THE BOOK--Playing The Percentages In Baseball

We missed you over at the blog tonight.

You may have overlooked the biggest mistake. Girardi was going to use Phil Coke to pitch the ninth, instead of Rivera, if the game was still tied.

I cannot enjoy a game while blogging.  Too old to do 2 things at once.

Can’t comment on a mistake that never happened!

Is there any positive side to McCarver?  At one point he wanted to use the re-sub rule from Junior Legion and bring Joba back into the game after Hideki PH’d for him.  If Tim says a pitcher “has” to throw a certain pitch, he almost certainly is not throwing that.  And to top off my list of complaints, Johnny Damon reaching 3rd is not why Brad Lidge threw a fastball to A Rod.  Please don’t congratulate Johnny Damon for A Rod’s hit.

MGL: Pitch F/X has Joba averaging 95.2 with his fastball since moving back to the bullpen, so 95-96 is nothing new for him in the playoffs.

#4, hmmm.  What did pitch f/x have Joba tonight?  I could have sworn that the entire post-season the TV gun had him at around 92-93 and tonight the TV gun had him at 95-96.

I’m starting to really not trust either my memory, pitch f/x or the TV gun.

I did look at the last 3 games for Joba on Gameday.  He averaged 94.75.  Tonight, he averaged 95.6.  Both are small samples of course, so they are probably functionally equivalent.

MGL: “Can’t comment on a mistake that never happened!”

Why not?  You did that with rumor that Girardi would paly Matsui in the outfield. 

#7, you got me.  Of course your best pitcher should be brought immediately into a tie game in extras even if you are the road team, otherwise there is a 50% chance he doesn’t get to pitch. Plus, that way you get to use him for 2 innings if you want or if he has a quick one inning.

#3, 95% (or 99% maybe) of the people who listen to the broadcast on TV don’t know whether McCarver is good, bad, or indifferent.  As long as an analyst has a good voice and sounds like he knows what he is talking about, even if he doesn’t, and gets along well with the play-by-play guy, he is fine for the job.  It is not like the guys who hire him know anything about analyzing baseball either - they don’t.  And it’s not like the network is receiving thousands of letters a day telling them how bad McCarver is.  No matter who was on the broadcast, there would some percentage of people who would hate them for whatever reason.  If I were doing the analysis on TV, even though I would actually know what I was talking about, a legion of people would hate me too and there would probably soon be a website, FMGL.com (no comments please).  You can never please everyone.  Don’t ever confuse unpopularity among some group of people with unpopularity with a majority of the people or even a large group of people.  Don’t confuse unpopularity among a group of people with incompetence either.  There is always someone who thinks that someone else is incompetent, whether they are or they aren’t.  The job of a sports broadcaster is not to educate the listeners.  Who cares about that?  The only people that care about that don’t need to be educated.  The broadcaster would be preaching for the choir.  The job of a broadcaster, even the analyst (as opposed to the play-by-play guy) is to entertain and make the average fan think that they are being educated.  All of these guys, McCarver, Morgan, Buck Martinez, etc., do just that or else they wouldn’t have a job.  To a very, very small majority of ultra-knowledgeable baseball fans, these guys are atrocious.  But they really are a very, very small percentage of the listeners.

I have a lot of issues here with your criticisms although we can both agree that Girardi isn’t a spectacular manager.

First, there’s the point you made about Sabathia and bunting. One thing you didn’t factor in was the hefty amount of times that CC will GDP. Unfortunately, we have to deal with a small sample size but Sabathia has GDP’d 5 times in 18 opportunities (28%) and 3.15 GO/AO. So, it’s highly likely that if Sabathia doesn’t strike out and doesn’t get a hit, he’s probably going to GDP.

Second, there’s the theory of replacing Sabathia with a PHer costing 0.1 runs. Are you factoring in that Sabathia is a better hitter than a typical pitcher? Or do you only do that when it helps your argument like in the anti-bunting CC one? Not really trying to be condescending here but there’s really no way to pose that without doing so since it seems like an obviously intentional deletion since you don’t seem like an unintelligent person.

Anyway, Sabathia has a .286 career wOBA compared to Matsui who is .367. But we have to penalize Matsui about 21 wOBA for being a PHer. That is worth about 0.052 runs or so… not 0.1, right?

But then we have to factor in later, in a much higher leverage situation, we have burned through Matsui and are forced to use Hairston or Hinkse. Hairston carries a career wOBA of .313, Hinske is .337 and in this PH role both carry the .021 wOBA penalty, also. Figuring there is 0 chance a reliever bats there, it’s probably best to chalk this up as:

REALITY - Sabathia (.286) + Matsui (.367-.021)

vs.

THEORY - Matsui (.367-.021) + Hairston (.313-.021) / Hinske (.337-.021)

Basically, in theory, it’s an upgrade of Hairston or Hinske over Sabathia, not really Matsui… unless, of course, Girardi goes to Hairston or Hinske which is much less than a 0.05 cost in runs.

In theory, this is an upgrade… but not as much as the 0.1 runs you are calling for. Theoretically, that later PH where Matsui is not available in the 9th inning of a tie game is a much more valuable PA than the early Matsui PA, right?

And each PHer following would be a downgrade… I’m not one to play for events that may never happen but I know you often use that in your theories on building lineups so you might.

So, not only is the cost of Sabathia less than 0.1 runs, down the road that decision tempers the improvement you earn from a PHer for a reliever.

Essentially, if we settle on the cost being 0.05 runs, PHing for Sabathia gets you a run every 20 PAs. The Phillies are still going to win 18.5% of the time at this juncture which means that there’s a strong likelihood that they will make this is a close game at least 4 or 5 times out of those 20 games. So, 4 or 5 times, more PHers in much higher leverage situations are likely to come into play, right?

On the surface, this seems barely break even. Digging makes me wonder if this is the strategic equivalent of using a winning checkers strategy to play chess.

Well, you have to regress Sabathia’s batting numbers (less than 100 PA sample size), and there’s the issue of present vs. future value that I can’t quantify. It would probably be something like each future pinch hitter is worth a fraction of his value based on the probable future, considering WE and expected future PH’ers.

Except that (and I’m stunned MGL didn’t mention this) we shouldn’t be using CC’s career wOBA as a judge of his true talent level, but regressing it rather heavily toward the mean (AL?) pitcher.  It’s something like ninety-one at bats.  CC’s probably somewhat better than average, just on the fact that he knows how to swing the bat, but he’s hasn’t hit much in his career, and he’s hitting for the first time in four months.  We shouldn’t be basing anything off of his career numbers, and we certainly shouldn’t be basing anything off of his career GIDP rate.

Completely agree on the short-leash comment.  What I said at the time was “two feet in either direction, and Victorino’s on second while CC’s in the shower.” Not sure what the logical reason for leaving the guy in there is when he’s pretty clearly tiring and just had the last two batters drill his offerings.  Girardi deserved the Utley home run for not going to Marte right there.

Upon further review, all MGL said was that CC is a good hitting pitcher - it was #9 who supplied the numbers.  Still, I’m not sure that’s a conclusion we can necessarily draw - Shane Spencer looked like a pretty good hitter in September of ‘98.

MGL, astute comment about broadcasters. From the network’s point of view, they’re entertainers and just about the only thing that will get them fired is if the network concludes that they’re having a negative impact on ratings.

I think your item “4” is a bit harsh. Isn’t “Not necessarily” the kind of non informative, non commital response you would want to give?

Other good choices would be “it depends on the game situation”, “we’ll see what happens” or “we’ll do what we think gives us the best chance to win” (my personal favorite).

#3 is the one I was most surprised by.  3 days rest, coming up on 100 pitches, tough hitters coming up.  Yeah, I’d have pinch hit Matsui there.  That could have cost them the game (if Brad Lidge was any good).  I first-guessed that one from my couch. 

Joba did have a little something extra last night.  He looked good until Feliz took that something extra and sent it over the wall.

#14, I think he was calling McCarver the idiot for thinking Girardi would divulge a tactic, not Girardi for giving the non-committal answer.

Unbelievable how some people think they are “smarter” than major league players just because they use percentages. Numbers will always be flawed, because you can never account for everything. They are merely there to provide some perspective. Does pinch hitting for Sabathia really make a difference of .1 runs? Absolutely not, there are so many external factors that aren’t being considered, that you would have to question the intelligence of someone who 100% belives that silly number.

Anyone who knows baseball would know that you don’t pinch hit for CC after hes only pitched 6 innings. You really don’t need to create a formula to make that decision for you. Maybe if you ever came up with a mental, or a common sense statistic, then we can take this a little more seriously.

Now, continue believing that you can solve everything with percentages, and that you are smarter than people who have actually played the game......

Most people here have actually played the game.  That’s why we all come here to discuss baseball.

Brian C, is that sarcasm or trolling?  Hard to tell this early in the morning.  It’s common sense, and I don’t need MGL to run the numbers for me, to PH for Sabathia in a situation where he has at most one more inning to give you, and is on a short leash anyway (since he came out as soon as he allowed a hit).

An additional factor to consider here is that if the series goes 7 games, Sabathia will be on short rest again.  So you don’t want to push him too far here.

First of all, Brian C., there’s no way you are a real person.  Your post is mglbait if I’ve ever seen it. 

Is there any research out there about a pitcher’s velocity (against his own average) vs. effectiveness?  I can’t find any, so I’m going to try to have a look at whether pitchers have better results when they’ve got better velocity, since it’s come up several times now.  Hopefully by Wednesday.

"It’s common sense, and I don’t need MGL to run the numbers for me, to PH for Sabathia in a situation where he has at most one more inning to give you, and is on a short leash anyway (since he came out as soon as he allowed a hit).”

No its not common sense, your “feel” for the yankee bullpen isn’t even in the same ballpark as joe girardi.

You have no idea what CC’s mindset is, nor do you know how his arm feels.

If your “numbers” somehow indicate that the leadoff hitter in the top of the 7th inning (with the yankees up 4-2) is somehow more important than the entire bottom of the 7th inning, then this is all BS anyway. Where is the common sense here? Try watching all 162 yankees games and then let me know if you would rather have CC go back out there or the yankee bullpen.

Unbelievable with this % stuff. Its nice in theory, but it has serious flaws that need to be taken into account. Theres a human element in sports that statistics will never be able to measure, so stop acting like you can.

And I am not against statistics. Statistics have a purpose and can be great when taken into context. But its clear from reading this page that there is no real “context”. Its hardcore stats and then when something is unquatifiable, you use qualifiers to cover yourselves. Thats all fine and dandy, but don’t confuse that with some sort of official analysis that makes you smarter than everyone else. Its comments like this that really get me:

“If I were doing the analysis on TV, even though I would actually know what I was talking about, a legion of people would hate me too”

Yes, you know exactly what you are talking about, and the championsip winning catcher is wrong 75% of the time. Maybe someone needs to re-examine things, just sayin’.

Question about:

“Do teams have radar guns in the bullpen?  Shouldn’t they?  Joba has been throwing 92 all year out of the pen.  Tonight he was throwing 95-96.  Don’t you want to know that to help you determine who comes in from the pen and when? “

Do pitchers throw as hard as they’re going to in the game when they’re warming up in the bullpen?  Information is power, and it seems silly to not place a radar gun in the bullpen, but how valuable would it actually be?  Certainly more valuable than not having a radar gun, but by how much?

Brian C: what is your purpose here? 

Do you really think that you are the first person to have ever said to us:

“Unbelievable with this % stuff. Its nice in theory, but it has serious flaws that need to be taken into account. Theres a human element in sports that statistics will never be able to measure, so stop acting like you can.”

You are obviously a first-time poster here, and presumably came over from Rob’s blog.  Think of this place like a classroom, not a soapbox.

Kevin, and Rollins could have been on first if the ball he hit was 2 feet in either direction as well.  The Yankees were lucky that the 7th inning didn’t lead to a big inning, as I’m not sure Sabathia would have been pulled on a hard hit single, leaving the possibility open that Victorino still hits that bullet of Sabathia that could have just as easily gone for a double.  Meaning that inning could have easily been 2nd and 3rd with no outs with Utley and Howard coming up, or maybe just a runner on 2nd, no outs, one run in.  And of course, what makes this so bad is that it was all totally foreseeable in the top of the 7th.  This, to me, was the mistake of the game, and very nearly cost the Yankees the game.

I agree that these were all bad decisions (except for number 4, which I don’t quite understand) and were clearly bad at the time. I wanted to bring up another bad decision, though. Maybe I’m missing something or maybe this one is just so obviously bad that no one (even MGL!) felt like mentioning it. Wasn’t the 2 SB play by Damon a ridiculously stupid bit of baseball by the Phillies? First, I’ve got to think the shift is a bad idea in general, unless it involves the third baseman protecting the 3b line somewhat. But that’s not a big deal, I guess - teams do it all the time and no one ever exploits it. But then what’s really bad is that if you’re going to do it, especially in the ninth of a tie game, with a good basestealer on first, you either have to position your shortstop so he’s covering second on the steal, or you have to make sure your pitcher knows to bust his ass over to third on a sb attempt. According to fangraphs, Damon taking third was worth .056 WPA and .14 runs on its own. That is huge and it’s easily preventable. Maybe I’m missing something, but I couldn’t believe what I was seeing at the time. Unlike the IBB to Ruiz or PHing for Blanton or Sabathia, that is a mistake that you wouldn’t even expect from a manager. There’s no commonly-held wisdom or baseball tradition that prevents you from doing the correct thing there. Just really awful.

Regarding Girardi’s comments on whether he would have CC bunt (point #4) and he said “not necessarily,” what the heck else was he supposed to say?  He didn’t say yes, he didn’t say no.  I suppose he could have said “no comment,” but that’s basically the same thing as “not necessarily.” I don’t see how his reponse gave anything away.

Sorry. Looking more closely at fangraphs, the entire play (Damon from first to third) was .056 and .14. Still, the point stands.

What I was wondering at the time of that play e poc, is that if you are going to put a shift on like that, then why isn’t the 3rd baseman (now playing SS) moving to cover 3rd, while the SS (now playing roughly 2B) covers 2nd.  When you move Felix over to cover 2nd, there is no one covering any part of the left side of the infield.  So if you’re intent on doing that, and the opposition knows it, its an easy hit and run that may even get Damon to 3rd on a ball that doesn’t leave the infield.  Seems you should probably have the SS (playing 2B) cover the bag as you already have 2 other guys on that side of the field with the shift, and that you probably want a position player, and not the pitcher, covering 3rd in the event of possible tag play.  Plus, you’d probably want the pitcher available to back up 3rd if possible. 

So, yeah, it just didn’t seem like they had the shift + steal attempt coverage assignments thought out very well.

"You are obviously a first-time poster here, and presumably came over from Rob’s blog.  Think of this place like a classroom, not a soapbox.”

If not for the insane cockiness of mgl I never would have brought it up. The problem isn’t with the statistics themselves, the problem is with the idea that your comments are superior to people who actually take reality into account.

The problem isn’t with the statistics themselves, the problem is with the idea that [MGL’s] comments are superior to people who actually take reality into account.

Good news! Everything on the Internet is optional.

Brain C: “Now, continue believing that you can solve everything with percentages, and that you are smarter than people who have actually played the game......”

I believe MGL has played semi-pro baseball. He has also been coaching for a very long time. Is that good enough for you?

"Of course your best pitcher should be brought immediately into a tie game in extras even if you are the road team”

You’re smart...well-known in Baseball circles...surely you have Theo Epstein/Tito’s E-Mail, or know someone who does. Please pass this along to them.

“If the first two batters had reached via a bloop single and a bleeder through the infield, Sabathia would be out in a New York minute.”

This is tangentially related to how I feel about mid-batter pitching changes. A couple of years ago, Beckett was in the middle of a tie game flailing. If the batter had hit an extra-base hit, you know Tito would have pulled him. As it was he hit a single and was followed up by a good hitter, but poor slugger. Tito leaves Beckett in knowing it’s very unlikely this guy would drive in the runner from first. Well, Beckett throws a wild pitch, and now the guy is on second. Does Tito pull him even though the game condidtions have changed and if he had hit a double earlier he would have?

Of course not. Mid-batter pitching changes ‘sends the wrong signal to a pitcher’ and will hurt his feelings. Of course, the guy got a single and drove in the go-ahead run. And Beckett promptly came out.

Any thoughts on not pinch running for Posada in the 8th?  With Posada on 2nd (or even when he was on first), 1 out, and a chance he won’t even bat again (or once more at most), wouldn’t it have been better to pinch run and put in Molina - a better defensive catcher anyway?

I agree, I need someone who has played baseball at the highest level.  So, all I should care about is what Tim McCarver, John Kruk, and Rob Dibble think.  And why should I listen to Theo Epstein anyway.

Boy, this is the kind of thinking that I try to avoid from the internet.  It’s too bad when it follows me to my own home (this blog).  How do you get rid of unwanted guests?  And preferably, without them kicking and screaming and farting on their way out?  Or even whispering.  Just quietly disappearing?  Is it possible?

I was just watching a Larry David repeat, where he goes to Julia Dreyfuss’s house and ransacks her place looking for his book of notes.  They couldn’t get rid of him.  Even though it was his house.  He was literally dragged about… by his own friends.

HER house, not his.

I don’t really want to get involved in this discussion, but if I want to know how to turn a double play or take a secondary lead, I’ll defer to someone who has played and/or coached for a long time. If I want to find out whether to IBB someone in a certain situation, I’ll defer to an analyst that also knows the nuances of baseball as most sabermetricians do (as opposed to a lot of academicians).  And there is certainly nothing wrong with the analysts getting input from the players and managers (in fact, that might be helpful), just as there is nothing wrong with the baseball guys getting some input from the analysts on “technique”.

If you want to learn something about technique, listen to Dibble, McCarver, Kruk, et al.  If you want to learn something about “analysis” and you listen to those guys, you will be sorely disappointed.

Dave Pelz never played professional golf in his life.  Not even close.  He has, however, studied from an analytical perspective, the “short game” of golf for over 20 years.  He is considered one of the foremost experts on golf’s “short game” (although not everyone agrees with or subscribes to all of his theories and techniques). Yet many players, including Phil Michelson, the number two (or thereabouts) golfer in the world, employ him as their short game and putting teacher.  How can that be?

"The Wire” is one of my favorite Curb episodes. Larry and Cheryl need to get permission from their nutty neighbors, the Weinstocks, to bury an usightly telephone wire. Jeff sponsors a kid to go to summer camp and he ends up burning the camp down. Afterwards the kid steals all the valuables from Jeff’s home.

BTW, I didn’t care for the last CYE episode, “The Black Swan”, which premiered last night on HBO. It really is a hit or miss show. Some episodes are great, others are terrible.

MGL, you’re making too much sense, so that must mean you are not a pro player, so that means I can’t listen to you.  If I listen to you, you must be a pro player, and that means I won’t learn much about analysis.

Basically, some men prefer to be the equivalent of groupies, and gosh darn it, Bryan Adams is a better singer than Luciano Pavarotti.  (Bonus point for getting the related trivia question.)

The point is that there is more to baseball than percentages. The fact that in the theoretical world, batting your pitcher leadoff costs .1 runs should be taken with a grain of salt. It doesn’t take into account that you are removing one of the best pitchers in the game. Nor does it account for how CC is feeling.

The problem is never the statistic, its using the statistic out of context. You are just making an argument, which is fine. But calling this article “Mistakes in Game 4” is absurd. You are merely disagreeing with professional managers. These aren’t mistakes, these are differences in opinion.

The fact that in the theoretical world, batting your pitcher leadoff costs .1 runs should be taken with a grain of salt. It doesn’t take into account that you are removing one of the best pitchers in the game. Nor does it account for how CC is feeling.

Yeah, you know what the analysis was missing?  How long CC was expected to continue, the quality he could be expected to give them, and the Yankees options out of the pen.  If only MGL had talked about those things, we might have had some context for the opportunity cost of saving or sacrificing that .1 run expectancy.

"Yeah, you know what the analysis was missing?  How long CC was expected to continue, the quality he could be expected to give them, and the Yankees options out of the pen.  If only MGL had talked about those things, we might have had some context for the opportunity cost of saving or sacrificing that .1 run expectancy.”

Like I said earlier, he uses incredibly precise statistics (like .1 runs for batting a pitcher leadoff), but then when it comes to analyzing everything else, he makes vague statments like “yankees have fresh options out of the pen.” Anyone who has a good beat on this yankee bullpen knows that the arms being “fresh” is not the problem. The bullpen is one of the most unpredictable parts of the game because it is so reliant on a reliever’s mindset.

These are not cut and dry decisions, statistics provide another perspective, they are not THE perspective. Calling these moves “mistakes” is the issue. If he just said he disagreed with the move there would be no problem.

Really?  Because Joba (sans one pitch) and Marte looked pretty good last night.  In fact, if we’re going to place stock in playoff performance only (which I think is silly, but I’ll humor you), Hughes isn’t in consideration.  The aggregate playoff numbers of Joba, Robertson, Aceves, Coke, and Marte: 16.1 IP, 2.20 ERA, 7.16 K/9, 3.86 BB/9, 0.55 HR/9.

Walk rate’s a tad high for comfort, but does that really look like a bullpen that’s not getting the job done?  MGL didn’t need to be specific with his numbers - a tiring CC on short rest with less than top stuff going through the lineup a fourth time simply isn’t as effective as this bullpen has been.  That’s fairly self-evident, and I don’t think he should be faulted for not spelling out every little detail of it to the willfully ignorant.  Since CC continuing to pitch was going to be a negative anyway, there was nothing wrong with point out how much of a negative it was to allow him to hit.

I can’t stand the parsing of comments and passing judgements on comments when you have nothing else to offer.  If that’s all you have to say, then you’ve said it.

C’mon dude.

Not here to defend McCarver - I agree he can be stunning with some of the dumb things he says and you ask yourself how is that possible from an All-Star MLB catcher.  But being “wrong” with pitch predictions 75% of the time does not necessarily mean he’s a bad pitch caller.  Just means he’s thinking differently from the battery on the field.  How do you know the battery is not “wrong” 75% of the time?  I watch YES alot and Flahery likes to predict pitches, too, and I notice he’s “wrong” a lot, too.  I’ve concluded there is no one self-evident “right” next pitch.  If there were, pitchers would be “predictable”, wouldn’t they?

Glenn, that is the whole point (and I have no idea whether McCarver is wrong 75% of the time - I SAID that it was a throwaway comment, did I not?).

The point is that you CAN NOT guess a pitch.  Every pitch is going to be thrown a certain percentage of time.  For example, Lidge throws 50% fastballs and 50% sliders.  At different counts and in different situations, that changes of course.  All a person can do is say, “I think there is an X percent chance of pitch A, B, or C being thrown.” Thinking that you KNOW what pitch will or should be thrown is not a smart thing unless the “correct” percentage is near 100% such as with a 3-0 count to a pitcher.

I officially changed the title of the thread to “A few things I THINK the managers got wrong in Game 4.”

Now Brian can be happy. If that’s all I did wrong - suggest that my opinions based on some analysis are definitely, 100% correct (which they are rarely, if ever) - then I really MUST be a genius!

Nice points Brian C.

“The problem isn’t with the statistics themselves, the problem is with the idea that your comments are superior to people who actually take reality into account.”

And my kudos to MGL for changing the thread’s title.

Also huge props to rwperu34 for comments over here: http://www.insidethebook.com/ee/index.php/site/comments/some_actual_data_and_research_on_hot_and_cold_pitchers_for_one_game_rather_/#5

Namely, “You ask if a pitcher is pitching well, will he continue to pitch well? Then you plug in the wrong data. The data you are using will answer, if a pitcher is lucky, will he contine to get lucky?

... whether or not a pitcher gets nine up and nine down has very little to do with how well he’s pitching.”

Exactly.

xyz re rwp: this is exactly what we say in The Book!  That the idea that you can focus on performance stats to tell you almost anything is silly.  There’s so little to be found in it.  And yet that is the crutch that managers and media and fans rely on.  You MUST go beyond the numbers.

MGL, you shouldn’t bend over to pacify Brain so much.  Him not liking your smugness, or what ever he might call it (I’d call it confidence in your process), is a very small part of his objection.  He doesn’t get, and more importantly, he doesn’t want to get it.  No point in bringing yourself down, even a little bit, for no cause what so ever.

"The point is that there is more to baseball than percentages. The fact that in the theoretical world, batting your pitcher leadoff costs .1 runs should be taken with a grain of salt.”

No.

We are not talking about the theoretical world. We are talking about real baseball games - we can look at all innings from 1977 on, and compare the ones in which the pitcher batted leadoff to the innings where the pitcher didn’t bat at all.

These percentages are based upon what actually occurs in baseball games. They are not made up - they are what happens in baseball.

Brian, maybe the fractions of runs grates you - perhaps it might seem more grounded in “reality” if we said that 10% of the time, it might cost the offense 1 run, and 90% of the time it turns out to make no difference.

If someone told you the average family in the USA had 2.3 kids, I’m assuming you can comprehend that means that some have zero, some have one, some have two, etc., and the average is 2.3.

As Colin pointed out, those percentages are actual outcomes from similar situations pulled from data in the Retrosheet database.  If that isn’t real enough, what would you recommend?

Greg,

I understand the process, the problem is that the number is just an average. Hence, it should be used as a rule of thumb. The real percentage for pinch hitting for CC in that exact situation isn’t .1, the real percentage could be much higher or much lower if you take all the factors of THAT specific situation into account.

For example, if you are pinch hitting barry bonds in his prime for CC, then the numbers are much different than if you were pinch hitting brett gardener. The .1 stat is merely giving a historical average that needs to be taken into context with the real situation.

You guys are very respectful here, and i’m sorry if my previous posts were a bit harsh.