Batter Walks

Last entry, I looked at a quick regression model for batter strikeouts based on contact percentage and swing percentage. This week, we’ll look at batter walk percentage based on swing percentage, zone percentage, and contact percentage.

Same rules as last time. All 2008 qualified batters, linear regression.

The results were pretty good, though not as accurate as last time. The r-squared of the equation is .7349, which, while good, isn’t quite as accurate as estimating batter strikeouts. I’m sure part of this is intentional walks, which wouldn’t likely have anything to do with swing%, zone%, or contact rate, but that is a topic for another day. Let’s look at some of the results.

More than Expected

Swing% Zone% Contact% ActualBB% Pred BB% Difference
Albert Pujols 0.415 0.471 0.901 0.166 0.125 0.041
Pat Burrell 0.42 0.497 0.813 0.16 0.121 0.039
BJ Upton 0.404 0.511 0.805 0.154 0.118 0.036

 

I did not say “lucky” on this one for a couple reasons. First, since intentional walks are undoubtedly going to be a part of the error margin, I don’t feel that “luck” is the appropriate term, as we use it so much in the statistics community. Second, while an r-squared of over .7 is certainly a good one, there are a number of other factors to be analyzed as well.

 

Worse Than Expected

Swing% Zone% Contact% ActualBB% Pred BB% Difference
Garrett Anderson 0.487 0.484 0.828 0.049 0.092 -0.043
Aubrey Huff 0.433 0.483 0.848 0.081 0.116 -0.035
Jeremy Hermida 0.435 0.492 0.778 0.087 0.121 -0.034

 

Close to Expected

Swing% Zone% Contact% ActualBB% Pred BB% Difference
Adam Jones 0.535 0.527 0.769 0.046 0.0464 -0.0004
Brian McCann 0.464 0.481 0.855 0.101 0.10127 -0.00027
Josh Hamilton 0.555 0.453 0.741 0.093 0.093057 -5.7E-05

 

While there is still some work to be done, most importantly, that with intentional walks, the model is fairly accurate for a basic linear model. Next time, we will see how accurate such a regression formula is with pitchers.

 

Thanks to Fangraphs.com for their contributions to this article.

Regression calculations performed by:

Wessa, P. (2009), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r4, URL http://www.wessa.net/

Mike Silver recently completed his requirements for the Sport Management Major at THE University of Massachusetts-Amherst, where he is a brother of Theta Chapter of Theta Chi Fraternity, the best house in the country. He is a huge Red Sox and Bruins fan, and longs for the days of the REAL Boston Garden, Cam Neely, and the ultimate Dirt Dog Trot Nixon. If you have any questions, you can reach him at mjasilver@gmail.com. Have a good night readers, and know that Mike hopes to hear from you soon. If you quote Mike in an article, please let him know. He’d love to hear it.

Link: Fans Scouting Report

The Book’s fan scouting report for this year is all set up and ready to go. Make sure to head over there and help them out.

Where oh where can my Joba be?

Ever since entering the league in late 2007, Joba Chamberlain was taking names and kicking ass. That is, until, 2009. So what happened?

Throughout his first two seasons (124 innings) Joba had rate stats of 11.03 K/9, 3.27 BB.9, 3.78 K/BB, and 0.44 HR/9. Moreover his FIP for 2007 and 2008 was 1.82 and 2.65; his tRA for 2007 and 2008 was 2.23 and 2.60. However, as everyone knows he split time between RP and SP. Before he got hurt his RP/SP splits in 2008 were…

RP: 23.7 IP, 2.28 ERA, 2.61 FIP, 11.4 K/9, 4.2 BB/9, 2.72 K/BB

SP: 60.6 IP, 2.23 ERA, 2.59 FIP, 10.2 K/9, 3.4 BB/9, 3.0 K/BB

Amazingly, he was performing better in a starting role last season, albeit a small sample size for both splits.

This year, to be blunt, he has sucked. His line is…

126 IP, 4.74 FIP, 5.68 tRA, 7.74 K/9, 4.41 BB/9, 1.76 K/BB, 1.14 HR/9.

Ouch. His K’s are way down, while his BB and HR are way up. That is not a recipe to success.

Looking at his BIP, he isn’t a dramatically different pitcher. His GB% is 44.4, and for his career it is 46.7%. His FB% is low at 34.3%. Yet his HR/FB is 12.7%. High considering his low FB%, but its not drastically higher than his career HR/FB. Also, a lot of the HR are due to NYS. His HR/9 at home is 1.77 compared to 0.90 on the road.

The big concern is his high BB rate and low K rate (for him at least). What is causing this? My belief is his FB.

His velocity is way down this season. Among SP last season, his FB velocity was tied for first with Ubaldo Jiminez at 94.9 mph. This year he is down to 92.5 mph. The consequence is that his once feared FB is now feasted upon. In 2007 and 2008 he was 3.2 RAA and 8.6 RAA respectively. This year he is -12.0 RAA his FB. Although his slider has remained a great pitch for him, his FB has become his downfall.

Considering he’s been healthy this season, this leads to me to believe he has been inconsistent in regards to mechanics. Within games, he’ll go back and forth between 95 mph FB and 90 mph FB.

Once he straightens out his mechanics, Joba will be back to kicking ass.

Strikeout Percentage

A player’s strikeout expectancy is among the most important parts of his value. A player that strikes out frequently has a short career ahead of him, unless he can walk and hit homeruns like Jack Cust. Lots of strikeouts means few opportunities to put the ball in play, which means a lower batting average, fewer home runs, and more losses. Take a look at the annual batting average leaders, you’re likely to find few players who strike out with high proclivity.

But, as with anything else, strikeouts are subject to randomness and statistical noise. This begs the question, how many strikeouts is a player expected to have given certain plate discipline characteristics? 

To shed some light on this question, I created a simple regression equation, regressing contact percentage and swing percentage against strikeout percentage, using batting statistics from the 2008 season. The r-squared of the equation was .8719, meaning that even regressing just these two variables yields a relatively accurate outcome.

As always, there are other considerations to think about, such as how often a player swings out of the zone, in the zone, how often they make contact with these pitches, and 2-strike contact percentage, among others.

But I digress. Below are some of the results of the equation. “Unlucky” hitters are those who struck out more than expected. “Lucky” hitters should have struck out more than they did according to the equation.

Unlucky Hitters

2008 K%

Ex K%

Difference

Swing %

Contact %

Gregor Blanco

0.23

0.1628

0.0672

0.4

0.862

Adam LaRoche

0.248

0.1965

0.0515

0.442

0.813

Fred Lewis

0.265

0.2147

0.0503

0.43

0.8

Pat Burrell

0.254

0.2053

0.0487

0.42

0.813

Lucky Hitters

Troy Glaus

0.191

0.2447

-0.0537

0.396

0.784

Russell Martin

0.15

0.1906

-0.0406

0.4

0.835

Lance Berkman

0.195

0.23228

-0.03728

0.466

0.769

Curtis Granderson

0.201

0.23361

-0.03261

0.393

0.796

 

Close Projections

Johnny Damon

0.148

0.1492

-0.0012

  0.416

0.869

Derek Jeter

0.143

0.1444

-0.0014

0.482

0.848

Miguel Cabrera

0.205

0.2065

-0.0015

0.515

0.775

Raul Ibanez

0.173

0.1749

-0.0019

0.465

0.825

 

More investigation is necessary, especially the consistency of these plate discipline statistics and their implications on future performance. However, there are a few conclusions that can be drawn from this data. 

The relatively low values of the standard errors show that total strikeouts are a pretty good indicator of how often a batter should strike out. Also, the observed errors indicate that other variables need to be considered, such as 2-strike contact percentage and other plate discipline statistics (i.e. O-Swing).

However, this simple 2-variable model is a good predictor of actual strikeouts and is a good tool for analyzing a player’s value.

Thanks to Fangraphs.com for their contributions to this article.

Regression calculations performed by:

Wessa, P. (2009), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r4, URL http://www.wessa.net/

Mike Silver recently completed his requirements for the Sport Management Major at THE University of Massachusetts-Amherst, where he is a brother of Theta Chapter of Theta Chi Fraternity, the best house in the country. He is a huge Red Sox and Bruins fan, and longs for the days of the REAL Boston Garden, Cam Neely, and the ultimate Dirt Dog Trot Nixon. If you have any questions, you can reach him at mjasilver@gmail.com. Have a good night readers, and know that Mike hopes to hear from you soon. If you quote Mike in an article, please let him know. He’d love to hear it.

 

Walking Albert Pujols with the bases loaded

Hello, my name is
Brian Kenney and I’m another writer from Mike’s blog 4parl.wordpress.
I’m a huge Cardinals fan, as you might notice from my first post-which
is about a week and a half old by the way. It took a while for me to
get publishing privileges on my account . In about a week I’m going to
go to The University of Missouri-Columbia for my first year of college
where I’m going to study mechanical engineering (so my posts might be
few and far between). Some of my hobbies include hockey, golf, and
poker.

Albert Pujols is the undisputed best hitter in the game. His batting
numbers this year are Bonds-esque, and he is receiving what is now
known as the Bonds treatment. He currently has 36 intentional walks,
which is a whopping 20 more than 2nd place Adrian Gonzalez. As most of
you I’m sure know, intentional walks are almost always an incorrect
play. There is one situation in particular, however, where an
intentional walk is plain ridiculous: when the bases are loaded.

However, many talking heads are debating whether it is a smart idea to
intentionally walk Albert Pujols when the bases are loaded. The basis
of their arguments comes from the fact that Pujols has been insane with
the bases loaded this year. 7/9 with 5 home runs. The sample is so
ridiculously small that almost no useful information could be obtained
from it. Anyway, just how bad of a decision would it be to walk Pujols
with the bases loaded? Let’s break it down.

For the year, Pujols’ at-bats results in the following x % of the time (discounting IBB):

Out-60%
1b-13.5%
2b-5.8%
3b-.2%
HR-8.4%
BB-10.7%
SF-1.2%

The mere fact that a Pujols’ AB with the bases loaded will result in an
out (and 0 runs) 60 percent of the time should tell you that walking
him intentionally is borderline insane. Let’s break down the numbers to
see just how insane it is, though.

(.60)(0)+(1)(.107)+[1(.135*.25)+(2(.135*.75)]+[2(.058*.5)+(3(.058*.5)+(.002)(3)+(4)(.084)+(.0117)(1)=
0+ .107+ .2025+ .683+ .058+ 087+ .006+ .336+.0117=.84785 runs.

*I assumed a single would result in 2 runs 75% of the time and 1 run
25% of the time. I also assumed a double would score 2 runs 50% of the
time and 3 runs 50% of the time.

So, an intentional walk will result in 1 run 100% of the time. Pitching
to Pujols will result in .84785 runs on average. The choice is clear,
especially when you consider the caliber of players hitting behind
Pujols. Matt Holliday and Ryan Ludwick are no slouches, and their
positive run expectancies make this decision even easier.

Shooting the Gap

For some reason, I was recently thinking about doubles and the types of players that are getting the two-baggers. Why? No idea, but it did bring about some confirmation of my ideas.

First off, there are two types of doubles hitters. There is the power hitter who narrowly misses a dinger and has to settle for a double, and there is the line drive hitter who knows how to hit the gaps and get to second. But which one is better at hitting doubles? Let’s go to the data.
First, here is a table of the top 10 doubles hitters this year.

http://spreadsheets.google.com/pub?key=t2WK5yoFd6pkfGv6j-VEsEg&single=true&gid=0&range=A1%3AF12&output=html&widget=true

The one thing to take note of is the line drive percentage. They don’t hit a huge amount of fly balls, but instead drive the ball allowing hitters with less power to take the extra base. Next, let’s move on to the top 10 home run hitters this year.
Notice the difference in LD and FB%? Also, you can see that the power hitters are pretty solid doubles hitters, due to home runs falling short.
Is this of any real significance? Not really, but it is always interesting to look at the data and confirm your thoughts on a subject.

Tired Arms

After writing about J.P. Howell a couple weeks ago, and looking into splits based on the number of times a pitcher throws in the order, I got to thinking about why and how pitchers fatigue during their outings.

As anyone who has ever seen a baseball game, when a pitcher gets hit hard in the late innings, the announcer blames it on the pitcher being physically exhausted and the manager makes the call to the bullpen. For anyone who is familiar with DIPS theory and the Laws of Voros McCracken, the first thought is that the pitcher was unlucky because the hitter made a good swing or because it must have been a cheap hit.

This is true sometimes, but fatigue can do some strange things to a pitcher, especially their ability to locate a pitch. Analyzing pitch locations is about to be the next big breakthrough in DIPS theory. Pitch location is extremely important to how hard a hitter hits a ball, just ask Dave Allen. When a pitcher gets tired, a few things happen. 

The most commonly cited effects due to fatigue are a drop in velocity and a downward change in arm angle. These can happen separately or in tandem, as the body does not tire globally at the same rate. Conditioning is important and so is the type of activity being considered. Just because a pitcher is used to throwing one hundred pitches per game doesn’t mean that their deltoids are at the same state of fatigue as their biceps or their triceps.

(From here on out, note that I am not a kinesiology expert, so these inferences are based on what I’ve read and from experience in athletics.)  

Lift your arm to your straight in the air as if you were raising your hand in class, or to do jumping jacks if you liked gym class more. The muscles in your back (i.e. trapezius) and shoulders (i.e. deltoids) are put to work, while biceps are relaxed. 

This motion is important when considering a pitcher’s arm angle. If shoulder and back muscles are tired, the arm will be lower than expected when the pitcher is releasing the ball. This has a number of effects on the pitch. First, the ball will go in a different direction simply because the release point is now different. Second, and slightly more subtle, is a change in the rotational axis of the baseball, which will cause it to break slightly differently.

If a pitcher who usually throws overhand is now throwing in a 3/4 motion, the ball will rise less and break more laterally to their arm side. When the difference between a ball and a strike, or a home run and a pop out are just fractions of an inch, this difference can be monumental. Less accuracy leads the pitcher to throw to poor locations more often: more hits, more BB, more HR.

Velocity is the other major factor. I won’t pretend to know how fatigue affects velocity, but there are a number of factors that do: arm fatigue, leg fatigue, torso, pretty much anything can affect it. When velocity drops (assuming the arm angle stays constant, the pitch will change not change much in break, so don’t worry about that), the locations where a pitcher can throw and prevent giving up home runs changes drastically. 

For an explanation of these locations, see this article by John Walsh at The Hardball Times. If you don’t feel like reading the link, the gist is this: if your velocity drops, you will give up more home runs, especially when throwing inside.

Now try to imagine what could happen to a pitcher when his velocity decreases, especially with location lapses thrown in. The location and velocity lapses will combine to put the hitters in more hitter’s counts, and the pitcher, when trying to thread the needle or hit corners, will now throw to the kill zone.   

In summary, pitcher fatigue can have drastic affects on effectiveness, due to differences in pitch break, release point, and velocity drops. So, next time you shout at a manager for taking out a pitcher who has given up a few hits late in an outing, remember, not all pitches are created equal.

Thanks to The Hardball Times  and BaseballAnalysts.com for their contributions to this article.

Mike Silver recently completed his requirements for the Sport Management Major at THE University of Massachusetts-Amherst, where he is a brother of Theta Chapter of Theta Chi Fraternity, the best house in the country. He is a huge Red Sox and Bruins fan, and longs for the days of the REAL Boston Garden, Cam Neely, and the ultimate Dirt Dog Trot Nixon. If you have any questions, you can reach him at mjasilver@gmail.com. Have a good night readers, and know that Mike hopes to hear from you soon. If you quote Mike in an article, please let him know. He’d love to hear it.

Who is the best pitcher in Marlins history?

Hello, I would like to introduce myself as the newest writer for Statistically
Speaking. I was recently a member of the blog http://4parl.wordpress.com until Zach
Sanders approached our blog and asked us to write for StatSpeak.net. My name is
Eric Cines, and I am a big fan of the Baltimore Orioles, though when I write I
try to stay as unbiased as possible. Other interests of mine include football,
basketball, and MMA.

In the Marlins
short history they have already won 2 World Series. To win 2 World Series, you
generally need very good starting pitching. So over the teams 16 years, who has
been there best pitcher? To Start with, I have narrowed down there pitchers to
a total of their 5 best.

Here they are,
with the stats they had as a Marlin

Kevin Brown- 2 years (470 IP) 2.30 ERA, 2.91
FIP, 13.9 WAR, 7.0 K/9, 1.9 BB/9 and 3.68 K/BB

Kevin Brown also
was an instrumental part of the Marlins 1997 World Series run. Because of that,
you could probably increase his WAR from anywhere from 1 WAR based on playoff probability
added. (Playoff stats weren’t that great though, so he didn’t impact the team
as much in the playoffs)

Josh Johnson- 5 yrs (420 IP) 3.34 ERA, 3.54
FIP, 8.5 WAR, 7.64 K/9 3.28 BB/9 2.33K/BB

Josh Johnson is still only 25, and is pitching
his best season yet. Look for him to only improve.

AJ Burnett- 7 yrs (853 IP) 3.73 ERA, 4.01
FIP, 11.2 WAR 7.9 K/9, 4.0 BB/9 2 K/BB

Not important to
the 2003 WS because he was injured most of the year.

Josh Beckett- 5 yrs (609 IP) 3.46 ERA, 3.52
FIP, 9.6 WAR 9.0 K/9, 3.3 BB/9, 2.72 K/BB

Also, in the
postseason of 2003, he had a 2.66 FIP, and a 2.11 ERA… that is deserving of at
least 1 WAR additionally.

Dontrelle Willis- 5 yrs (1022 IP) 3.78 ERA, 3.97
FIP, 14.9 WAR 6.7 K/9, 3.0 BB/9, 2.2 K/BB

Willis though
was horrible in the 2003 postseason, pitching 12 and 2/3 innings giving up 12
runs. But he was important to the playoff run in his rookie year, which negates
the effects of his innings in the playoffs.

Overall, though
Dontrelle Willis has the highest amount of WAR at 14.9, I would give the award
of the best Marlins pitcher to Kevin Brown. In Half the amount of Marlins
innings, he had almost as much WAR, and had a much better ERA and FIP. He had
the best season pitching in Marlins history, and helped take them to the World
Series.

Two years from
now though, I would guess Josh Johnson may be the leader of WAR for the Marlins…
unless they trade him for more prospects.

Sources include http://www.baseballprojection.com ,
http://www.fangraphs.com, and http://www.baseball-reference.com 

Quick F/x: Jorge Sosa is back

Do you remember Jorge Sosa? He was a pitcher for the Devil Rays and Braves back in the day. He has recently spent time with the Mets, Mariners and Astros, before joining the Nationals. Oh yes, the Nationals are desperate for bullpen help.

Now is the perfect time to debut the newest version of my Pitch F/x flight paths. Thanks to Harry Pav for creating the first template, and answering my questions last night when I was updating it.
sosa_fp_8-02-09.pngThe plate/strike zone are for reference, and should not be treated as perfect. However, they should be pretty close. Click on image to enlarge.

The fastball/slider combo is solid, and he’s still throwing in the low 90’s. He has never been much for controlling his pitches, so it’s no surprise the pitches are over the plate. However, the slider stayed low, so it’s not too bad.
Congrats, Nationals, you have yourself an average pitcher.

J.P. Howell and the Great Soft-Tossing Reliever

Once upon a time, in a land far, far away, there was a great man named… OK, this may not be story hour, but at once upon a time, being called a soft-tosser in the MLB was a lot like being Cinderella, minus the happy ending. Every once in a while a low-velocity pitcher would rise through the minor league ranks like the Little Engine That Could, chugging their way through the minors with guile, accuracy, and a lot of hard work. Few completed the journey.

 

But that was then. A lot has changed in the MLB in recent years. Groundball specialists have become quite the growing fad in baseball. Where Chad Bradford once stood alone, now every team seems to want their own double-play specialist. With so much downward break on the baseball, batters consistently swing over the top of the pitch and bury it into the ground. Who imagine a better situational reliever than one who can induce a doubleplay? Even if they cannot accrue Ks, two outs is always better than one. Who wouldn’t want to see Cla Meredith or Brad Ziegler enter from the bullpen with a runner on first? At least you know they won’t give up a homerun.

 

The relief pitcher is a curious animal. They come in all shapes and sizes: Jon Broxton at 800 lbs, Juan Cruz weighing slightly more than Calista Flockhart. They can have great command or walk the ballpark. They can make a career throwing one pitch, as long as its a cutter. They seem to be the only pitchers that can defy the Laws of Voros McCracken and post substantially low BABIPs. Just check out Troy Percival if you need an example.

 

Further making relievers the strangest players in the clubhouse (aside from their rituals) is that low velocities don’t doom them to failure. In fact, the bullpen is a prime destination for a soft-tossing pitcher who can’t cut it as a starter. Since deception is be among the most important aspects of the hitter-pitcher interaction, a soft-tosser could have a slight deceptive advantage, especially when following a starter who brings the heat. When a reliever enters the game, the opposing batters have usually seen the starter for about three plate appearances. Therefore, they have adjusted their approach and internal timing to a pitcher who throws harder than our subject. Therefore, if a pitcher like J.P. Howell comes in, the velocity of his fastball could be different enough from the previous starter that he can take advantage of a slight timing difference.

 

Howell has been among the best relievers in the majors for the past two seasons, after looking dead in the water as a starter for Kansas City. The problem was never his breaking stuff, which is excellent. Instead, it was his fastball, which was tattooed while he was a starter. In three seasons  as a starter from 2005-2007, Howell showed consistently poor fastball effectiveness (wFB/C: 2005: -0.91, 2006: -0.25, 2007: -1.96). This trend was immediately bucked in his 2008 transition to the bullpen, when he posted his first positive wFB/C values, of 0.60 in 2008 and 1.00 in 2009. Howell’s fastball all of a sudden became a good pitch – all 86 mph of it.

 

While sample size may be an issue, Rich Hill comes to mind as a player who may be having a problem similar to Howell’s, and could benefit from a switch to the bullpen. Hill’s 2009 has been marked by some polarizing performances. Hill’s fastball has been hammered this season, but so have all his pitches. More interesting, however, is Hill’s splits based on the number of times he’s seen a batter in a game. In his first time through the order, he has been great, ostensibly because the hitters don’t see stuff like his often; having trouble timing such a slow fastball and an onslaught of breaking pitches. In this first turn, opponents have hit .204/.347/.316.  However, he has been annihilated in his second time through the order (.384/.460/.674), and continues to get pounded in the rare outings when he sees a third rotation (.333/.400/.511). While some of this is due to a BABIP mirage, not all pitches are created equal. Is it possible that batters have adjusted to his low velocity and have reset their timing? 

 

Howell may have suffered a similar fate as a starter for Kansas City and for a while with Tampa. Lending evidence to this theory is a similar progression during Howell’s first stint in the majors in 2005. In his first time through the order, batters hit .234/.358/.324. In the second turn, they hit .245/.344/.462, followed by a .350/.409/.567 line. But, again, there are sample size and BABIP issues here, but recent research has shown that BABIP has limits, and this could be one of them. However, it must be noted that these extreme splits were not seen in Howell’s 2007 season, and it is certainly possible that these are the exceptions. Either way, these are logical conclusions that will add to our understanding of soft-tossers and, perhaps more importantly, the idea of a selection bias in sabermetric analysis. For those readers who need some perspective, the league average of slash stats through the order are as follows: 1st time: .254/.329/.405, .293 BABIP; 2nd time: .271/.333/.431, .302 BABIP; 3rd time: .282/.345/.459, .306 BABIP.

 

But back to Rich Hill for a moment. If Baltimore is to make a run at a playoff spot in the next couple of years, they need to put together a bullpen. It looks like they could have a nice reliever in their back pocket right now. I mean, he used to be good. Maybe a transition to the bullpen could help him recapture his old form.

 

While the idea of velocity contrast demands more investigation before a definitive conclusion can be made, if one lesson can be pulled from this analysis, it is that low-velocity pitchers can be incredibly valuable in relief roles. Further, any team can draft any number of soft-tossing pitchers in the draft at minimal cost. Teams with this approach, assuming the player has the right combination of secondary stuff and command can make a killing drafting relievers at below market value and having a stockpile of relievers in their minor leagues. You can never have too many relievers, and there will never be a shortage of soft-tossers. That seems like a match made in Heaven to me. 

 

Thanks to Fangraphs.com  and Baseball-Reference.com for their contributions to this article.

Mike Silver recently completed his requirements for the Sport Management Major at THE University of Massachusetts-Amherst, where he is a brother of Theta Chapter of Theta Chi Fraternity, the best house in the country. He is a huge Red Sox and Bruins fan, and longs for the days of the REAL Boston Garden, Cam Neely, and the ultimate Dirt Dog Trot Nixon. If you have any questions, you can reach him at mjasilver@gmail.com. Have a good night readers, and know that Mike hopes to hear from you soon. If you quote Mike in an article, please let him know. He’d love to hear it.

 

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