THE BOOK--Playing The Percentages In Baseball

Question for Tango: Are you only using nighttime numbers because of the slightly lower offensive environment during ‘twilight’ time? Thanks for the research.

Right, I’m using the night-time numbers as a direct result of the research I posted a few weeks ago.

How many of your starters in your list actually didn’t finish the 9th inning because they lost the game in the 9th inning?  Now compare that to how many times that happened to Motte.  I’m guessing that problem is going to do a lot more to Motte’s numbers than to your elite starters’ numbers.

mccoy/3:  I won’t be able to do your research because some starting pitchers will get removed in the 9th inning before they lose the game.

Regardless, I showed their wOBA at .313 and I showed the pretty good reliever’s wOBA at .317.  It’s pretty much a wash.

Here is the rest of my comment that for some reason got cut off

I would think the real reason something like ERA would be decieving is because a starter who is facing the order for the 4th time is generally pitching in 7th, 8th, and 9th inning and generally around 100 pitches or more.  So if he gives up a couple of hits or walks or some kind of baserunners the manager is going to pull him and bring in a reliever.  While it is true that some of those runners will score it is also probably true that far less of them will score against the reliever than they will against the tiring starter.

Tango#4

I don’t disagree that looking at runs can be decieving.  I do disagree on why that is though.

Ok, so you are saying that there is an ADDITIONAL reason for not using ERA, and that is because in partial innings, ERA is not really that good, because of the scoring rules.  In addition, the quality of reliever that is brought in for the presumably tiring starter might be even better than the starter,and so, those runners won’t come in.

Definitely a great point.

I don’t disagree with tango either, I just think the effect in this case is overstated. 

First, there is no walk off possible when the pitcher is at home.  That should eliminate approx half his innings, probably more as it is more likely he would pitch the 9th at home due to one less PH opportunity. 

Second, walkoff’s aren’t common.  I don’t know how frequent, but I would guess they happen less than half the time.  So now we are down to less than 25% of their (starters) 9th innings.

Third, of those walkoff’s that do occur, few of them are of the variety where runs are ignored because the game ended. 

Finaly, to the extent it does have an effect, I see no reason why it would impact one group (starters) more than the other (relievers).

Good work, Tango!

McCoy, the point is, there are problems using RA or ERA, so why not use wOBA or some other component stat?  It is far less noisy anyway.

Tango, do you think walkoffs where the batter only gets credited with a single (but it would have been a double or triple) will impact the numbers?

BTW, I have always said that you should bring in a reliever in the late innings as long as it is not an elite starter.  I don’t see anything here that contradicts that.

I may have been a little over-zealous with my statement that bringing in Motte was a no-brainer.

Actually I would have taken out Carpenter and brought in a lefty against Howard in the 9th. I think that was a no brainer.

And I think that pinch hitting for Carp in the 8th and then bringing in a reliever or two would have been correct.  The reliever starter thing is always going to be close at worst.  Once you throw in batting your pitcher in a high or medium leverage situation in the 7th inning on (in a non-sac bunt situation), I don’t think it is even close.  IOW, not only does the starter have to be better than the reliever, but he has to be a lot better to make up for the RE/WE you lose by batting your pitcher rather than a pinch hitter…

So, in the original thread, did I say anything egregious or is the entire post egregious enough to warrant the vitriol on BBTF and even here?

I made the point about Punto, which I think is correct, at least according to my sim, and a 1.5% WE is pretty big.  And I have not heard anyone refute that with evidence other than stupid batter/pitcher matchups which we have already discussed (and hopefully put to rest), or the proverbial, “The manager must know something that you don’t know.”

I made the point about the two bunts, which I think are correct, and, again, I have not heard any refutation with evidence.  A few people excoriated me for saying that Carp would have been safe anyway, which is debatable (or not) but completely irrelevant to my argument.  I simply said that with him running, the bunt win expectancy is going to be very poor compared to the WE from batting.  That is because a bunt is always marginal.  Throw in a poor/slow runner on the bases such that he is going to get forced a significant percentage of the time, and the bunt is not likely to be correct, even against a very good pitcher.  Any arguments there?

I said that bunting with a 2-0 count, when the bunt at the outset of the PA was probably bad, is an egregious error, and I am pretty confident it is, and I have not heard any refutations on that either.  Problems with that?

I said that not pinch hitting for Carp in the 8th was bad, but I did not harp on that.  I still think the numbers will show that was bad.  I admit that probably no manager would have done that - although that does not make it correct. I am strictly speaking of mathematically correct things, and not what would make the manager look good or bad. That is not my job to determine that.

And finally (the 4th or 5th thing I criticized), I said that bringing in Motte was correct. It looks like that may be a tossup, but with Carp not being a top tier starter (according to my projections and others - see ZIPS, Oliver, Pecota, Steamer, etc.) and with Motte being a very good closer, I think that bringing in Motte IS the correct choice, but perhaps marginally so.  Again, whether a manager “should” do that is not my business. I am talking strictly numbers.

So why the universal hate, condemnation, criticism, mockery, etc.?

Someone please explain what I did to deserve that?  And I am taking about substance and not tone. If someone wants to criticize me for my tone, so be it.  I don’t give a hoot about that. Those are all ad hominem arguments anyway for people who sadly have nothing substantive to contribute…

Tango, did you look at the pool of pitchers in your 4th time sample?  When I did similar research I found that the sample of pitchers the 4th time through the order were the best of the best, weighted by PA of course.

So when you compare the .293 to the .313 is that apples to apples?  IOW, did you control for the pools of pitchers and number of PA from each pitcher in each bucket (1st-4th times through the order), or use a delta method?

Wow, using ninth inning runs allowed is way off. Cool.

Is it possible that starting pitchers will have a better wOBA against in the ninth inning, as opposed to the fourth time through the order overall? If Justin Verlander hits the top of order for the fourth time in the seventh inning, he probably doesn’t have as good stuff as the nights when he sees the top of the lineup for the fourth time in the ninth inning. Maybe an ace pitcher is a better bet when he’s cruising into the ninth instead of just surviving into the seventh? Because it seems that sometimes a starter will face the lineup for a fourth time because he’s having a great night, but sometimes it’s because his manager is just trying to squeeze an extra inning out of him.

I’ll say again that I’m not a talented researcher or statistician, but these twelve pitchers—Carpenter-Halladay-Sabathia-Verlander-Lee-Felix-Haren-Lincecum-Beckett-Vazquez-Maddux-Big Unit—combine for a .224/.272/.311 slash line against in the ninth inning. 1879 PA. Jason Motte is .223/.289/.352 for his career, 760 plate appearances.

Or is there something wrong with looking at it this way that I don’t see?

I don’t understand the purpose of the runs allowed discussion.  We don’t talk about R and RBI for hitters do we?  We talk about OBP and SLG and wOBA.

So, why talk about runs allowed by a pitcher, in the 9th inning no less, when there is so many issues to resolve there.  There are no issues to resolve with wOBA like that.

***

MGL: if I equally weight each of the 15 pitchers, it’s .293 1st three times thru and .319 for all other times.

"So, if the choice is between Carpenter or a pretty good reliever, it’s probably a wash.”

I think that Carp this year is quite a bit worse than the average pitcher in your group - maybe .25 to .5 runs per 9. 

If that’s true, we are talking around 10 points in wOBA.  That would be .323 the 4th time through the order (using .313 for the pitchers in your list).

If Motte is .315 or .320, which I think he is, then I think Motte is the better choice, although I’m not going to scream about not using him…

I’ve done some research already and it does look like perhaps starters facing the order the 3rd time or later in the 9th (and even the 8th) do considerably better then in earlier innings (when facing the order the 3rd time or later).  I even controlled for the pool of batters being faced (just in case managers tended to leave in starters when the bottom of the order was coming up).  I didn’t look at platoon issues though.  Maybe that is a factor.

Tango, can you redo your numbers but only look at the 4th time through the order in the 8th or later innings?  And then compare this to the 4th time through the order in earlier innings?

BTW, I always like to combine the 3rd and 4th (and later) times through the order.  Remember we found some funny things from the 3rd to the 4th, some of it being do to the colder weather later in the game.

Perhaps this is part of the reason for the 8th and 9th inning difference.  In any case, it is still fair to compare our elite starters in the 8th and 9th (and not earlier), cold weather and all, as long as we compare that to our elite relievers in the late innings as well (which most of our elite relievers will normally pitch anyway)…

In regards to the two bunts.  I would quibble with your view that Carp only cares about pitching thus they should bunt with him on base.  Even if it is true that all he cares about is pitching I seriously doubt he is going to phone it in in that particular situation and it doesn’t look like he did.  He hustled all the way which created a chance for a mistake and that mistake did happen.  At the time I did question the prudence of the sac since you were forcing your starting pitcher to hustle around the basepath and risk bumps and bruises. 
I questioned Tony’s tactics on the second bunt as well.  Once the count went to 2-0 I shook my head when I saw the bunt being laid down and initially I questioned the wisdom of creating an open base for Pujols.  But then I figured that bases loaded for Berkman and Holliday basically turns them into Pujols anyway so I could understand the wisdom of that.

By the way, if I weight the “pre” group based on the number of PA of the “post” group, it’s .293 for pre and .313 for post.  That’s the same if I didn’t bother to weight them properly.

The reason I get the same answer is that my top 15 guys have a pre wOBA of .279 to .301, with most of them in the .289 to .301 range.  Therefore, with that tight a range, it doesn’t matter how many PA each of the 15 had the 4th time through the order.  I was going to get the same answer.

Anyway, for those who want the numbers:

Please don’t pick out each pitcher one at a time and say why he should not be in here or whatever.

” I would quibble with your view that Carp only cares about pitching thus they should bunt with him on base.”

Fine.  That doesn’t change my view.  He is much more likely to be thrown out at second or third than a position player.  Pitchers are terrible base runners and are usually either slow or can’t or won’t run hard and/or slide well or hard.

Do you remember what Carpenter did on a previous AB where he bunted?  He stood at home plate without moving a muscle because he thought the bunt was foul.  It was not.  Not that that necessarily is/was representative of his base running desire or ability. I don’t know.  It sure didn’t look like a player who cared too much about running the bases to me.

In any case, I am pretty confident that if you looked at game logs with pitchers on base and a sac bunt, you will find a lot more FC outs on the bases than with position players running.  But you can check on that.  As I said, bunts are usually so marginal that anything negative for the bunt (bad base runner, slow or bad bunter at the plate, hitter’s count) will make a bunt attempt a clearly poor play…

I don’t disagree with you on the view that a position player is way more likely to execute the various plays that Tony wants to implement correctly but I don’t think Tony viewed the situation the same way as you did.  Which can be an issue on whether or not he is a good manager.  TO me it looked like Tony was willing to concede the out when he let Chris lead off the inning.  When he got on base he looked at it like it was a freebie.  He certainly wasn’t going to pitch run for Carpenter and I think he tried to avoid the double play with the first sac bunt.  When that play resulted in a man on first and second and no outs I think he decided to again remove the double play on a ball in play and get Carpenter to third which would probably result in bases loaded for some very good hitters. 

I think with the very real possibility of a DP the first sac bunt is not really a bad call.  That is if you assume that Carpenter is almost certain to get forced out at second sometime in the inning and it will result in two outs then I think it is a good call to try and get out of that situation with a sac bunt.  If Carpenter gets forced out at second on the sac bunt then you basically have replaced the slow and plodding pitcher at first with a much faster runner and one out.  Which would have been the scenario if Carpenter had simply grounded out or struck out and the next batter hit a single.

OK, I get that using component stats has less noise than runs allowed, but I’ve been thinking about this from the original post:

“So, from innings 1 through 8, the home team scores 0.44 more runs.  But in the 9th, they score 0.13 LESS.  That’s a 0.57 RA9 swing.  Why is that?  Because of partial innings.  Once the home team wins, the bases get cleared.  Those runners on base have the effect of being considered as “out on base”. “

The partial inning effect certainly has something to do with the run drop, but I would argue it’s not the biggest factor, and may in fact be a small component.

See, there is a very large negative run bias for the bottom of the 9th.  Unlike the other 17 half innings of a 9 inning game, the mere existence of the bottom of the 9th depends on the prior game performance of the home team.  It only happens when the home team is tied or losing.  That in itself is a large negative run bias vs an average half inning which has nothing to do with partial innings.

Second, if the score is tied or the home team down by 3 or less, then they are very likely facing the other teams closer, almost always a very good pitcher, at least an above average one (no Jo Bo jokes please).  That’s another large negative run bias again with nothing to do with partial innings.

Third, and this may be small but still perhaps meaningful, if the home team is down by a lot, that also has negative run bias.  Teams down by a lot are usually not scoring a lot of runs.  True, it could be 12-7, but it is more likely 6-1.  It may be because they are facing superior starting pitching, maybe their hitters are having an off day, maybe some starters are injured or just getting a rest day. 

Also, while they may not be facing the closer, it’s still probably an above average pitcher.  In addition, a team down by a lot frequently takes out starters, decides the starters who were getting rest just remain on the bench, etc. 

I don’t know how or even if these effects can be quantified and separated out from the partial inning effect, but they certainly exist, and my gut feeling is that they are a lot more meaningful than the partial inning effect.

re: partial bottom of the 9th innings.

In 2011, the AL as a whole played approx 2266 half innings innings 1-8 (1133 tops and 1133 bottoms of innings), and 1768 9th half innings.  From that, we can estimate they played 635 bottom of the 9th’s by subtracting 1133 from 1768.  They averaged 4.30 PAs per half inning from 1-8, and had 7274 PAs in the 9th.  Multiply 4.30 by 1133 and subtract that from 7274 leaves an estimated 2402 bottom of the 9th PAs, or 3.78 per inning.

How much that 12% drop in PAs due to partial innings affects the 22% drop in bottom of the 9th runs I’ll leave to the experts.

It should be fairly easy to figure out what is happening in the 9th, but I can’t do that now.

McCoy, you can do all the speculation and “thinking” you want, and you might be right about conclusions, but without any numbers, they are meaningless.  Sorry. Either one strategy or the other yields a greater win expectancy, or it is close in which case I have no problem yielding to the gut, experience, instinct, etc.  But, unfortunately, you can’t figure out the answer without “running the numbers.”

addendum to #21.  I may have overestimated the number of top of the 9th PAs.  Since it has the second lowest runs average, it probably has a lower than average number of PAs, leaving more for the bottom of the 9th.  Probably not a big factor, but maybe enough to move the needle a % point or 2.  maybe the bottom of the 9th is 10 or 115 fewer rather than 12.  I’m sure there’s exact data somewhere.  Just spitballing here on a Sunday morning.

Freddie/20: good job all-around for identifying the variables.

What I’ll do is run the wOBA by half-inning, so we can see what kind of performance is being put up there, and the implied runs per 27 outs that wOBA contributes.

The gap would be the partial-inning, or small ball strategy variables, the only two (I think) parameters that the wOBA won’t control for.

One thing you could do is look at the RE in the base/out situation at which the game ended.  This won’t be quite right, because on non-HR hits, (and I guess errors also), the game ends when the winning run scores, so if more bases could have been gained on that play, including more scoring, it won’t show up on the scorecard.  E.g., if a hit is made in a tie game with runners on 2nd and 3rd, it will always be scored as a single and one run, leaving the RE of runners at the corners, when maybe it would normally have been a double with both scoring.  Giving another run in and the batter at 2nd, thus a higher RE.
There are also other biases from the score.  In a tie game with a runner on 3rd, the defense will play in, especially with < 2 outs, increasing the BA.
I think we can estimate some of these systemic biases to the RE numbers, and get some useful estimates.

Right, good point about the abbreviated base movement with multiple runners.  Those all contribute.

Anyway, I’m running the wOBA and runs per 27 outs by half inning, including extra innings, as we speak, so I’m eager to see the results!

Here’s the data (which replaces the data at the top of the thread).  The impact of the abbreviated inning is most visible in the “10th inning” (which is really all extra innings).

The last column is wOBA translated into runs.

So, the bottom of the 9th inning however is fairly muted in terms of the impact of the partial inning. 

This makes me think therefore that if you have great pitchers posting really low ERA in the bottom of the 9th, though they still have higher than their usual average in wOBA, then something else must be going on, perhaps the leaving runners on base scenario (they leave runners on base, and then are removed, and the closer shuts the inning down).  Maybe.

"So why the universal hate, condemnation, criticism, mockery, etc.? Someone please explain what I did to deserve that? 

“...If someone wants to criticize me for my tone, so be it.  I don’t give a hoot about that.”

You’ve answered your own questions. And by asking those questions, you clearly do give at least a little hoot.

It has been awhile since I had a database setup for PBP so I set one up again but forgot that BEVENT doesn’t setup all the fields possible and I’m a bit lazy right now so I didn’t go back and pick just the fields I wanted.  Anyway, last year it looks like a pitcher got to first with 0 or 1 outs 371 times (and nobody was on base at the end of his PA).  I did not setup the pinch runner field so I don’t know just yet how many times they got pulled for a pinch runner.  From what I can find with a pitcher on first and with 0 or 1 outs there have been 64 double plays and 58 fielder’s choice.  Now I didn’t setup the batted ball type so I don’t know yet how many of those FC were busted SH.  It does look like they only executed 6 SH all year last year with a pitcher on first and 0 or 1 outs.  But if we, just for a second, assume that all 58 FC were not botched SH then it is quite possible that 64 out of 122 groundballs that didn’t leave the infield resulted in a DP.  How does that rate compare to a positional player on first?  I would think that a positional player would get doubled off at a slightly lesser rate.

The next step, besides obviously getting the batted ball type, times a infield groundball happened and everyone safe, and pinch runner stuff, would be to see baserunning ability of pitchers and positional players from the various bases based on batted ball types and locations.

One more thing.

An elite SP who faces the batting order a 4th time through is facing the top of the order a high proportion of the time whereas a reliever will face a more varied bunch of hitters. 

A SP pitcher who gets to the 4th time through means that he has faced every position an equal number of times but in that 4th time through it is highly doubtful that he will face all 9 lineup positions.  So a SP might get 60 PA against the 4th time through and 45 of them might be against batters 1-4.  Simply accounting for quality of opponent might very well explain a large chunk of the jump from 3rd time through to 4th time through.

While a RP isn’t likely to face a fellow pitcher in the 9th inning he is likely to face the back end of the lineup a lot more often than a SP would in the 9th inning.

You are right.  I should have controlled for that.  I’ll do that later.

I took a look at 4 names on the Tango’s list:
Cain, Tincecum, Hamels, and Halladay.  Of those four only Hallday got through the entire lineup 4 times and he did so once.  He is also the only guy who got to the 8th spot as well.  One other pitcher got to the 7th spot and he did so once while Halladay did so 8 times.

PA per lineup spot:
1st: 65
2nd: 54
3rd: 40
4th: 27
5th: 20
6th: 14
7th: 9
8th: 3
9th: 1

If we add Zambrano and Peavy to the mix it becomes even more heavily skewed towards the top of the order.

I then looked at Kimbrel, Axford, Putz, Bell, and Storen.  The leading saves leaders in the NL this year and who they faced.  I’ll do this by %.

1- 10.71%
2- 9.93%
3- 10.93%
4- 10.43%
5- 10.79%
6- 12.29%
7- 12.29%
8- 11.93%
9- 10.71%

And here is the 4 SP I did:

1- 27.90%
2- 23.18%
3- 17.17%
4- 11.59%
5- 8.58%
6- 6.01%
7- 3.86%
8- 1.29%
9- 0.43%

A starting pitcher facing the batting order a 4th time through will face hitters 1-4 in 80% of those PA while a closer in the 9th will only face batters 1-4 42% of the time.  The most likely 4 batters a closer will face are batters 5-8 and he’ll face one of them 47% of the time.

Thanks for that.  No surprise.  I’ll control for that tonight.

Is it possible to also control for when the SP faces the 4th time through?  I would think the closer we can to getting a dataset that mimics the environment Tony and Chris faced the other night the better off we are to tackling this question.

Yes, that’s what i’ll be doing.  I’m going to control for qhality of opponent, times thru order, park, day/night.  If there’s anything else, let me know.

If I did it right it looks like last year a SP in the NL faced batters in the 9th inning 165 times. Their composite line was:
.189/.218/.289 with 7 doubles, 3 homers, 5 walks, 1 HBP, 28 strikeouts, and DP.

Sorry, forgot one caveat.  I setup my starting pitcher filter by only looking at pitchers who had 30 or more starts last year to quickly eliminate relievers.

I also noticed that my data only factors in NL home games which means IL games in the AL are not counted and IL games in NL parks did get counted.

I picked out some pitchers, Doc, Steve Carlton, Nolan Ryan, Tom Seaver, Roger Clemens, Felix, and one or two others.  ALL of them pitched better (using component numbers) in the 9th inning than other innings.

I’m going to control for quality of opponent when I get home.

It’s either they had an easier lineup to be able to get to the 9th inning, AND/OR, they were “on”.

Will be interesting to see what the numbers say.

Another thought: baserunners who do not represent the tying or go ahead run will be ultra-conservative about advancing and risking outs in a “last licks” frame.  (The runners who do represent the tying or go ahead run might be extra aggressive, but I suspect the first effect will dominate).

In extra innings, multi-run deficits are much rarer than in the ninth, so the effect I’m suggesting would be muted then.

#38 @ Tom

My guess is that they just lock it down in the 9th.

The names mentioned are guys that are highly competitive, ruthless to a degree.

I know that we do not rely on such things like emotion, confidence, etc because they are hard to quantify ... but all that matters is that the guys mentioned lock down the 9th. Whether it’s because they know they can put everything they have into the last 15 pitches (or 3 outs), or because they will it to happen, or because they were saving something for th e9th or whatever is secondary to the situation of the 9th being locked down.

My personal opinion based on experience is that adrenaline fuels concentration, combined with the end being in sight, supplmented by an offense that has already been beaten down for 8 innings and may have mentally surrendered by now.

That was my point in regards to saving Jaime Garcia for the home start in the LCS instead of having him pitch the 2nd game beca8use he’s their 2nd bets starter. I don;t care what the reason is but at home he’s aweosme on the road he’s poop. He pitched on the road against MIL, and I’m not sure why. I’d have saved him for StL. As much as I hate Lohse, Lohse-Jackson in MIL and Garcia-Carp-Jackson in StL is the best move.

I think you need to control for umpire.  Starters may reach the ninth disproportionally in games where the umpire has a large strike zone.  That may make it look like they are “on.” But, close games where the starter pitches the ninth are low scoring for both teams, which suggests something depressing scoring for both teams.  That surely includes park, but also probably includes the home plate umpire.

Larry/42: ohhh!  I like that.

Great, I forgot about that too!  I looked at weather and park, but not umpires.  There are a few umpires that are around plus or minus half a run per game, which is a lot. That is around 17 points in wOBA, which is huge! IOW, if there were an extreme pitchers umpire on the mound, like Eddings or Miller, we would expect a wOBA in all innings to be 15 points or so less than usual.

So we would have to look at all innings versus the 9th inning when starters do pitch the 9th and see if only the 9th was depressed or all innings were depressed. Or maybe these “under” umpires really expand their zones in the 9th - I have no idea…

"I picked out some pitchers, Doc, Steve Carlton, Nolan Ryan, Tom Seaver, Roger Clemens, Felix, and one or two others.  ALL of them pitched better (using component numbers) in the 9th inning than other innings. “

How evenly spread across the years is the 9th inning data? I’d guess a disproportionate amount of goodens (for example) 9th innings come from the mid 80’s when I presume his component numbers were better than his career averages.

I would think the real reason something like ERA would be decieving is because a starter who is facing the order for the 4th time is generally pitching in 7th, 8th, and 9th inning and generally around 100 pitches or more.  So if he gives up a couple of hits or walks or some kind of baserunners the manager is going to pull him and bring in a reliever.  While it is true that some of those runners will score it is also probably true that far less of them will score against the reliever than they will against the tiring starter.

We don’t look at ERA but woba.  Your point doesn’t stand.

Is there a difference between pitch counts vs. times through the order?

Im not sure we ever tried to separate times thru the order from pitch counts but I suspect that the times through order penalty is pretty much independent of pich counts. Of course pitch counts could have their own penalty as well.

Pizza Cutter did something on pitch counts, similar to what I did on times thru order.  Ideally, you’d put the two together, but the reality is that they are going to be so dependent on each other, you’ll probably see little differentiation.

Yes the problem is that, for example, when a pitcher starts to face the order for the 3rd time, he has faced 18 batters already.  The spread of pitch counts is going to be like 65 to 75 pitches 90% of the time. Basically the number of batters faced is a pretty good proxy for pitch counts so to try and separate them is going to be difficult.

What I would do is create 2 buckets:  One bucket would be half of the pitchers with the least number of pitches thrown through 18 batters and the other bucket would be the rest. So bucket one might average 62 pitches over the first 18 batters and bucket two, 72.  Then I’d compare the 3rd time through the order penalty for the two groups.

Or you could do a multiple regression analyses I suppose.

The spread of pitch counts is going to be like 65 to 75 pitches 90% of the time.

The actual 90% spread for starting pitchers after facing 18 batters and left in the game to face number 19 is 55 pitches to 81 pitches.  Median is very close to 67 pitches.  Mode is 68 pitches.  The 100% spread is 38 pitches (!) to 103 pitches (also !).

The 38 pitch games were by Mark Mulder on June 3d, 2006 and Kyle Kendrick on August 6th, 2007.  Both pitchers were losing at the time they faced their 19th batter.  Mulder had already given up 5 runs, although he went on to complete the game.

The 103 pitch game was by Shairon Martis on June 5th, 2009.  He had actually only given up one run but was only allowed to face one more batter.