Archive for April, 2014

Giancarlo Stanton: Please Stay Healthy

Giancarlo Stanton. What a trip this guy is. One second he is hitting home runs and the next he is running to first and coming up lame with a pulled hamstring, or a knee injury, or even an eye injury. He is an enigma that we seemingly know little about. He is hard to project into the future because of the injuries, but the one concrete thing we know about him is that he possesses monstrous power.

Recently I have come to see Stanton as similar to Ken Griffey Jr., in that he hammers the ball and could put up single season home run figures similar to Griffey’s, who hit 56 home runs in consecutive seasons. In addition, Griffey averaged 32 doubles per season, while Stanton averages 36, Griffey had a career OPS of .907, while Stanton’s is .892, and they are only .001 point apart in slugging percentage. I could go on with more statistics, but you get the point, these guys are like statistical clones. Stanton does not have the benefit of playing in the Kingdome like Griffey did, so we should even take into account the fact that Stanton currently plays half of his games in the Petco Park of the East.

Unfortunately, they are also similar in the injury department. I’m not saying Stanton will miss as many games as Griffey, but Stanton has missed 95 games due to injury since the beginning of 2012. What is even more worrisome is that he is hurting in many different regions of the body. I alluded to the numerous injuries in the opening; he has missed time for arthroscopic knee surgery, shoulder issues, and hamstring issues. The ability of each of these separate injuries to flare up again is something that should concern all fans of Stanton, as well as fantasy owners. In fact, I owned Stanton last year in my own fantasy league and we had a running joke going that we couldn’t call him “Giancarlo” (we referred to him as “Mike”) until he hit five home runs. I thought this was a very trivial joke at first, but the other owners had the last laugh because Stanton did not reach five homers until June 15th, mainly due to injuries.

If Stanton can stay healthy, he may be this generation’s Griffey. He does not have the flair, mechanically perfect swing, or happy-go-lucky attitude that Griffey seemed to carry on and off the field, but Stanton is similar to him where it matters most — in the statistics category. As an avid baseball fan I would certainly not be opposed to watching Stanton bash 600, or even 700 homers over the next 15 years and I know every Marlins fan would thoroughly enjoy that kind of production, assuming he stays in Miami. He may not have quite the average that Griffey achieved (Stanton career: .267, Griffey career: .284) but he can certainly smash the ball at a consistent clip.

Strange as it is, I want Stanton to be like Jeremy Renner in Hurt Locker. I want him to step up to the plate and discern what puzzle the pitcher (or the insurgent) is putting in front of him and then solve the riddle and hit the ball 450 feet, like when Renner disarms a circle of six IEDs. Then, I want him to keep the bomb suit on and run around the bases so he doesn’t injure himself. In fact, he should keep the mask on so he doesn’t get an eye injury again.

I am basically asking for Stanton to break numerous batting records all while playing at half speed (or maybe in a bomb suit) so that he will stay healthy. I know that is unfeasible, but we basically have a prior tale of what will happen if he keeps getting injured. We can always just take a look back at Griffey’s career and see what Stanton’s production will be if he keeps landing on the disabled list at his current pace. But the interesting and exciting thing is that if we want to know what could’ve been if Griffey’s career hadn’t been riddled with injuries, we might get a realistic clue if Stanton can get healthy and remain that way for the years to come. Hopefully we will be able to sit back and enjoy the moments of Stanton’s career where he “disarms” pitchers and launches moon shots off the Marlins’ scoreboard.


Why the White Sox Should Relocate

On opening day of this season the White Sox attracted a crowd of 37,422 in a win over the Minnesota Twins. In much contrast to their sell out crowd on opening day, their 2nd and 3rd home games drew much less people. The White Sox reported that their 2nd home game of the year was attended by 10,625 people however, there appeared to be much less people in the park then the club reported. You can decide for yourself, but there are clearly less than 10,000 people at this game and the attendance figure was probably closer to 1,000. The Sox saw very similar attendance in their 3rd home game of the season as well. These numbers are pathetic but people might argue it’s because the team is in a rebuilding stage and fans have no expectations for their team this year.

That might be part of the issue but the amount of people that have attended their games so far is embarrassing to the organization. Also, in White Sox history when the team is contending for a playoff spot they have always struggled to sell to tickets to very important games. A prime example of their woeful attendance when they are in contention was on September 25, 2012. The White Sox were tied atop the AL Central with the Detroit Tigers. With 8 games remaining in the season, the Sox were facing the Cleveland Indians in a crucial home game. Almost any other big league team would get a sell out crowd but the Sox only attracted 13,797 people which filled about a third of their stadium. These attendance figures should be very alarming to the Sox organization and show that changes of some type are needed.

Another interesting part of the Sox’s attendance problems is that offseason signee Jose Abreu isn’t helping draw crowds at all. Typically if a big name player, is debuting for a team, fans will come out to see them play. Abreu, had tons of hype surrounding him as he had shown elite power and the ability to hit for average in the Cuban league. The signing of Abreu is obviously not a publicity stunt, and is a move to improve the quality of the team. fans however, have shown no interest is seeing their potential all-star 1st baseman play. The fact that this young, exciting player is a negligible factor in whether or not fans will attend games is problematic to the franchise.

Another problem with the White Sox is that the games are fun to go to, yet people still don’t go. From first hand experience going to White Sox games, I actually really enjoy the environment there. As an fan who will go to US Cellular Field not to root for a particular team but just to watch baseball, I have always enjoyed my experiences there. The park is in very good condition and the food is unique and pretty good. The firework shows at the end of night games I have always found to be very cool and have been known to attract people to games who aren’t necessarily big baseball fans but just want to have a good time. Ticket prices aren’t unreasonably high as the average ticket cost $29 as of 2012. Going to White Sox games are an enjoyable and affordable experience yet nobody goes.

Not attracting crowds when in contention, when having high profile players, and having a quality stadium suggests that people in Chicago flat out do not care about the team at all. The organization might need to do something drastic to attract more fans. An option for the Sox that might help the organization is relocation. There are many cities that would love to have and MLB franchise and I think that Portland, Oregon would be an excellent option for the White Sox.

Portland is a city populated with just over 600,000 people similar to Seattle and Denver. Portland only has one major sports team (Portland Trail Blazers, NBA) and has shown in their attendance figures that they love and will support their team (5th in the NBA in attendance). Another notable piece of information is that the Portland Timbers the Major League Soccer franchise based out of Portland sells out every single game and attracts over 20,000 people for home games. In a very low market sport that is in the shadow of the major four sports in the USA, Portland has supported their MLS team. If Portland were to receive the Chicago White Sox, attendance figures would skyrocket and the team would be a much more relevant part of the city. The change from Chicago to Portland might be a problem with the fact that the Sox are in the AL central and Portland is dead west, but the MLB could easily realign to make things more easier in terms of travel.

Another problem people might point out is that Portland is a much smaller market than Chicago and the franchise might not make enough money. However, around the MLB the White Sox are widely considered a smaller market team as they are in the shadows of the Cubs who have a much larger fan base and is the more prominent team in Chicago. A move to Portland would allow the team to receive much more attention, and would help the organization sell more tickets. This is why Portland would be an excellent fit for the Sox and would drastically improve the state of the franchise.


What the Cubs Need to Do to Be Successful

The Chicago Cubs have gotten off to a very slow start in the 2013-14 season scoring a total of 9 runs in their first 5 games and as a result of that they are 1-4. The buzz around the city of Chicago is all about the excitement of top prospects Javier Baez, Albert Almora, and Kris Bryant tearing up minor league pitching and rapidly moving up in the Cubs System. All of these players have fantastic stats but the stats don’t truly matter until these players can be productive big league players. The problem is is that these prospects have shown day in and day out that they are ready to move on to the bigs. Almora, might not be quite there yet but Baez and Bryant have proven they are by dominating minor league pitching and posting good spring training numbers. Cubs GM Theo Epstein won’t pull the trigger on sending these guys up. Bringing these players up will significantly improve the quality of the team but many more changes will need to take place in order for the Cubs to be a team to win games on a consistent basis. Here are 3 other things that need to happen for the cubs to start their path to being successful

1. The cubs need to find a reliable, all-around, everyday 2nd baseman. There are many different solutions the their problem at 2nd but first let’s establish what the problem is. Darwin Barney has proven that he is an excellent fielding 2nd baseman but he is an absolutely horrendous hitter. In 2013, Barney posted an atrocious slash line of .208/.266/.303. Not only does this show that he rarely gets hits or gets on base, but when he does it’s mostly because singles. The Cubs have many possible solutions to this problem. One possible solution is to bring up Javier Baez and play him at short and Starlin Castro at 2nd or vice versa. Doing this might slightly weaken the 2nd base spot defensively, but drastically improve it offensively. With the Cubs pitching being surprisingly good in the first few games of 2014, their offense is a glaring problem and Baez would improve it instantaneously.

Another solution would be to slide Luis Valbuena over to 2nd and make Mike Olt the everyday 3rd baseman. Currently, Olt and Valbuena are splitting time at third which is detrimental to the team because both players have shown offensive value to the cubs. Valbuena had an excellent eye and has proven to be adept at drawing walks. He also has shown solid power as he hit 12 homeruns in 108 games in 2013. Olt has also shown the ability to hit for power as he had 5 homeruns in a very good spring training that earned him a spot on the opening day roster. Either of these solutions would be a much better fit for the Cubs then having Barney as the everyday 2nd baseman.

2. If the Cubs want to be good now, their bullpen needs to be consistent, and deeper. The bullpen has been a problem for the Cubs for a very long time. However in 2014 they might show some signs of improvement. In 2013, reliever Pedro Strop Posted a solid 2.83 ERA in 35 innings with the Cubs. In his time in Chicago, he only gave up 11 earned runs, 5 of which were in one performance. Along with solid numbers Strop possesses a 97 MPH power sinker in addition to his best pitch which is his slider. Strop will be put into a much bigger role this season and if the cubs want to succeed he will need to continue to pitch at a high level. In the offseason the cubs also signed lefty Wesley Wright and Jose Veras who in recent history have proven themselves as reliable bullpen options to their clubs. Players like Brian Schlitter and Hector Rondon will also need to step up for the Cubs. If Strop can continue pitching at a high level and the rest of the pen can consistently pitch in late innings. The Cubs will improve as a team very much.

3. Lastly if the Cubs want to succeed Anthony Rizzo and Starlin Castro must have bounce back years. There are many things that I could criticize about these 2 players but there a few problems in their games that are in the most need of fixing. In 2013 Rizzo only hit .233 if Rizzo continues to hit in the heart of the cubs line up, a .233 average is unacceptable. If he was hitting 50 homeruns it might be a different story but .233 with only 23 HRs isn’t going to cut it. In order for the Cubs to succeed, Rizzo will either need to hit 10-15 more homers or improve is average by around 30 points.

Starlin Castro is a much bigger problem for the Cubs. Spending most of the season in the 3 spot, Castro posted a weak slash of .245/.284/.347. Castro’s numbers were only a bit better than Barney’s which makes him a big problem. In addition to his poor offensive play, Castro has been an extremely inconsistent defensive SS his entire career. There is optimism for Castro though. In Castro’s first 2 full big league seasons, he was voted to the All-Star Game and hit close to .300 in both of those seasons. Castro has shown in his career that he has the ability to hit, the question. is will he be able to have seasons reminiscent to his all-star years. Only time will tell for Castro but if he can bounce back along with Rizzo the Cubs might actually be a legitimate team.

Although many things need to happen for the Cubs to be a playoff contender, fans should be optimistic for the future. With a farm system fortified with elite prospects throughout and an improving bullpen, the cubs need their “key players” to perform at a higher level. If all of these things can happen, there might be October baseball played at Wrigley sometime in the near future.


Estimating Plate-Discipline Stats for Earlier Players

The plate discipline stats at FanGraphs are fantastic. Lots of stuff can be drawn from them – and the articles I’ve linked to are only scratching the surface both of what’s already been done and what we can still do with them. So many things are great about them: they’re very stable, they’re good indicators of other statistics that might be less stable, and they’re  completely isolated to the batter and pitcher. The problem is, they only go back to 2002 (for the BIS ones) or 2007 (for the Pitchf/x ones). So what if we want plate discipline numbers for players from before then? How do we know how often Babe Ruth or Willy Mays or Hank Aaron swung at pitches inside the zone, or how often they made contact on pitches outside the zone?

Regressions, that’s how.

Using the Baseball Info Solutions plate discipline data (only because it goes back farther, and also has the SwStr% and F-Strike% stats), I ran a multivariate regression with R to find all the plate discipline numbers provided on FanGraphs: O-Swing%, Z-Swing%, Swing%, O-Contact%, Z-Contact%, Contact%, Zone%, F-Strike%, and SwStr%. I used the following stats as variables in the regression: BB% and K% (for obvious reasons), ISO (I figured maybe power hitters were more prone to different types of numbers), BABIP (same goes for hitters who could maintain higher BABIPs), HR% (same thinking as ISO), and OBP (combining hitting ability and plate discipline, even if somewhat crudely). My dataset was every qualified hitting season from 2002 until now. I couldn’t use any batted ball data (GB%, FB%, etc.) as a variable because we don’t have that prior to 2002 either. So that was what I had.

Some stats worked better than others – for example, the r^2 for Contact% was an excellent 0.8089, while for Zone% it was a measly 0.1551. And of course, it’s possible that the coefficients would be different for prior eras than they are now. But, hey, what can you do. Here, first, are the r^2s for each statistic, so you know how much to trust each number:

Statistic r^2
O-Swing% 0.3615
Z-Swing% 0.2450
Swing% 0.5222
O-Contact% 0.3956
Z-Contact% 0.7328
Contact% 0.8089
Zone% 0.1551
F-Strike% 0.4374
SwStr% 0.7072

And now for the actual coefficients:

Statistic Intercept BB% K% ISO BABIP HR% OBP
O-Swing% 0.32183 -0.99231 0.09971 -0.18619 0.50728 1.96589 -0.54037
Z-Swing% 0.64669 -0.66798 -0.03129 0.16784 0.23244 1.43928 -0.15409
Swing% 0.4852 -1.15845 0.03932 0.08247 0.14074 1.05097 -0.05289
O-Contact% 1.0226 1.1915 -1.5965 -0.5266 1.4718 1.3388 -1.8966
Z-Contact% 1.0124 0.02288 -0.66107 0.05412 0.02545 -0.8396 -0.04233
Contact% 1.0084 0.40198 -0.95703 -0.01352 0.25118 -0.77417 -0.36001
Zone% 0.48603 -0.72667 0.01344 0.22752 -0.53755 -1.59305 0.71355
F-Strike% 0.61752 -0.66725 0.14433 0.01348 0.04169 -0.2285 -0.02461
SwStr% 0.000416 -0.433719 0.449711 0.014265 -0.125661 0.493577 0.204283

(If you can’t see the whole table, here)

Note that for all the percentages – including the plate discipline numbers – I turned them into decimals: for example,  a BB% of 12.5% will be turned into 0.125, and  an O-Swing% of 20.7 will be 0.207, so if you’re calculating these on your own, keep that in mind.

There are some strange things in that table that I wouldn’t really expect. Here’s one: a higher O-Contact% leads to a much lower OBP, or maybe vice-versa*. The only logical explanation that I can offer is that balls out of the zone that are hit fall for hits less often, so BABIP and therefore OBP will each be lower. League average BABIP on balls out of the zone in 2013 (based on a quick search I did at Baseball Savant) was .243, well below the league average of .297. But that -1.89 coefficient still seems like too much. Some more explainable ones: HR% and Zone% are strongly inversely correlated (the more dangerous a hitter’s power, the fewer pitches they’ll see in the zone), BB% and O-Swing% are strongly inversely correlated (the fewer pitches you swing out of the zone, the more you’ll walk), and K% and SwStr% are fairly strongly correlated (the more you swing and miss, the more you’ll strike out).

To first examine these stats a little bit more, let’s take a look at the regressed numbers for players who have played since 2002 and compare them to their real numbers. Here’s Barry Bonds’s 2002 (the asterisk means it is the regressed, not real, numbers)

O-Swing% Z-Swing% Swing% O-Contact% Z-Contact% Contact% Zone% F-Strike% SwStr%
11.5% 70.1% 36.7% 39.6% 89.8% 80.8% 43.1% 45.1% 6.5%
O-Swing%* Z-Swing* Swing%* O-Contact%* Z-Contact%* Contact%* Zone%* F-Strike%* SwStr%*
-7.1% 59.5% 24.3% 54.2% 91.3% 87.4% 46.7% 40% 1.5%

Hmmm… not off to the greatest start. Z-Contact, Zone, F-Strike, and Contact percentages were pretty good, but the rest were waaaay off. O-Swing gave out a negative number. As good as Barry Bonds might have been, that just isn’t possible. SwStr% is also pretty off – only pure contact hitter Marco Scutaro has ever posted a swinging strike percentage that low since the BIS data started being recorded, and nobody has every been lower. (Scutaro had 1.5% in 2013). Not terrible, though. How about Miguel Cabrera’s 2013 MVP season?

O-Swing% Z-Swing% Swing% O-Contact% Z-Contact% Contact% Zone% F-Strike% SwStr%
34.1% 77.5% 52.1% 69.6% 87.6% 80.8% 41.5% 60.3% 9.6%
O-Swing%* Z-Swing* Swing%* O-Contact%* Z-Contact%* Contact%* Zone%* F-Strike%* SwStr%*
22% 71% 45.2% 58.1% 87% 80% 47% 53.9% 8.8%

Hey, not bad! The O-Swing is pretty off, and the O-Contact is a little too low, but other than that they’re all fairly close to the real values. I think we’re getting somewhere here.

Now let’s look at some seasons for which we don’t have the real numbers. Ever wondered how Babe Ruth’s plate discipline was in 1927?

O-Swing%* Z-Swing* Swing%* O-Contact%* Z-Contact%* Contact%* Zone%* F-Strike%* SwStr%*
14% 70.9% 40.8% 52.5% 86.9% 80.2% 46.6% 49.2% 7.8%

Not bad. We obviously can’t verify this (at least not without a lot of painstaking effort, and likely not at all) but that seems reasonable enough. Average contact rates in the zone, good swinging strike percentage, not very many swings outside the zone. How about the king of plate discipline, Ted Williams? Here are his numbers from his 1957 season, in which he had a 223 wRC+ and nearly 10 WAR:

O-Swing%* Z-Swing* Swing%* O-Contact%* Z-Contact%* Contact%* Zone%* F-Strike%* SwStr%*
8.8% 66.1% 36.1% 61.1% 91.2% 86.5% 47.4% 47.5% 4.1%

Wow. Really, really good. That’s a crazy low O-Swing% and yet a fairly middle-of-the-pack Swing% overall, which goes exactly with what we would expect from a man with a famed, disciplined plate approach. He rarely swung and missed, making contact on nine out of ten swings and only whiffing on one out of every twenty five pitches he saw.

I could really go on and on, but I think I’ll end by showing you the (supposed) single worst season by these regressed plate discipline numbers between 1903 and 2001. See if you can guess who it is:

O-Swing%* Z-Swing* Swing%* O-Contact%* Z-Contact%* Contact%* Zone%* F-Strike%* SwStr%*
34.4% 75.1% 53.5% 43.3% 78% 67.1% 46.4% 60.8% 16.2%

This will shock you, I’m sure, but… It’s Dave Kingman.

 

* Most likely, high O-Contact% causes low OBP and not vice-versa. This brings us into dangerous territory, however, because we don’t want to assume that everyone with low OBP has high O-Contact%. There are other factors that go into low OBP as well, and somebody could very easily have a low O-Contact% and a low OBP. It is like this with each of the regressed stats. But this is the best I could really do.


What Your Fantasy Settings Say About You, Collectively

On March 31, Eno Sarris posted a RotoGraphs article analyzing what his fantasy settings and preferred players say about him. If fantasy settings were beer, Eno appears to view deep, auction format h2h keeper leagues with the same affection he holds for a High-ABV Pacific Coast Double IPA.

However, most fantasy baseball writing and analysis is tailored to a far more mainstream palate. The “standard 5×5” settings– shallow (10-12) mixed league rotisserie scoring on AVG, RBI, R, HR, SB x ERA, W, K, SV, WHIP–are the Coors Light of the fantasy world.

I created a simple Google Form to poll RotoGraphs readers on our preferred fantasy settings. After about a week and nearly 150 responses, I have first results to report.  With even more data this year–or collected across multiple years– we may be able to identify trends in the way fantasy baseball is played by, if not the public generally, the average RotoGraphs reader.

Original Form available here
Complete Responses are available here

Based on the first 148 responses, 26.3% are only in 1 league for 2014. 62% of respondents are in 2-5 leagues. While there are a dedicated few of us who are in more than 5 leagues, the overwhelming majority is clearly more capable of achieving a healthy fantasy baseball-life balance.

Here is a basic breakdown of the data as of April 4:

Total Leagues: 470
Head to Head: 205
Keeper: 234
Mixed: 403
Deeper than 12 teams: 140
5×5: 176
OBP or OPS instead of AVG: 222
Holds or Saves+Holds: 156
Auction: 158

Bonus Questions (that Eno didn’t ask himself)
Leagues using FAAB: 136
Leagues with Minor League Reserves: 126
Preferred sites:

  • Yahoo!: 67
  • ESPN: 60
  • CBS: 27
  • Ottoneu: 15
  • Other: 11

The primary takeaway, based on results as of this writing, is the number of non-“standard” leagues reported. One respondent is in 17 leagues, and all 17 are standard 5×5 format. That’s great for this sir or madame who is clearly an advocate of the more-is-more approach, but he’s really skewing our poll here by being so far from the mean. If we remove his response, the results show only about 35% of the league settings reported are standard 5×5. More data about the specific settings used, and the demographics of the respondents, would embiggen our collective understanding here. It may be that the responses captured are not from a representative sample of RotoGraphs readers.

But scientific rigor and caution have never been effective barriers when it comes to anonymous website readers providing criticism or opinion. So allow me to extrapolate wildly based on this extremely limited data set:

5×5 is a dinosaur. It is a relic. Dinosaurs and relics are a lot of fun, and can be pretty awesome, and really everyone loves dinosaurs and relics both. Just like most red-blooded humans can shut up and stomach an ice cold serving of the Silver Bullet on a given day, and some days feel refreshed.

There is a type of person, though, who is content to leave dinosaurs and relics in museums, and to tolerate a vent-mouth can of the taste of the Rockies only when it is the last option available in your brother-in-law’s fridge. Let us call this person “the RotoGraphs reader.” He or she is more apt to try a new taste, to reach for something a bit more complex and perhaps even more challenging. The stats represented in the standard 5×5 format no longer represent how this RotoGraphs reader evaluates the baseball player, genearlly. The brand of fantasy baseball she or he plays reflects this. Standard is no longer the standard.

And perhaps, just as the statistical revolution has won in the real measurement of performance for actual game of Baseball, it is on the cusp of a major victory in the virtual game of Fantasy Baseball. AVG and Saves have long been abandoned as helpful or relevant stats by discerning fans and front offices alike. For the RotoGraphs reader these stats are less relevant every day to his or her enjoyment of the fantasy game.

What do your settings say about you? This is the question Eno, in his wisdom, posed to us. Each of us will have individual answers, but collecting those answers can reveal possible answers to a bigger question: what do our settings say about the state of the game?


Possible Side Impacts of Base Stealers

Having grown up playing catcher from Little League through college, I always recognized the temptation and situational changes that occurred in terms of strategy and pitch selection with runners on, particularly base stealers, versus with no runners on base.  As a catcher, my thought process with a base stealer on, is always to try and have my pitcher get the ball to me as quickly as possible.  An earlier study I read dealt with the correlation between pitchers’ times to home, and that being a much stronger factor in throwing out a base-stealer than catcher pop times.  Logically, in thinking of pitch selection as a way of controlling the run game, the quickest way to get the catcher the ball is with one’s fastest pitch.

To evaluate the impact of base-stealers I defined a base stealer as a player who swiped 20 plus bags in 2013.  Using Baseball Reference, I slotted 6 pairs of base stealers and their following hitters.  The criteria for those hitters being 400 plus plate appearances in the same slot in the batting order.  Nick Swisher however is an exception because he had 250 plus appearances behind both Michael Bourn and Jason Kipnis, but I decided to include him.  I should also note that all the statistics in this study are from 2013.  Using Baseball Savant’s Pitch f/x database I defined a fastball as a 4 seam, 2 seam, sinker, splitfinger, and cutter and every other pitch as a breaking ball.  I then compared the fastball and breaking ball rates with each hitter with a runner on 1st or nobody on.

It is taken from granted that for a hitter the best pitch to hit is a fastball.  While there are many different approaches, one of the most common is “fastball adjust,” meaning the hitter always looks, or anticipates, a fastball as you get in the box.  However, if you recognize something different out of the pitcher’s hand, you should have more time to adjust.  Hitters are always fastball hunters first, that’s why we call 2-0, 3-1 counts “hitter’s counts” because they will most likely get a fastball and at the same time are sitting fastball.  As proof we used the probability of scoring a run per 100 pitches of a certain pitch above the prototypical average players.  The league average probability of scoring runs against what I defined as a fastball type pitch for every 100 pitches in 2013 was 0.0167 and for every 100 off speed pitches was -0.07.  That is over an 8/100ths difference in the likelihood of scoring a run above average, which added up over the thousands of pitches a player can see a year can make an impact.  Below are the 6 hitters I used for this study and their run probability rates against different pitches:

 

Name Team wFB/C wSL/C wCT/C wCB/C wCH/C wSF/C wKN/C
David Wright Mets 1.74 -0.13 2.75 1.95 2.01 -4.82
Shane Victorino Red Sox 1.53 1.29 -1.28 -0.52 -0.33 1.16 0.11
Dustin Pedroia Red Sox 0.11 -0.72 3.87 1.86 1.47 9.6 -2.77
Nick Swisher Indians 1.02 0.23 0.97 0.37 -0.55 -0.77 -4.47
Jean Segura Brewers 0.19 0.45 0.82 -0.18 2.7 -5.61
Manny Machado Orioles 0.17 0.23 1.15 -1.73 1.2 2.31 -1.34

 

As the data above supports, the best pitch to hit, the pitch a hitter is most likely to score more runs from, is a fastball.

So that being said, if a reputed, or habitual, base stealer is on base, then will the hitter at bat see an unusually high rate of fastball-like pitches?  With a higher rate of fastballs the hitter should therefore have a greater chance of success.  The theory being that an offense built more on speed and base stealing should see a higher rate of fastballs which then gives that team a greater probability of scoring more runs.

Now the total overall fastball rate for the league as a whole for the 2013 season was 57.8%.  The total fastball rates I arrived at were derived from simply taking the situational fastball rate and dividing it by the total pitch percentage or fastball percentage plus breaking ball percentage: fastball% / (fastball% + breaking ball%).

 

Base Stealer: Following Hitter: Runners on Fastball%: Runners on Breaking Ball%: Nobody on Fastball%: Nobody on Breaking Ball%: Total Fastball% with runner on: Total Fastball% with Nobody on:
Norichika Aoki Jean Segura 20.3001% 9.5322% 37.5552% 20.4325% 68.05% 64.76%
Jacoby Ellsbury Shane Victorino 16.8302% 9.5191% 38.2237% 22.8165% 63.87% 62.62%
Daniel Murphy David Wright 21.0498% 9.534% 33.5833% 18.3717% 68.83% 64.64%
Nate McLouth Manny Machado 18.1782% 11.9856% 36.5961% 21.8138% 60.26% 62.65%
Shane Victorino Dustin Pedroia 22.1729% 11.0694% 34.1647% 17.2532% 66.70% 66.45%
Michael Bourn/Jason Kipnis Nick Swisher 19.8731% 12.0587% 31.4954% 21.4597% 62.24% 59.48%

 

Looking at the results, in particular the totals, there is no significant difference in percentages of fastballs vs off speed seen with a runner on first or not.  The biggest difference is a 4.46% difference with David Wright.  And David Wright scores 21.1 runs above average against fastball type pitches (wFB).  While maybe an extra 4.46% increase does not make a world of difference it still contributes to overall run production and as we know in baseball 1 run can decide a game and 1 game can decide a season.  However, it appears that my hypothesis is false and there is no significant difference in situational pitch selection with a base stealer on 1st.

Now I will be the first to admit that there are definitely ways to improve upon the accuracy of my theory.  The biggest problem being that I could not find a database on the internet that allowed me the option of isolating at bats with only specific runners on, so the next best thing was Baseball Savant’s option of isolating at bats with the option of runners on certain bases or a combination thereof.  So all these plate appearances measured are just with a generalized runner on 1st who could be anybody or nobody on at all.  This study is assuming that the runner on 1st, for a majority of the time, is the base stealer who hits 1 spot in front of the selected hitter.  BIG assumptions I realize.  Also this is only covering 6 hitters in their 2013 season, which is a small sample size considering.  Unfortunately I did not have all the resources necessary for the most accurate representation for this study as a whole and on that note I hope many of you who perhaps have more available to you, can dig deeper and build on my theory.

This is my first time posting something like this so if you have any helpful questions/comments/criticism/advice please feel free to comment.  And if you have a way to more thoroughly complete this study please do so!  Thanks and I hope you enjoyed.


Will-power?

Will Middlebrooks is a popular pick for a breakout player (at least according to the local Boston media).  Now breakouts aren’t really something you can predict, but I will not go into that whole can of worms.  On the surface Will Middlebrooks seems like an obvious choice, a young player with power, coming off a down year with no serious injury history.  The hopes for a Middlebrooks breakout upon closer inspection seem to be driven by hope and optimism rather than actual facts.

Middlebrooks’s glaring flaw last season was his sub .300 OBP (.271), which was driven in large part by his low walk rate (5.3%) and high strikeout rate (26.2%).  Believing that Middlebrooks can improve those numbers is central to any hope that he will have a breakout season.  Alex Speier  showed that it’s not unprecedented for young power hitters with sub .300 OBPs to see a large improvement in the OBP area, but it’s also not guaranteed.  Of the players Speier looked at only 18% saw their OBP increase by 30 points or more (which is what it would take to get Will over .300), so why does the Boston media believe that Middlebrooks will experience this rare transformation?

The main driving narrative behind this optimism is that Middlebrooks was over aggressive and had terrible plate discipline last year, and this allowed pitchers to dominate him. But now that he has worked on his approach at the plate during spring training everything will come together.

This “Willpower” narrative goes all the way to the top

Red Sox manager John Farrell told reporters “I think last year we saw some at-bats where maybe he was pressing a little bit, maybe trying to make up for some previous at-bats where it would cause him to be a little overaggressive or expand the strike zone, That willingness to swing, pitchers didn’t have to challenge him all that much” when explaining Middlebrooks past struggles.  We are led to believe that this former Achilles heel is no more after his successful spring training, as Middlebrooks told reporters “The one thing that sticks out to me is I’ve swung at one pitch outside of the zone this spring.”

Will Middlebrooks had a great spring training ( .353/.389/.667) but spring training stats are useless for predicting regular season success.  And, as it turns out, are far from the only problems with this “Willpower” narrative.  The idea that Will Middlebrooks was overly aggressive and had bad plate discipline is something that can be checked very easily by looking at Middlebrooks’s plate discipline stats vs the league average for last season.

Did Middlebrooks have poor plate discipline last season?

2013

pitches/PA Swing% 1stP Swing Contact O-Swing% Z-Swing% Z-Contact Zone% Swstr%
Will

4.11

46.6%

26.2%

75%

30.8%

64.5%

81.4%

47%

11.5%

Lg ave

3.86

46.4%

25.3%

79.5%

30.9%

65.8%

87.2%

44.5%

9.2%

Will Middlebrooks plate discipline compared to the average major leaguer.

Checking the number reveals the surprising fact that Will Middlebrooks’s plate discipline was not terrible but surprisingly average.  He appeared to be a little bit aggressive, swinging a bit more at the first pitch but those 0.9 percentage points translated three more plate appearances with Will swinging at the first pitch hardly enough to ruin his triple slash line.  The next surprising thing that the numbers reveal is that pitchers were actually throwing Middlebrooks more strikes than the average hitter (and more compared to what he saw the previous season), so while pitcher might not have had to challenge him, they didn’t shy away from throwing him pitches in the zone.  Middlebrooks actually saw a lot more pitches in the strike zone than other power hitters.  For players with at least a 0.190 ISO and at least 350 PA only Jayson Werth saw more pitches in the strike zone .  These facts throw the whole premise of this “Willpower” out the window.

How does the image of Will Middlebrooks the aggressive hacker persist when it’s clearly untrue?

Well whenever you see such a low walk rate coupled with such a high strike out rate the easy first assumption is that the player swings at everything, this is a fare guess if didn’t have better data, but we do.  But what about some on who watched every single Middlebrooks plate appearance such as his manager, how could they have such a distorted view.  Well everything is relative, relative to an average major-leaguer Middlebrooks’s plate discipline and his approach were average but compared to other players on the Red Sox Middlebrooks was aggressive and undisciplined.  The Red Sox as a team swung at the first pitch less often than any other team in the majors.  So when not watching Middlebrooks, John Farrell was watching some of the most patient and disciplined hitters in baseball so this is an understandable bias.

The highly improbable feat of chasing only one pitch out of the strike zone over 26 plate appearances.

Now let’s look at Will’s assertion that he only chased one pitch out of the strike zone over his first 26 plate appearances (that’s the number he had prior to his quote).  This would be incredible and might even be meaningful if it were true.  We don’t have spring training plate discipline numbers so we will do a Gedankenexperiment (what Einstein called thought experiments because he was German) and assume the Will saw 100 pitches over those 26 plate appearances (lower than his career average rate and a bit below league average) and half of those were out of the strike zone (also generous considering that usually more than half of pitches are out of the strike zone and in spring pitcher are rusty and of a lower talent pool) this would give Will Middlebrooks a 2% chase rate ( chances are it would have to be lower than that for him to only chase one pitch over 26 plate appearances but we are giving him the benefit of the doubt).  This would be really impressive for a guy who normally chased around 30% of pitches (it would actually be impressive for anyone), and it’s a number that no one has ever sustained for a full season.

How rare is 2% chase rate over that short a time frame?  It’s so rare that no one even came close to it last year.  The closest was Shane Robinson, when last year in the month of June he had 27 plate appearances and only swung at 7.7% of pitches outside the strike zone, that was the lowest chase rate any player had during any month last season (assuming they had at least 20 plate appearances).

Given our prior knowledge about Will Middlebrooks and major-league hitters in general I will go out on a limb and say that I believe Middlebrooks swung at more than one pitch out of the zone.  I bet Middlebrooks believes he only swung at one pitch out of the zone, and this more than anything might point to a flawed understanding of the strike zone.  So while any player can improve by improving their plate discipline (case in point that Joey Votto can still benefit from it) its not a cure-all for baseball problems, and Will Middlebrooks’s problems extend beyond his plate discipline.

If plate discipline wasn’t the reason Middlebrooks was terrible last year then what was the problem?

Part of Middlebrooks’s problem was his abysmal .263 BABIP, this will likely be closer to league average in 2014 and is probably one of the best reasons to believe that Middlebrooks will be better than he was last year.  Unfortunately it sounds much better to say you are working on your plate discipline in spring training than to say you are hope your BABIP will regress towards the mean.  But BABIP is only part of the picture it doesn’t explain his 5.3% walk rate and 26.2% strikeout rate (the low BABIP and therefore production might have led pitcher to throw Will more strikes thus diminishing his walk rate, but this would only be a small effect).

Middlebrooks’s real problem seems to be with making contact, especially when it comes to pitches in the strike zone. He was 212th out of the 237 players with at least 350 PA last year in terms of zone contact (that means 89% of players are better than him), making contact only 81.4% of the time when he swung at a pitch in the strike zone.  This low zone contact rate is probably a large part of the reason pitchers felt comfortable throwing him so many pitches in the zone.  This issue was further compounded by the fact that when Will did make contact the ball went foul slightly more than half of the time (50.4% compared to the league average of 48.1%).  This leads to his high strike out rate.

Look at it this way:

a)      when Middlebrooks swung his chance of making contact with the ball was below average, and

b)      when he did make contact the chance of that ball going in fair territory was below average, and

c)       if that ball was put in play the chance of it being a hit was well below average.

These issues meant pitchers could throw Will lots of strikes, and if a player with average discipline sees fewer balls than average then they are going to walk less than average.

Will Middlebrooks will most likely be better than he was last season (more of a bounce-back than a breakout), and he might even have a breakout season but it will take more than improved plate discipline for that to happen.

 

All stats are from FanGraphs (used the regular plate discipline stats not the pitch f/x ones) with the exceptions of pitches per PA, 1st pitch swing%, and foul ball stats which are all from baseball-reference.com

Also the quotes are from the Alex Speier article, although I believe they were given to the media in general.


Is Matt Holliday’s Run of Consistency Over?

Ever since Matt Holliday came into the league in 2004, he has been a model of consistency. His WAR increased after each of his first two seasons before peaking at 7.2 WAR in his fourth MLB season. Since reaching 7.2 WAR, Holliday has yet to fall below 4.5 WAR. While Holliday has yet to experience any significant declines in production, he has seen a few areas of his game begin to decline, especially in his power production. For a 34-year-old player, this is not incredibly surprising, but as a power hitter, it is a little concerning. With Holliday heading into his age-34 season, it is important to question whether he is still the model of consistency that he has been since reaching the MLB. For the 2014 campaign, the ZiPS Projection System sees Holliday declining a career high 1.4 wins all the way down to 3.1 WAR. This is still a very respectable total, but it is a quick drop for such a steady performer and could indicate further drops in production.

As I mentioned above, Holliday’s power production has been on a steady decline. His SLG% has declined for 3 straight seasons and settled in at .490 in 2013, which is his lowest SLG% since his rookie campaign in 2004. Holliday’s Isolated Power has dipped each of the past two seasons and even reached a career low of .190 in 2013. Both these numbers are very impressive, especially since they are at or near his career lows; however, they still represent an alarming trend with his power production. As would be expected with a lower SLG% and ISO, Holliday’s HR/FB% has declined for two straight seasons falling to 15%. While Holliday has never been considered a plus fielder, his UZR/150 has declined each of the last 3 seasons all the way down to -7.0. With all these statistics declining, Holliday’s WAR has dropped each of the past three seasons.

While Holliday has seen some dip in his power production, many other areas of his game have improved or stayed relatively constant. Also, despite his SLG and ISO declining, Holliday has still topped 20 homers in each of the past 8 seasons. He has also had a very healthy BB% since 2008, as it has remained above 10% each season and reached 11.5% in 2013, just under his career high of 11.9%. Even more impressive than his steady walk rate is that he lowered his K% to 14.3% in 2013, which was just above his career best K% of 13.8%. Altogether, Holliday was able to set a career best BB/K ratio of .80 in 2013.

In recent years Holliday has maintained both a high Batting Average and a high On-Base Percentage. Holliday has remained such a strong contributor at the plate, despite his worsening power, in large part because his OBP has remained extremely high. OBP is something that usually ages very well, which is encouraging for Holliday because so much of his offensive value hinges on his ability to reach base. In each of the last 7 seasons, Holliday’s wRC+ has been over 140 and was even 148 in 2013. For reference, 100 wRC+ is considered average, so 140 is excellent. There is no doubt that Holliday has remained an outstanding hitter over the past few years, but the real question is whether he will see a significant drop in production as he enters his age-34 season.

While his overall production has remained impressive, it is important to look at his contact rates and balls in play data in order to determine if this production is likely to continue. Throughout his career, Holliday has had an incredibly high Batting Average on Balls In Play (BABIP), with his career BABIP at .343. However, his BABIP dropped to a career low of .322 in 2013. Despite his BABIP falling from the previous season, he was still able to increase his batting average, which suggests he can continue to hit for a strong average even if his BABIP falls a little more. While his SLG and BABIP were down last year, Holliday actually increased his LD% above his career average, but also saw his Infield Flyball% (IFFB%) spike to 13.6%. Another encouraging sign with his LD% increasing was the fact that he also increased his Contact% to 81%, which marked a career high. His high contact rate no doubt helped him cut his K%, which will be important moving forward.

As Holliday continues to age into his mid-30’s, it will be interesting if he can remain the model of consistency that he has been for his entire career. It is clear that Holliday cannot sustain his current level of success for the remainder of his career, but little evidence suggests that 2014 will be the first year he experiences a significant drop in production. His lessening power is not a major concern to his overall game as long as he is able to maintain his high OBP skills and low K%. Turning back to the ZiPS projection of a 3.1 WAR, I do not see Holliday’s production taking that big of a hit, as their projection also calls for a .029 drop in OBP, which seems unlikely given his consistency in being able to get on base and the fact that OBP tends to age well. I expect Holliday to continue his slow decline, but I still see him posting a WAR above 4.0 and an OBP north of .375, especially if he can maintain a BB% in the double digits.


Pitch Count Trends – Why Managers Remove Starting Pitchers

I. Introduction

A starting pitcher should have the advantage over opposing batters throughout a baseball game, yet as he pitches further into the game this advantage should slowly decrease.  The opposing manager hopes that his batters can pounce on the wilting starting pitcher before his manager removes him from the game.  But what would we see if the manager decided against removing his starting pitcher?  The goal of this analysis is to determine the consequences of allowing an average starting pitcher to pitch further into the game instead of removing him.  There are several different ways this situation can unfold for a starting pitcher, but we should be able to tether our expectations to that of an average starting pitcher.

We will focus on how the total pitches thrown by starting pitchers (per game) affects runs, outs, hits, walks, strikes, and balls by analyzing their corresponding probability distributions (Figures 1.1-1.6) per pitch count; the x-axis represents the pitch count and the y-axis is the probability of the chosen outcome on the ith pitch thrown.  Each plot has three distinct sections:  Section 3 is where the uncertainty from the decreasing pitcher sample sizes exceeds our desired margin of error (so we bound it with a confidence interval); Section 1 contains the distinct adjustment trend for each outcome that precedes the point where the pitcher has settled into his performance; Section 2, stable relative to the others sections, is where we hope to find a generalized performance trend with respect to the pitch count for each outcome.  Together these sections form a baseline for what to expect from an average starting pitcher.  Managers can then hypothesize if their own starting pitcher would fare better or worse than the average starting pitcher and make the appropriate decisions.

Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6

II.  Data

From 2000-2004, 12,138 MLB games were played; there should have been 12,150 games but 12 games were postponed and never made up.  During this period, starting pitchers averaged 95.12 pitches per game with a standard deviation of 18.21.  The distribution of pitch counts is normal with a left tail that extends below 50 pitches (Figure 2).  It is not symmetric about the mean because a pitcher is more likely to be inefficient or injured early (left tail) than to exceed 150 pitches.  In fact, no pitcher risked matching Ron Villone’s 150 pitch count from the 2000 season.

Figure 1.1

This brief period was important for baseball because it preceded a significant increase in pitch count awareness.  From 2000-2004, there averaged 192 pitching performances ≥122 pitches per season (Table 2); 122 is the sampling threshold explained in the next section.  Since then, the 2005-2009 seasons have averaged only 60 performances ≥122 pitches per season.  This significant drop reveals how vital pitch counts have become to protecting the pitcher and controlling the outcome of the game.  Now managers more frequently monitor their pitchers’ and the opposing pitchers’ pitch counts to determine when they will expire.

Table 2:  2000-2009 Starting Pitcher Pitch Counts ≥122

Year

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

Pitch Counts ≥122

342

173

165

152

129

81

70

51

36

62

III. Sampling Threshold (Section 3)

122 pitches is the sampling threshold deduced from the 2000-2004 seasons (and the pitch count minimum established for Section 3), but it is not necessarily a pitch count threshold of when to pull the starting pitcher.  Instead this is the point when starting pitcher data becomes unreliable due to sample size limitations.  Beyond 122 pitches, the probabilities of Figures 1.1-1.6 violently waver high and low as very few pitchers threw more than 122 pitches.  A smoothed trend, represented by a dashed blue line and bounded by a 95% confidence interval was added to Section 3 of Figures 1.1-1.6 to contain the general trend between these rapid fluctuations.  But the margin of error (the gap between the confidence interval and the smoothed trend) grows exponentially beyond 3%, so the actual trend could be anywhere within this margin.  Thereby, we cannot hypothesize whether it is more or less likely that the pitcher’s performance will excel or plummet after 122 pitches.

To understand how the 122 sampling threshold was determined, we first extract the margin of error formula (e) from the confidence interval formula (where  zα/2 = z-value associated with the (1-α/2)th percentile of the standard normal distribution, S = standard error of the sample population, n = sample size, N = population size):

Figure 1.1

Next, we back-solve this formula to find the maximum sample size n for when the margin of error exceeds 3%; we use S = 0.5, z2.5% = 1.96, N = 2 pitchers × 12,138 games = 24,276:

Figure 1.1

There is no pitch count directly associated with the sample size of 1,022, but 1,022 can be bounded between the 121 (n=1,147) and 122 (n=971) pitch counts.  At 121 pitches the margin of error is still less than 3%, but it becomes greater than 3% at 122 pitches and begins to increase exponentially.  This is the point the sample size becomes unreliable and the outcomes are no longer representative of the population.  Indeed only 4% (971 of 24,276) of the pitching performances from 2000-2004 equaled or exceeded 122 pitches thrown in a game (Figure 3).

Figure 1.1

A benefit of the sampling threshold is that it separates the outcomes we can make definitive conclusions about (<122 pitches) from those we cannot (≥122 pitches).  If were able to increase the sampling threshold another 10 pitches, we could make conclusions about the throwing up to 131 pitches in a game.  However, managers will neither risk the game outcome nor injury to their pitcher to accurately model their pitcher’s performance at high pitch counts.  Instead, the sampling thresholds have steadily decreased since 2005 and the 2000-2004 period is likely the last time we’ll be able to make generalizations about throwing 121 pitches in a game.

Yet, even for the confident manager, 121 pitches is still a fair point in the game to assess a starting pitcher.  Indeed the starting pitcher must have been consistent and trustworthy to pitch this deep into the game.  But if the manager wants to allow his starting pitcher to continue pitching, he is only guessing that this consistency will follow because there is not enough data to accurately forecast his performance.  Instead he should consider replacing his starting pitcher with a relief pitcher.  The relief pitcher is a fresh arm that offers less risk; he must have a successful record based on an even smaller sample size of appearances, smaller pitch counts, and a smaller margin of error.  The reliever and his short leash are the surer bet than a starting pitcher at 122 pitches.

IV.  Adjustment Period (Section 1)

The purpose of the adjustment period is to allow the starting pitcher a generous period to find a pitching rhythm.  No conclusions are made regarding the probabilities in the adjustment period as long as an inordinate amount of walks, hits, and runs are not allowed.  The most important information we can impart from this period is the point when the adjustment ends.  Once the rhythm is found, we can be critical of a pitcher’s performance and commence the performance trend analysis.

In order to be effective from the start, starting pitchers must quickly settle into an umpire’s strike zone and throw strikes consistently; most pitchers do so by the 3rd pitch of the game (Figure 1.5).  Consistent strike throwing keeps the pitcher ahead in the count and allows him to utilize the outside of the strike zone rather than continually challenging the batter in the zone.  Conversely, a pitcher must also include (pitches called) balls into his rhythm, starting approximately by the 8th pitch of the game (Figure 1.6).  Minimal ball usage clouds the difference between strikes and balls for the batter while frequent usage hints at a lack of control by the pitcher.  Strikes and balls furthermore have a predictive effect on the outcomes of outs, hits, runs, and walks:  a favorable count for the batter forces the pitcher to deliver pitches that catch a generous amount of the strike zone while one in favor of the pitcher forces the batter to protectively swing at any pitch in proximity of the strike zone.

On any pitch, regardless of the count, the batter could still hit the ball into play and earn an out or hit.  Yet as long as the pitcher establishes a rhythm for minimizing solid contact by the 4th pitch of the game (Figure 1.2-1.3), he can decrease the degree of randomness that factors into inducing outs and minimizing hits.  A walk contrarily cannot occur on any pitch because walks are the result of four accumulated balls.  Pitchers should settle into a rhythm of minimizing walks by using minimal ball usage; so when the ball rhythm stabilizes (on the 8th pitch of the game) the walk rhythm also stabilizes (Figure 1.4).  After each of these rhythms stabilizes, a rhythm can be established for minimizing runs (a string of hits, walks and sacrifices within an inning) by the 12th pitch of the game (Figure 1.1).  It is possible for home runs or other quick runs to occur earlier, but pitchers who regularly put their team in an early deficit are neither afforded the longevity to pitch more innings nor the confidence to make another start.

V.  Performance Trend (Section 2)

Each of the probability distributions in Figures 1.1-1.6 provides a generalized portrayal of how starting pitchers performed from 2000-2004, but in terms of applicability they do not depict how an average starting pitcher would have performed.  Not all pitchers lasted to the same final pitch (Figure 2).  The better a pitcher performed the longer he should have pitched into the game, so we would expect each successive subset of pitchers (lasting to greater pitch counts) to have been more successful than their preceding supersets.  Thereby, in order to accurately project the performance of an average starting pitcher the probability distributions need to be normalized, by factors along the pitch count, as if no pitchers were removed and the entire population of pitchers remained at each pitch count.

The pitch count adjustment factor (generalized for all pitchers) is a statistic that must be measurable per pitch rather than tracked per at-bat or inning, so we cannot use batting average, on-base percentage, or earned run average.  The statistic should also be distinct for each outcome because a starting pitcher’s ability to efficiently minimize balls, hits, walks, and runs and productively accumulate strikes and outs are skills that vary per pitcher.  Those who are successful in displaying these abilities will be allowed to extend their pitch count and those who are not put themselves in line to be pulled from the game.

We accommodate these basic requirements by initially calculating the average pitches per outcome x, Rx(t), for any pitcher who threw at least t pitches (where PCt = sum of all pitch counts and xt = sum of all x for all pitchers whose final pitch was t):

Figure 1.1

This statistic, composed of a starting pitcher’s final pitch count divided by his cumulative runs allowed (or the other outcome types), distinguishes the pitcher who threw 100 pitches and allowed 2 runs (50 pitches per run) versus the pitcher with 20 pitches and 2 runs (10 pitches per run).  At each pitch count t, we calculate the average for all starting pitchers who threw at least t pitches; we combine their various final pitch counts (all t), their run totals (occurring anytime during their performance), and take a ratio of the two for our average.  At pitch count 1, the average is calculated for all 24,276 starting pitcher performances because they all threw at least one pitch; the population of starting pitchers allowed a run every 32.65 pitches (Table 5.1).  At pitch count 122, the average is calculated for the 971 starting pitcher performances that reached at least 122 pitches; this subset of starting pitchers allowed a run every 57.75 pitches per game.

Table 5.1:  2000-2004 Pitches per Outcome

Pitch Rate

Pitches per Outcome
(t=1; All Pitchers)

Pitches per Outcome
(t=122; Pitchers w/ ≥122 pitches)

Pitches per Run

32.65

57.75

Pitches per Out

5.37

5.57

Pitches per Hit

15.44

20.38

Pitches per Walk

45.05

44.03

Pitches per Strike

2.38

2.23

Pitches per Ball

2.64

2.62

Starting pitchers will try to maximize the pitches per outcome averages for runs, hits, walks, and balls while minimizing the probabilities of these outcomes, because the pitches per outcome averages and the outcome probabilities have an inverse relationship.  Conversely, starting pitchers will also try to minimize the pitches per outs and strikes while trying to maximize these probabilities for the same reason.  Hence, we must invert the pitches per outcome averages into outcomes per pitch rates, Qx(t), to be able to create our pitch count adjustment factor, PCAx(t), that will compare the change between the population of starting pitchers and the subset of starting pitchers remaining at pitch count t:

Figure 1.1

The ratio of change is calculated for each outcome x at each pitch count t.  The pitch count adjustment factor, PCAx(t), will scale px(t), the original probability of x from the starting pitchers at pitch count t back to the expected probability of x for an average starting pitcher from the entire population of starting pitchers at pitch count t.

The increases to the pitches per run and pitches per hit rates strongly suggest that the 971 starting pitchers remaining at 122 pitches were more efficient at minimizing runs and hits than the overall population of starting pitchers.  The population performed worse than those pitchers remaining at 122 pitches by factors of 176.85% and 131.98% with respect to the runs per pitch and hits per pitch rates (Table 5.2).  Thereby, we would expect the probability of a run to increase from 3.40% to 6.01% and the probability of a hit to increase from 7.21% to 9.51% if we allowed an average starting pitcher from the population of starting pitchers to throw 122 pitches.

Table 5.2:  2000-2004 Average Pitcher Probabilities at 122 Pitches

Outcome

Original Pitcher Probability
px(t=122)

Pitch Count Adjustment
PCAx(t=122)

Average Pitcher Probability
px(t=122) x PCAx(t=122)

Run

3.40%

176.85%

6.01%

Out

19.26%

103.77%

19.98%

Hit

7.21%

131.98%

9.51%

Walk

3.50%

97.72%

3.42%

Strike

45.21%

93.78%

42.40%

Ball

39.44%

99.21%

39.13%

We apply the pitch count adjustment factors, PCAx(t), at each pitch count t to each of the original outcome probability distributions (black) to project the average starting pitcher outcome probabilities (green) for Section 2 (Figures 5.1-5.6); the best linear fit trends (dashed black and green lines) are also depicted.  The reintroduction of the removed starting pitchers noticeably worsened the hit, run, and strike probabilities and slightly improved the out probability in the latter pitch counts.  There were no significant changes to ball and walk probabilities.  These are the general effects of not weeding out the less talented pitchers from the latter pitch counts as their performances begin to decline.

Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6

Next we quantify our observations by estimating the linear trends of each original and average pitcher series and then compare their slopes (Table 5.3).  The linear trend (where t is still the pitch count) provides a simple approximation of the general trend of Section 2 while the slope of the linear trend estimates the deterioration rate of the pitcher’s ability to control these outcomes.  The original pitcher trends show that the way managers managed pitch counts, their starting pitchers produced relatively stable probability trends as if the pitch count little or no effect on their pitchers; only the out trend changed by more than 1% over 100 pitches (2.00%).  Contrarily, the average pitcher trends increased by more than 2% over 100 pitches for the run, out, hit, and strike trends, indicating a possible correlation between the pitch count and the average pitcher performance; the walk and ball trends were unchanged from the original to the average starting pitcher.

We must also measure these subtle changes between the original and average trends that occur in the latter pitch counts of Figures 5.1-5.6.  There is rapid deterioration in the ability to throw strikes and minimize hits and runs between the original and average starting pitchers as suggested by the changes in slope.  The 368.21% change in the strike slopes clearly indicates that fewer strikes are thrown by the average starting pitcher in the latter pitch counts.  The factors of 222.53% and 1206.13% for the respective hit and run slopes indicate that the average starting pitcher is not only giving up more hits but giving up more big hits (doubles, triples, home runs).  There is a slight improvement in procuring an out (14.45%), but the pitches that were previously strikes became hits more often than outs for the average starting pitcher.  Lastly, the abilities to minimize balls (4.87%) and walks (8.23%) barely changed between pitchers, so control is not generally lost in the latter pitch counts by the average starting pitcher.  Therefore, the average starting pitcher isn’t necessarily pitching worse as the game progresses but the batters may be getting better reads on his pitches.

Table 5.3:  Section 2 Linear Trend

Linear Trend

Correlation

Trend

Range

Original
Pitcher

Average
Pitcher

% Change in Slope

Original Pitcher

Average Pitcher

Run Probability

[12,121]

0.03+0.16×10-4t

0.02+2.13×10-4t

1206.13%

0.17

0.8

Out Probability

[4,121]

0.18+2.00×10-4t

0.18+2.30×10-4t

14.45%

0.75

0.76

Hit Probability

[4,121]

0.06+0.66×10-4t

0.06+2.12×10-4t

222.53%

0.54

0.85

Walk Probability

[8,121]

0.02+0.74×10-4t

0.02+0.78×10-4t

4.87%

0.57

0.6

Strike Probability

[3,121]

0.43-0.50×10-4t

0.44-2.33×10-4t

368.21%

-0.19

-0.7

Ball Probability

[8,121]

0.39-0.97×10-4t

0.39-1.05×10-4t

8.23%

-0.29

-0.32

The correlation coefficients also support our assertion that the average starting pitcher became adversely affected by the higher pitch counts, but even the original starting pitcher showed varied signs being affected by the pitch counts.  There were moderate correlations between the pitch count and hit and walks and a very strong correlation between the pitch count and outs.  So even though some batters improved their ability to read an original starting pitcher’s pitches, this improvement was not consistent and the increases to hits and walks were only modest.  Contrarily, the original starting pitcher did become more efficient and consistent at procuring outs as the pitch count increased.   We also found weak correlations between the pitch count and strikes and balls for the original starting pitcher, so strikes and balls were consistently thrown without any noticeable signs of being affected by the pitch count.   However, out of all of our outcomes, the pitch count of the original starting pitcher had the weakest correlation with runs.  Either the original starting pitchers could consistently pitch independent of the pitch count or their managers removed them before the pitch count could factor into their performance; the latter most likely had the greater influence.

It is also worth noting the intertwined patterns displayed in Figures 5.1-5.6 and Table 5.1.  Strikes and balls naturally complement each other, so it should come as no surprise that the Strike Probability Series and Ball Probability Series also complement each other; a peak in once series is a valley in the other and vice-versa.  The simple reason is that strikes and balls are the most frequent and largest of our outcome probabilities – they are used to setup other outcomes and avoid terminating at-bats in one pitch.  However, fewer strikes and balls are thrown in the latter pitch counts as evidenced by the decline in the Strike and Ball Probability Series, which make the at-bats shorter.  Consequently, there are fewer pitches thrown between the outs, hits, and runs, so these other probability series increase.  Hence, the probabilities of outs, hits, and runs become more frequent per pitch as the pitch count increases (further supported by the drop in pitches per strike and ball rates in Table 5.1).

VI.  Conclusions

Context is very important to the applicability of these results, without it we might conjecture that these trends would continue year over year.  Yet, the 2000-2004 seasons were likely the last time we’ll see a subset of pitchers this large pitching into extremely high pitch counts.   Teams are now very cautious about permitting starting pitchers to throw inconsequential innings or complete games, so the recent populations of starting pitchers have shifted away from the higher pitch counts and throw fewer pitches than before.  Yet, these pitch count restrictions should not affect the stability of our original probability trends.  The sampling threshold will indeed lower and the length of stable Section 2 will shorten, but the stability of the current original trends should not compromise.  Capping the night sooner for the starting pitchers only means they are less likely to tire or be read by batters.

We also cannot generalize that these original probability trends would be stable for any starting pitcher.  The probability trends and their stability are only representative of the shrinking subset of starting pitchers before their managers removed them due to performance issues, injury, strategy, etc.  These starting pitchers subsets may appear unaffected by the pitch count, but their managers created this illusion with the well-timed removal of their starting pitchers.  They understand the symptoms indicative of a declining pitcher and only extend the pitch count leash to starting pitchers who have shown current patterns of success.  Removing managers from the equation would result in an increased number of starting pitchers faltering in the latter pitch counts as their pitches are better read by batters.  Likewise, any runners left on base by the starting pitcher, but now the responsibility of a relief pitcher, would have an increased likelihood of scoring if the starting pitchers were not removed as originally planned by their managers.  Starting pitchers do notice these symptoms and may gravitate to finishing another inning, but each additional pitch could potentially damage the score significantly.  Trust in the manager and let him bear the responsibility at these critical points.