ve explained sabermetric concepts on this blog before. Some, such as leverage and WAR, can take a while to explain for the uninitiated.

Run expectancy, despite its fancy-sounding name, is not one of those things.

Run expectancy, as a concept, is one of the easiest to understand: given situation x, you may expect y runs to score. For example, with a man on first base and two outs in the inning, you can expect y numbers of runs to score.

The mathematically-inclined stats geeks (ie, not me), have done the actual, hard-core math, and found out the exact numbers.

They’ve done funky database things, and now you can go here, and then set your criteria, so you can figure out the run expectancy for whatever parameters you want to set.*

So if we leave it at the default for 2010, what the columns read, left to right are thus:

1) Year
2) How many men on base. “1″ means runner on first, “2″, runner on second, etc. A “0″ means no runner on that base.
3) Run expectancy with 0 outs
4) Run expectancy with 1 out
5) Run expectancy with 2 out.

The higher number, the more likely you’ll score a run.

As you would expect, with the bases loaded and no one out, you have the highest chance of scoring a run–in this case, 2.47 runs. The lowest expectancy comes with two outs and no one on base.

Really, you don’t need sabermetrics to understand that the more runners and fewer outs you have on base, the more likely you are to score runs. It’s really a very basic concept to understand.

Now, in terms of tonight’s game, we have the following set of data for the ninth inning:

1) With a runner on second, and no one out, the run expectancy is 1.11.
2) With a runner on third, and one out, the run expectancy drops to 0.927.

This isn’t exactly dropping off a cliff here, but when we’re dealing with numbers in these ranges, it is significant.

Now, if you’ll excuse me, we’re going to take a brief detour, but I promise I’ll get back to the point, quickly.

In baseball, there is no clock in the sense that we think of one–nothing ticking down, stopwatch-ing or otherwise counting to 0:00.

What you have, instead, are outs. These are precious commodities, things you guard with your life, like porn in a jail cell.

The entire premise of Moneyball, sabermetrics, and modern baseball statistical geekery, as relates to a team’s offense, is predicated on the notion that you never, ever, ever, ever give away an out.

So, then, understanding this, let’s get back to the issue for discussion here: bunting.

When Francisco Cervelli bunted with Canó on second base and no one out, he changed the run expectancy situation from #1 above to #2–that is, lessened the number of runs the Yankees could be expected to score.

Now, there is an argument–and a legitimate one–that you sacrifice the out to have Canó on third with less than two outs, because Thames, Miranda and Winn were on deck, who are, well, not the best hitters in the Yankee lineup. With Canó at third, he can score on a wild pitch, on a long fly ball or fortuitously placed ground out, lessening the necessity of Thames, Miranda or Winn to actually get a hit.

The problems, however are these:

1) Cervelli, thus far, has shown himself to be a decent, if lucky, hitter. Miranda and Winn are much more likely to make outs against Papelbon, if their current season statistics count for anything.

2) If Cervelli reaches, and there is still no one out (and Canó hasn’t scored, so a walk or an error or some such), then only one of Thames/Miranda/Winn would need to actually reach base to ensure, barring a double play, that Derek Jeter gets an at bat. I know I’ve been hard on Jeter as of late, but the top of the line up is what you want batting in the bottom of the ninth, not the bottom of the lineup.

3) The current pitcher, Jonathan Papelbon, had been able to successfully retire two of the last eight batters he faced. Which, you know, says that he wasn’t performing well and raises the likelihood Cervelli may have actually done something with the bat.

4) Giving up the out decreases the run expectancy, as stated above.

In The Book, Tom Tango and his co-authors argue that one should bunt more with low-OBP hitters on deck. In that case, Thames/Miranda/Winn certainly fill that category, as the bottom of the line up usually does, but it’s relative.

Thames/Miranda/Winn, whatever their faults, are not Peña/anyoneontheMarinersPiratesorAstros/pitcher. All three of the Yankees, not including last night’s game, have OBPs of .300 or over. No, that might not be sparkly, but it’s far shinier than what you’d expect from an NL ninth hitter–which is probably what Mr. Tango, et. al, had in mind when they wrote that passage.

So basically, if we want to keep it simple, we can sum up in this: by bunting, Cervelli decreased the number of runs the Yankees could expect to score in that situation, given the data thus far assembled for the 2010 season.

Outs are shiny, precious nuggets. They are Guttenberg Bibles, Tolkien manuscrips, Honus Wagner rookie cards, Mariner runs.

They are near and dear and the most valuable asset a baseball team has to work with.

They should be parted with willingly under no circumstance, while a baseball team is batting.

Francisco Cervelli should not have bunted.

*there is another table to look at here, and the entire article is worth a read, but their data comes from years past as opposed to this year.

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[All individual player stats are as of before today's game].

As of Cinco de Mayo 2010, the Yankees are eleven games over .500. They’re only a half game behind the Tampa Bay Rays, a team that’s prompted comments by the likes of Buster Olney about similarities to the 1998 Yankee squad.

Four of the Yankees’ five starters have ERAs under 3.00, and there had only be one game–one, out of 27 played–the entire season in which the Yankee offense has failed to score three or more runs. Only one starter not named Vazquez has a loss on his record–and that’s CC Sabathia.

Mix those two things together, and, injury concerns not withstanding, good things are probably going to happen.

Here, however, is the kicker: the Yankees are finding ways to win–pending the outcome of the Rays/Mariners game, the Yankees could end the evening in first place–and they are doing such while the 2-3-4 hitters in their lineup have an average OPS of .653.

For comparison’s sake, the Pittsburgh Pirates, a team that’s, as of this posting, scored 93 runs (the Yankees have scored 151) have a team OPS of .677. (Since you’re probably interested, Johnson, Teixeira and Rodriguez have combined to score 36 runs, not including today’s game.)

If we break it down individually, we can find the following:

Nick Johnson might only be batting on the interstates, but he has an on-base percentage near .400. He might not be tearing the cover off the ball (though this is exactly what he did in the first inning of today’s game, holy bejaysus that was a monster shot), but he’s not exactly making outs, either.

Johnson’s also been tremendously unlucky–with a BABIP of .182. There is almost no conceivable way he can remain that unlucky all season.

Mark Teixeira’s also been unlucky, but he hasn’t been unlucky, and while he is drawing some walks, it’s not nearly enough to make up for a batting average of .175 (just ask my fantasy team). However, slow starts for Teixeira are nothing new–thus far this season, Teixeira has had three multi-hit games; last season, on May 5th, Teixeira had had four.

Since Alex Rodriguez didn’t make his 2009 debut until May 8, it’s hard to compare his stats this year with those of last season, but here we may have the most cause for pause–he hasn’t hit a home run since April 20th at Oakland, no small thing since he’s the Yankees’ clean-up hitter, and since then he’s batted to a tune of .204/.226/.265/.492. That’s a slump if ever there was one.

Even so, there’s a very good reason to remain optimistic about Teixeira, A-Rod and Johnson: long histories of producing. Logic and statistics tell us that the three of them will recover and play to something more similar to the back of their baseball cards–we perhaps saw some of that with Johnson today.

When they do that, it’s entirely possible they take an offense already on pace to score 907 runs (they scored 915 last season) and turn it from being merely good into something bordering on historic.

At that point, the Yankees could very well be unstoppable.

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[Yes, it is very early in the season and unlikely that these stats will last...however, a full month, or 1/6th of the season, is not entirely insignificant]

1) After AJ Burnett’s great, eight strike-out, one run performance tonight, he now has a 1.99 ERA. This means the Yankees now have 2 starters with ERAs under 2, (Phil Hughes is at 1.44) and Pettitte is just over at 2.12.

This means that CC Sabathia, the Yankees’ number one starter, at 2.74 is the highest non-Vazquez ERA on the Yankee starting staff.

During the game today it was mentioned that the non-Vazquez starters’ combined ERA was 2.15; as Burnett pitched to a few batters after that, that number is lower (albeit probably only by a hundredth or two)

2) Two of the four lowest Yankee OPS’s belong to Mark Teixeira and Alex Rodriguez (.622 and .767, not counting tonight), the 2-3-4 hitters have a .661 OPS combined, and yet the Yankees have had just one game–out of 26 played–in which they have scored less than three runs, and just three when they have scored less than four.

3) Apparently, no one has told Francisco Cervelli that you’re not supposed to go from AA to the Major Leagues and all of a sudden become a better hitter at this level than the others.

Also, the catch he made over the dugout railing tonight was fantastic. Dreamy eyes of doom and all.

There is a lot you can say to qualify these–ie, about ERA being a bad stat and that Teixeira and Nick Johnson are having some really, really bad luck on the baseballs they do put in play–but for the moment, I’m just going to enjoy this.

It’s good to be a Yankee fan.

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Early season statistics can be funky.

For example, right now, the league leader in ERA is…Livan Hernandez? Huh? (Mike Pelfrey and Carlos Silva also make the top ten, along with the names you’d be more expectant to find there, such as Halladay, Lincecum, and Wainwright).

So, as I’m sure you, the astute fan you are, know that it’s not really a great idea to put too much into the early season leaderboard.

That said, when Andy Pettitte makes an appearance there, with an ERA of 1.29 after four starts and a WHIP of 1.07, you start to wonder: can this be a fluke? Or can this be like Cliff Lee in 2008 or Zack Greinke last season?

****

Going into this season, any Yankee fan worth his or her salt would have told you that the number one concern for this team was their dependence, still, on the “Core Four”, a quartet (Derek Jeter, Jorge Posada, Mariano Rivera and Andy Pettitte) that seems to have somehow gotten a hold of naked pictures of Father Time, or something. Year after year, writers and fans inscribe their doom; year after year, they like to prove us wrong.

Okay, so there are some signs that they may be slowing just a little, but the dramatic fall off and collapse many have predicted has never materialized.

In fact, switching Derek Jeter to the leadoff role last season seemed to spur a renaissance, and Mariano Rivera had the best season (thus far) of his career at the age of 38.

Given the hijinks of this quartet, then, is it really any surprise that Andy Pettitte is off to one of his best starts in career history?

****

The question, then, is thus: how can we tell if it will last? Logic tells us that there is no possible way Pettitte will end this season with an ERA of 1.29; experience tells us that with a member of the Core Four, anything, really, is possible.

For what it’s worth, there have only been two seasons in Pettitte’s career–two out of fourteen completed–where he has finished with an ERA under 3.00 (1997, and 2005 when he pitched for Houston), and only six where he has finished with an ERA under 4.00. This would seem to indicate that there’s no way Pettitte could maintain his start, but if that was the end-all of the argument, you wouldn’t be reading this.

The sabermatician in all of us knows that there’s really only two ways to figure out if Pettitte’s tremendous start is a fluke or not:

a) Watch all of his starts from now until the end of September and look at his final statistics, or
b) Look at his peripheral statistics.

So let’s start by analyzing the most basic of these.

Walks = good. Strikeouts = bad.

In Pettitte’s career, he has average 2.33 strike outs for every walk–while it’s always good to strike out more than one walks, Pettitte is hardly (nor has he ever been known as) a strikeout specialist.

In 2010 thus far, Pettitte has 22 strikeouts to 9 walks–a not-so-different ratio of 2.44.

What does this mean? Whatever the secret to his early season success, it’s not that he’s striking out any more batters.

Still, we’ve known for a while–since 1995, really–that Pettitte isn’t really a strikeout pitcher. That’s why the almost-no-hitter he had in Baltimore last year, the one where Hairston’s error caused him to lose a perfect game, was so weird. Out of all the starters on the Yankee staff, Andy Pettitte is the one guy you’d least expect to do it–he’s a “ground ball” pitcher, and as BABIP will tell you, sometimes balls get through.

Ground Ball pitchers may not have all the flash of the CC Sabathias or the Tim Lincecums, but they can be pretty effective in their own right when they’re on–ever watch Roy Halladay pitch?

Actually, one of the cool things about good ground ball pitchers is that since they can induce swings early in the count, they can keep their overall pitch count down. It’s certainly not the only reason, but it’s likely one of the reasons Halladay seems to pitch a complete game every single time he steps on the mound.

The converse, however, might be what we saw from Chien Ming Wang last season–when ground ball pitchers get hit, they can get hit hard. Pettitte’s not traditionally considered a sinkerballer in the way that Wang is; it’s perhaps less imperative for him to keep his pitches low than it is for Wang, but if Pettitte starts giving up lots of fly balls and home runs, there’s probably something wrong.

By now we’re pretty familiar: a hallmark Pettitte start involves some base hits, a couple double plays, and more likely than not, some sort of caught stealing or successful pickoff.

ANYWAY, the point here, is that just as for some pitchers we look at strikeout-to-walk ratios, with Pettitte, we need to look at groundball-flyball ratios as well.

Our friends at Fangraphs tell us that, career wise, Pettitte pitches to a tune of a 49% groundball percentage (for comparison, Javier Vazquez is at 39% ).

Fangraphs has yet to update with today’s start, but through three starts in 2010, Pettitte’s groundball rate was…dun dun dun…48%.

So, once again, we have a peripheral statistic that’s pretty much in line with his career norms.

Where, then, is the difference? Pettitte’s career norms aren’t that of someone who pitches to a 1.29 ERA, so something’s gotta be going on, right?

Right.

This is where we take a journey over to the BABIP column. As many of you will know, batting average on balls in play is basically an indicator that tells us how often batted balls “find holes” or otherwise eschew fielders. It’s basically a measure of luck–though maybe (and I stress maybe here) someone could find a way to include BABIP in an analysis of a team’s defense.

A normal-ish BABIP is about .300. For his career, Pettitte’s BABIP is .315. Through three starts, as Fangraphs lists it, Pettitte’s BABIP is .260.

Simply put, then, either Pettitte is getting some really, beyond-the-pale help from his defense, or he’s just been pretty darn lucky.

This doesn’t mean Pettitte’s pitched poorly (so don’t fret); just that a season long ERA of 1.29 is probably unsustainable.

Thus far, if we’re to be encouraged by anything, it should be that Pettitte’s given the Yankees four quality starts by the standard definition (6 IP with 3 ER or less), and that in each of his past two starts, he’s given the Yankees eight innings. In fact, I’m personally encouraged that Pettitte’s worked deep into his most recent games considering that due to the weather deities, he didn’t pitch nearly as much as he would have otherwise during Spring Training.

So, there will probably be a clunker in the near future, but even if Pettitte only pitches to his career norms, that should suit the Yankees just fine.

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And those who have their noses pressed against their computer screens and think VORP is a valid means of measuring a player’s performance ought to get a life and a credential that would allow them to see and hear the game up close. Then determine the players whose numbers actually contribute to winning and those who are equipped only add the next run in a 15-3 game.

–Marty Noble, here

There is, of course, an obligatory joke here about Mr. Noble being a Mets beat writer and the inability of anything or anyone associated with the Mets to, you know, get it, but in the interest of good sportsmanship I’ll let it pass.

So now, of course, being the blogging nerd he’s so desperately railing against, where do I start?

How about this:  where is it written, in the grand constitution of baseball rules and by-laws, that one would have to actually have a clubhouse credential to be able to see a game?

I assume that it’s not me, that when I pay for my ticket, or even when I tune into YES or FOX or ESPN or whomever, that when I see the game being played, I am, in fact watching the same game that Mr. High-and-Mighty is watching from the press box.

Look, there’s one thing, and one thing only that a clubhouse credential actually gets you:  access to players, coaches and staff.  It’s a pretty big thing, I will admit–access means you get to do the breaking of the news, that you get a feel for the players and staff as people, and that sort of thing helps when you’re writing a story.

The credential, however, does not change the game that’s played on the field.  It doesn’t change how good or bad a player is, and it doesn’t on its own bestow any sort of enlightenment.

That enlightenment–that ability to discern good player from poor–that comes from watching the game on the field, and it comes from the ability to balance first-hand viewing (through whatever medium one so chooses) with the information one can gleam from the box score, and, yes, the advanced metrics.  You should not have to be able to calculate WAR or FIP if you’re not a GM’s assistant (they pay people to do that for you), but having the numbers to back up while Mariano Rivera is more valuable than Jonathan Albaladejo should matter.

Now, here I hate to generalize–I know some sportswriters to whom this would not be applicable–but in Mr. Noble’s case there seems to be an instance in which the credential is seen as this all-powerful document that grants legitimacy to a few and keeps out the masses.  A case of “I have a credential, thus I know what I am talking about and you do not.”  Or, in simpler terms, it’s a case of “I’m better than you.”

This is, of course, not true.

In fact, I could argue that the best analysis (and here we are talking about analyzing criteria and ascertaining whether player X or Y should enter the Hall of Fame, and not waxing poetic about our favorite athletes for a human interest, Bob Costas-laden special) comes not from the credentialed beat guys, but from those basement-living bloggers Mr. Noble so rails against.  Now, of course, there are plenty of credentialed writers who have an excellent analytical mind, but it would seem that Mr. Noble has yet to access his.

Instead, what we are left with is yet another instance of a holier-than-thou bias, as though Joe fan is utterly insginificant.

Look, I don’t want to suggest that actually seeing a player is not important.  It is, especially when it comes to scouting.

When it comes to the Hall of Fame, however, I’m a little more skeptical.  I mean, for one, Ty Cobb’s in the Halll and many consider him to have been, well, if you pardon my language, a racist asshole who was not above hitting women, either.  The thing is, Cobb was also a damn good baseball player, and that should be the primary criteria.

It’s the Hall of Fame–not the Hall of Saints.

Yet Mr. Noble would have us believe that only credentialed reporters are capable of understanding who deserves to go to the Hall of Fame and who does not, because it is apparently impossible to objectively quantify how good a player is in baseball.

Never mind the fact that Moneyball* has been a best-seller because it proves exactly the  opposite.  (Not just Moneyball, but The Numbers Game, which is better, should be considered too.  Oh, and then there’s this thing called Baseball Prospectus…)

Yeah, I wish I had a press credential.  For one thing, it would mean that I might actually get paid (albeit a pittance) to write about baseball, but as far as I understand it, a home run hit by Derek Jeter on my TV doesn’t become a home run hit by Alex Rodriguez just because someone has a press credential.

If a player’s statistics show that he’s one of the best second basemen of all time, he should be in the Hall of Fame.

Most fans understand this.  Maybe, someday, the writers will, too.

*I have certain issues with Moneyball I may or may not remark on at a later date.

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Please see Part I for acknowledgments.

Hey, so now that I’ve missed the last 100 years or so, what’d I miss?

Anyway, here’s what we’ve got in terms of a final tally:

This will give us our totals:

PREWAR:                                 4.17
CONVERTED PREWAR:   24.016
Now, before we can go into what this data actually means, we need a couple of notes:

1)  The data is slightly skewed because of the years in which the Yankees lost in the first round of the postseason.  Just look at how much lower the numbers are for 2002, 2005, 2006 and 2007 to get an idea.

2) The Sandy Alomar Jr home run in 1997 kills Mariano’s PREWAR.  For comparison’s sake:  in 1997, Mariano’s postseason FIP was over 8.6(!)  In 2003, his best postseason (and it’s not even close), the number is 1.28.

Okay, so now that we’ve cleared that up, go pour yourself a nice glass of wine as we discuss what the numbers mean.

The raw, unconverted PREWAR figure is 4.17, so let’s do that one first.

The unconverted number says that Mariano is worth over four wins in the postseason–the equivalent of one round, all by his lonesome self–but there’s a caveat here.

The raw numbers here measure a win as having the same value as a win during the regular season–ie, one win in 162 games.  In the postseason, one win is worth a lot more.  Since Mariano pitches relief innings only, his innings totals in the postseason are thus supressed–he’s never thrown more than 16 innings in a postseason–which in turns suppresses the value for WAR.

Now, the raw PREWAR numbers are useful, but they will be most useful when we can compare them to other postseason relievers–this is the epilogue post that you will see following this one, which, if I can figure out how to make one, will have a nice shiny graph.

Anyway, enough with the digressing.

So what we want to do here, then, is to convert Mariano’s PREWAR numbers to a number that would be representative to what Mariano would be worth if he pitched at the same scale in the regular season.

The conversion has been done in the table above, but just a refresher:  to convert the numbers using the Magical Calculator Thingy, you change the input for Innings Pitched to 70, which is roughly what a closer would pitch over a full season (since becoming a full-time closer, Mariano has pitched between 60 and 80 innings per year, so this number actually works very well).

When we total up the CONVERTED PREWAR numbers, we get 24.016.

That would be, then, 24 wins.

Now, let’s go back and remember our very basic assumption, that it takes eleven wins to win a Championship.

Twenty four divided by 11 is, of course, just over two.

This means, adjusted to a regular-season scale, the Yankees have won two of their last five World Series, potentially for no other reason than that Mariano Rivera, and not another closer, was on the mound in the ninth inning.

Every time we go and we think that Rivera is the Hammer of God,  something else comes around to show us that he’s even greater…

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Please see Part I for acknowledgments.

Let’s start with the 2009 postseason.

We take the Magic Calculator Thingy and input the following:

Innings pitched: 16.
Fangraphs’ FIP: 2.28

Next, we go to Baseball Reference and click on the ‘postseason’ tab. We look at every box score of every postseason game and add up every single run.

ESPN also has run totals here, per team, but they only go back to 2002 and we will need to (eventually) go all the way back to 1995, so knowing how to do it just looking at the BR box scores is of some use.

That gives us a total of 260 runs scored.

We then add up the total number of games played–13 in the division series (three 3-game sets, one four gamer), 11 in the League Championship Series (six and five) and six in the World Series, for a total of thirty games played.

We divide 260/30 to get a total of 8.66 runs scored per game, and we divide that by two again and get a total of 4.33 runs scored per team on average.

Whew.

We’ve got our first three variables, the fourth, park factor, has been preset at 0.975, so now we just need the fifth, the leverage index.

We’re going to use gmLI, because that’s the leverage index that gives us an average leverage number for when a pitcher enters a game, and, well, Mariano loves him some high leverage.

As we journey back to Fangraphs, we find a gmLI of 1.45, but don’t enter that in just yet. As discussed above, we need to modify it a little bit.

We do this by adding one (1.00, a neutral leverage) and then splitting the sum. That gives us our split leverage of 1.225.

NOTE: Postseason gmLI has only been calculated for the 2002 postseason onwards.  To get Mariano’s PREWARs for the years before, the regular season gmLIs will be used, minus .44–which is the average difference between regular season gmLIs and postseason gmLIs taken from the years 2002-2009.  It should be noted, however, that this figure is slightly skewed by the years in which Rivera appeared in just one postseason inning (mid 00s are chock full of these), and that the actual postseason leverage is probably a tad higher.

So we take our variables, enter them into the Magical Calculator, bada bing, bada boom, we come out with 0.542 PREWAR for the 2009 postseason.

WAIT! You say, how do you know that it works?

It’s pretty simple–plug in the values for the regular season (which uses pLI), and compare the results to the WAR listed on the Fangraphs’ leaderboard. Since those numbers are equal, we can assume they are correct and thus proceed.

So we have our 0.542 PREWAR. How does that compare to regular season WAR?

We change the IP from 16 to 70, or roughly a closer’s regular season innings, and get a result of 2.37, which is better than Mariano’s 2009 regular season WAR, though less than his 3.1 WAR in 2008 (3.1 is an utterly monstrous number for a reliever, even a closer, and Mariano’s 2008 was that good).

Anyway, so, in our PREWAR spreadsheet, we can fill in our first three columns, under the columns “year”, “PREWAR” and “converted PREWAR”.

2009: 0.542, 2.37

Now, it’s a question of doing the same for every postseason from 1995 onwards, with the exception of 2008, because the Yankees weren’t in it, and 2009, because, well, we just did that.

I’ll see you all some time next century.

****

Or at 4 PM.

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Please see Part I for acknowledgments.

Back? Good.

So what do we have so far?

1) We’re attempting to figure out Mariano’s WAR for his postseason innings and then convert that to the number of championships Mariano is worth all by his lonesome.
2) We’ve explained the theory behind WAR and replacement level (though we haven’t gotten into the nitty gritty just yet)
3) We’ve discussed why it’s still all about the leverage, how really smart people have come up with absolute numbers for every conceivable innings-baserunners-outs situation, and how WPA, while shiny and a fun toy, is not as helpful as we would like because it’s a probability stat more than an absolute number.

Fortunately for us, since Fangraphs provides us with LI numbers, it’ll save us a bit of work.

The other key component of WAR is FIP, or fielding-independent pitching. The goal of FIP is simple: figure out how well a pitcher pitches in terms of events that are not dependent on the fielders–strikeouts, walks and home runs.

A little more advanced: the theory here is that things such as singles, doubles and triples, may be affected as much by the way the fielders play as by the way the pitcher pitches. The only events a pitcher directly controls occur when a batter does not make contact with the baseball, or when he hits a home run. Basically, all or nothing.

The formula provided by Beyond the Box Score for FIP is:

(HR*13+(BB+HBP-IBB)*3-K*2)/IP.

This formula will give you an odd looking decimal result; generally speaking you add 3.20 to it to get the FIP.

A note of caution: I was never able to get the formula to add up to the same results given by Fangraphs; since different sources do use different formulas (some don’t account for hit-by-pitches, some don’t account for intentional walks, etc), I’m going to attribute the difference to using a different formula than Fangraphs–since my results were generally close.

What we need to do, then, is to figure out the WAR numbers.

Let me state this as simply as I can: I have no issue understanding the theory behind WAR, as hopefully I have successfully explained above; however, WAR is a very complex calculation that is way beyond the scope of my doing. Fangraphs and Beyond the Box Score give formulas as to how to calculate them for pitchers here and here , but the problem is that every time I tried doing the formula myself, I’d end up with very, very wacky numbers.

Like, 74.

I know Mo’s the Hammer of God, and all, but even the Hammer of God isn’t worth 74 wins all by his lonesome.

To make a very long and frustrating story short, I was saved by an Angel of Mercy (who has asked their identity not be revealed–which, alas, means no revelation of formula. Don’t worry, though, I still can’t figure it out). Said AoM sent me a magical calculator thingy (okay, a spreadsheet), and, well, now it’s just a question of doing the following:

1) Calculating Mo’s WAR for each of his postseasons
2) Adding the totals together.
3) Converting them to a scale that will allow us to compare what he’s done in the postseason with what he’s done in the regular season.

Simple, right?

Alas, this is the part that is incredibly time-consuming.

WAR involves constants in their formulas that change from year to year, and since Mo’s been pitching in postseasons since 1995, that’s a lot of constants to go back and find.

Anyway, before I go into the hard data and the results I got, here are a couple of caveats–so if you want to try this on your own (masochist!), you might choose to adjust accordingly. I’d recommend that if you try (masochist), you use the link to the Fangraphs explanation, which calculates WAR for Felix Hernandez from scratch. The theory’s easy to follow, but because there are so many components to it, just one not-so-hot constant can throw it off. This is, of course, why they pay people to do these things.

1) We need to understand park factors, but this is a simple concept.  Some ballparks favor pitchers and some favor hitters; the park factor is simply a number that attempts to describe whether a ballpark favors hitters or pitchers.  The park factor used for 2009 is 0.975, which would make Yankee Stadium (and here you will laugh) a slight pitcher’s park–A neutral park that favors neither pitchers nor hitters will have a park factor of 1. What’s that you say? That can’t be right?

Well…yes. And no.

ESPN has a handy-dandy Park Factor sheet. Now you’ll see for 2009 the New Yankee Stadium is actually middle of the pack and registers 0.965. So why increase it to 0.975? New Yankee Stadium has only been around a year, which is a very small sample size.  The extra 0.010…let’s just say it’s a nod to all those home runs.

For all the years before 2009, I took an average of park factors from 2001 to 2008 and came up with 0.962.  Don’t worry–2005 had a park factor of 1.4+, but this was balanced by an absurdly low 2004.  Our 0.962 constant is really right there in the median.

(Going backwards, the numbers we use are 1.040+0.987+0.877+1.403+0.694+0.933+0.957+0.805)

2) The leverage used is a modified gmLi (see above) that gives the pitcher some credit for the leverage of his situation, but not all–basically it says that it’s not Mo’s fault that Brian Bruney left the bases chucked with no one out, but if Mo puts his own runners on base and then lets them score, he’s gotta be accountable for that, too.

3) The FIP stats are from Fangraphs.

4) As for the constants in the formulas? People get paid to figure those things out. I rely on the AoM’s Magical Calculator Thingy.

So how does one use the Magical Calculator Thingy?

One needs five pieces of data:

1) The pitcher’s FIP,
2) The league’s RA (this is the average runs per game per team. Here we’re going to use the postseason).
3) The park factor-we’re using the 0.975 constant for 2009 and the average of 0.962 for every other year.
4) The pitcher’s innings pitched.
5) The modified gmLI

Since numbers 1, 2, 4 and 4 will change season to season, the calculations have to be done separately for each season.  Depending on the park factor you use, this number can also vary.

As I’ve said before, calculating FIP is itself complex, but we can cheat and just look at advanced pitching stats from Fangraphs. Like many of the advanced stats, can use various formulas depending on the publication you are reading.

Anyway, the bottom line here is that we use Fangraphs’ Data because super smart people have already done this for us.

Doing the RA isn’t hard, but it IS tedious.

RA is simple–it’s just the total runs scored, divided by games played, and then divided again so you get an average runs scored per team. This takes into account all runs, not just earned runs–since earned runs are a somewhat sketchy stat. It’s easy enough to find the RAs for a particular season, since ESPN handily lists average runs at its stat page, but the numbers haven’t been done for the postseason.

What does this mean?

We’ve got to total every run scored by every team in every game in the ALDS, NLDS, ALCS, NLCS and World Series, and then divide that by the total games played in the postseason, and then divide again to get the number per team. Normally you just used it for the AL or the NL, but I like to consider the postseason a league in its own right.

Again, this isn’t hard, it’s just tedious.

Innings Pitched–this one’s easy. Google “mariano rivera stats” and click on any of the links. Since WAR is heavily dependent on innings pitched in terms of value, relievers’ PREWAR (postseason reliever WAR, don’t look at me like that, I just think it sounds cool) will be low–anything over 1 being positively insane.

To compare it to what a WAR would be at the same FIP over a full season, we’ll also plug in the numbers not just for postseason IP, but also for 70 IP, which is about what a closer will pitch over a full season.  This will give us an idea of how valuable Mariano would be if he pitched at that same level over the course of a regular season (I’ve explained it more after we get our results).

When we get our numbers and we’re doing our aggregate totals, we’ll use both the PREWAR numbers and the converted PREWAR numbers, so if you want to try some fancy stats work on your own, you can go right ahead and do so.

So, let’s get to the nitty-gritty.

Well.  In a litle bit.  Check back at 2 PM…

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Special acknowledgement: This is far and away the most advanced, in depth thing I’ve ever tried. Without question, the best similarity I can come up with is asking someone who’s taken only high school Economics course to run the IMF, that’s basically what’s happened. As with any such endeavor, most of the actual work was done by others. With thanks to Jonathan Mayo, Will Moller, Joe Pawlikowski, Mike Axisa, Jim Johnson, Jamal Granger, Dave Cameron, Brent Nycz, Joshua Rosenberg, Dan Dilworth and Greg Fertel

This started out as one post but quickly got so big that it would not be fair to make you sit through all of it at once. It will thus be serialized, and as I do so, I will provide links back and forth. I’d provide a better introduction, but I’ve got to go scrape brains off the wall.

In this article, which is worth your time, Rob Neyer dares us to come up with a way to measure how many Championships Mariano has been worth.

Guess who enjoys masochism?

So, as you may know, there’s a myriad of stats out there, many of which I can only understand in theory, but there’s one measure that’s been created for the regular season that is very useful. You may have heard of it, as it’s called WAR–wins above replacement player.

NOTE: There are two measures we could use here, WAR and WARP, which try to accomplish the same thing (discussed below), but use two different sets of stats/data to do so. I’m going to stick with WAR because I think it sounds cooler. ANYWAY. So to understand WAR, two concepts are crucial: replacement level and leverage.

I understand that many of you reading this will already be familiar with both of these, but since my hope is that those that don’t delve into stats very often can follow, and for the sake of my sanity, hope you won’t begrudge me a refresher.

Just so you know where I’m coming from, I haven’t done proper math since I was 16/17, so anything you see is going to be pretty easy to understand.

ANYWAY, again. What’s with the digression, Rebecca? So Replacement Level. The idea behind replacement level is that you take any player in any line up on any given day and replace him with someone whose level of performance is what an average team can expect when trying to replace a player at minimal cost. In English, it’s saying that if, say, Andrew McCutchen went down on the Pirates with the flu, what’s the baseline production that the Pirates could expect from John Doe, who’s the cheapest available player to fill the spot? That production is replacement-level production.

Why not just use a league-average performance as a replacement? The answer is that the MLB statistics are largely skewed–MLB “regulars”, the guys putting up the big enough numbers to stay in lineups every day are a minority–while fringe players, those that struggle to stay in the big leagues, are much more common. Simply put, it’s easier to find a player that hits .250 than one that hits .330, but, like that student you wanted to kill because he got an A on that Spanish test while no one else did above a C, the one that hits .330 destroys the curve.

So, instead, you take into consideration what a GM and manager is likely to go for in the event of a player suddenly going down for a game or two–ie, your utility infielder. Most teams–and the Yankees, of course, are not most teams–will go for whatever option is least costly–dipping into the pool of fringe Major Leaguers, the pool considered “freely available talent”. Of course, if a player is lost for a season, it’s an entirely different thing, but that gets beyond our scope.

What you end up with is on one end, you have your normal team–say the 2009 Yankees, and on the other, replacement-level team you’ve a line up where Wil Nieves is your best hitter, or Sidney Ponson as your best pitcher. What WAR does, then, is like having Nick Swisher go up to Joe Girardi before game six, and say, “Dude, I gave the Yanks, like x number more wins this season than you would have if Jerry Hairston had been your every day right fielder.”

(Note: via fangraphs, Hairston’s 2009 registered a WAR of 1.0, which indicates he performed above replacement level. Actually, this is helpful to give you an idea of how poorly a team with all replacement-level players would perform over the course of a season. Replacement Level is not the bench guys on the Yankees; it’s the bench guys on the Nationals and the Pirates.)

So before we move on, let’s make sure we–okay, I–understand everything we’ve discussed:
1) The concept of Replacement Level enables us to compare performances of MLB “regulars” vs low-cost, “freely-available” replacement players.
2) WAR is designed to measure how many more wins player X will net his team over player Replacement Level (ie, our Swisher/Hairston faux metaphor).
3) The values set for what a RL-performance entails varies by position–ie, shortstops aren’t supposed to hit like right fielders, etc. Pitchers, too, have WAR. Over here you can see the rankings for pitchers, by WAR, for the 2009 season. To no one’s surprise, Zack Grienke tops the list. The type of season he had will do that to you.

Now here, what we want to do is find the WAR for only Mo’s postseason innings, and then convert that to Championships–one championship being eleven wins. A reliever’s WAR is likely to be lower than a starter’s because a reliever pitches so many fewer innings–and innings pitched/endurance is a relevant stat–ie, when you’re looking for “innings-eaters” and the like, that’s to what you are referring.

That said, a reliever’s innings–especially a closer’s–are often more high stress and involve more critical game situations. So what we need, then, is a way to account for leverage–which is one of the main components of a reliever’s WAR. You’ve seen leverage stats before–just think about those WPA graphs you see. This is the WPA graph from Game Six of the World Series: .

Game Six doesn’t exactly have a ton of high leverage situations–the Yankees took a lead fairly early and then built on it, eventually leading 7-1 and the game never being in much doubt. Many times when a reliever comes in, that line (there’s a technical term for it, of course, that went out my head the day the bell rung in 7th grade) is closer to the middle.

To explain further: the closer to the top or bottom of the graph that the line gets, the more in favor the outcome of a game is for a particular team. For example, in this game, we see the line go more and more towards the top of the graph–and on the side you see the top half labeled as “Yankees”. So the more this game went on, the more in favor of the Yankees it was–80% and then 90%, etc. Many times when a reliever comes in, that line is closer to the middle, not pointing decidedly towards either team, and the bars on the bottom of the graph give you an indication as to how important that particular situation in the game is–the higher the bar, the more critical the situation.

Now here’s where, depending on your outlook, things get really cool or, if you’re me, your head explodes: you can calculate WPA with “series probability added”–which would mean the probability that takes into account the current situation in a series–ie, are the Yankees up 3-1, down 1-2, tied with the Phillies or something else? Without going into specifics for the moment, this is a pretty simple concept–the deeper into a series you go, the more high leverage each at bat becomes.

Think about it this way: in 2004, before Roberts steals second, the Yankees are up 3-0 in the series and up in that game. The likelihood they’re going to win–only a few outs away from the World Series–is probably around, say 90% (this is a total guess, but you can probably find the data somewhere) for the game–and probably the series too.

Now, move forward a few days and it’s game seven, and things have changed drastically–the series is now 3-3, and thus every pitch thrown matters that much more, every at bat that much more high leverage. Of course, there was that early Damon grand slam, and whatnot, but, yet again, I digress.

What does all this matter? It comes down to this: you cannot accurately measure a reliever’s WAR, especially a postseason WAR, without taking into account the leverage situations in which they pitch.

Now, of course, the question is: how do we do this? Some suggest that we use WPA–win probability added–but there are problems with this. WPA is a team-oriented stat at it’s core, and the idea is to measure how much more likely a team is to win a game given a certain event, and it’s so dependent on leverage that it’s not a decent measure of raw talent. Read up for more info. I especially recommend clicking on the link to The Hardball Times that explains how WPA is more about a “feeling” than anything concrete That said, WPA stats do exist for individual players–the link in the paragraph above puts it much more succinctly than I can while running on three hours’ sleep.

Now, here’s where it gets really cool: the Leverage Index on which WPA is based is not an abstract concept; it’s based on real numbers. I direct you to this article from The Hardball Times that explains the math (ie, goes mostly way over my head), and then, the shiny finished product, the chart of Leverage Index, which has the actual numbers.

Take that in for a minute.

We can find out, for any team, any inning and any situation–men on base and number of outs–exactly how much more or less likely that team is to win the game, and how important that particular situation is.

For individual pitchers (since we’re dealing with pitchers), we can also calculate their average leverage index based on a) a player’s LI for all game situations (pLI), b) A pitcher’s LI for when he enters the game–as in a reliever that enters the game in the seventh, etc. (gmLI), c) A pitcher’s LI based on the inning in which he enters (inLI) and d) a pitcher’s LI when he leaves the game (exLI).

If you go back to this chart, you can see Rivera’s average numbers for these situations. For comparison’s sake, here are Ryan Madson’s numbers of the same. As you can see, the leverage situations in which the pitchers enter is roughly the same–they’re both back-end relievers pitching the most or some of the most critical innings for their teams–but that the WPAs are different.

Pitchers can’t control the leverage when they enter a game, but the leverage is a good indicator of the stress a pitcher might face coming in to relieve and how that pitcher responds to it is perhaps most valuable as a measure to determine how composed a pitcher remains in a tight spot. Hence our need for the Leverage Index.

Okay, so I realize my head might explode from all this, so take a break, get a snack, do some processing and come back here when you’re good to go.

(or, you know, at noon, when I post the next part).

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