We’re halfway through November and the winter meetings are right around the corner. Teams are gearing up for next year and taking a look at their rosters, deciding what direction they want their team to head. Today I want to look at the Toronto Blue Jays and hypothesize a direction they could go.

The Blue Jays had a great 2015 and continuing that momentum is crucial for the newly recharged fan base. They have a number of quality young players who contributed this past year. Kevin Pillar, Chris Colabello, Ryan Goins, Marcus Stroman, Roberto Osuna and Devon Travis (when healthy) all had nice seasons and remain under team control in some shape or form for the next 3-5 years. The Jays also have some large expiring contracts after the 2016 season in the form of R.A. Dickey, Edwin Encarnacion and Jose Bautista who have been important pieces to Toronto’s success. Add in Russell Martin, Josh Donaldson and Troy Tulowitzki and the Blue Jays should once again compete in the AL East in 2016. One of the glaring issues however is their starting rotation and bullpen.

With Marco Estrada signed the Blue Jays have a starting rotation of Dickey, Stroman, Estrada and Hutchison. Reports have come out and the Jays will reportedly have a similar budget to last year, around $140 million. After the guaranteed contracts, arbitration estimates and league-minimum salaries are accounted for the Blue Jays will have about $18-$19 million to spend on starting pitching and bullpen help. There are a number of directions the Blue Jays could go; it’s a solid class of starting pitching this year and with the $18 million left in the salary they could for sure pick up a quality starting pitcher to fill out the rotation. They could also spent the money on a lockdown relief pitcher and try to transition either Aaron Sanchez or Roberto Osuna to the rotation. Or they could split up the money and get an older starting pitcher and get whatever reliever is available for the remainder of the money. Another option, and the one that I’m going to explore, is the trade route.

With all the moves the Blue Jays made at the deadline, their farm system isn’t as strong as it was at midseason last year but the recent developments with the Atlanta Braves got me thinking about trade ideas — mainly Julio Teheran. With the Braves set to open a new stadium in 2017 the mentality has been to shed money and stock prospects for the opening season in the new stadium. This works out great for the Blue Jays who have some talent left in the farm system that could be useful to the Braves. The fourth-ranked prospect in the Blue Jays system and coincidentally the fourth-ranked catching prospect in baseball is Max Pentecost. Atlanta has been stocking arms in recent trades but with Christian Bethancourt struggling in his time in the majors, the Braves clearly don’t have a long-term solution behind the dish. The former 1st round pick, 11th overall is currently in advanced-A ball and his estimated time of arrival in the majors is 2017, perfect for their rebuilding plans. If the Jays were to include one maybe two young pitchers on a similar timeline like Conner Greene and/or Marcus Smoral, perhaps that would be enough to pluck Teheran away from Atlanta.

Teheran is only 24 years old and will turn 25 for the 2016 season. He’s owed a bargain-basement price of $3,466,666 for next season, is under contract through 2019, and has a club option for 2020. With starting pitcher salaries estimated anywhere from $10-$25 million and up this offseason, Teheran and his $3.5 million in 2016 season seem like a steal. Plus the Blue Jays would be getting Teheran for the prime years of his career and although last year was an off year, he’s shown signs of being an ace. Teheran would complete the starting rotation for the Jays in 2016 and after Dickey’s contract expires, Toronto would be left with a rotation of Stroman, Teheran, Hutchison and Estrada for the 2017 season. The other nice thing about Teheran is that his $3.5 million contract leaves Toronto with roughly $15.5 million left over to fill out the bullpen or upgrade other areas. Teheran would be an affordable and valuable piece to a rotation that desperately needs it and would be far better then spending 3 to 4 times his annual 2016 salary on a pitcher that may already be or not far away from the decline of his career.

As I mentioned above, with the money saved on the Teheran trade, the Blue Jays could add a piece to the bullpen or upgrade other areas but in compiling data for this article, I got to thinking about what the Jays could do for the future. 2017 has roughly $36 million coming off the books for Toronto and with a young core of controllable players, the Jays have some room to make a move. One of the contracts expiring is RF Jose Bautista. I personally think the Jays should re-sign Bautista after 2017 but I don’t think putting him in right would make sense. With Encarnacion’s contract set to expire as well, the DH spot would be available for Bautista, should he choose to stick around. That would leave RF empty and looking at the outfield class of 2017 (Beltran, Suzuki, Gregor Blanco, Josh Reddick, Brandon Moss, Mark Trumbo and of course Bautista) the group leaves something to be desired.

That brought me to the 2016 class, led by arguable the best right fielder in the game, Jason Heyward. The Jays have been rumored to be after SP free agents David Price and Zack Greinke but for the amount of money they’ll command and the stages they’re at in their career, I think the money might be better spent on a player whose best days are ahead of him. That in my opinion is Jason Heyward. We know Heyward is a solid player, who’s shown flashes of brilliance and is young enough to still put it all together consistently. In a lineup like the Blue Jays’, Heyward would thrive much the way Josh Donaldson officially broke out as a superstar last year. Heyward would have the protection and opportunities to truly develop into the player he’s about to get paid to be. The problem with signing Heyward would be the Blue Jays would have to free up a sizable amount of money and the only real place to look is at shortstop in the form of Troy Tulowitzki.

Tulowitzki was a surprise addition for the Blue Jays last year and definitely added strength to an already dangerous lineup but with the depth that Toronto has with Ryan Goins able to play SS and the return of Devon Travis, the 31-year-old Tulowitzki becomes an expensive option for the remainder of his career. Perhaps the Jays should trade Tulowitzki to free up money to sign Heyward to a long-term deal? Instead of watching the expensive decline of Tulo for the remainder of his contract, Toronto could still sell high to a team willing to take on the contract, receiving bullpen help and possibly an extra outfielder to help address current needs.

I then started going through MLB teams to see which ones would possibly be in a situation to make the trade happen. The Diamondbacks, White Sox and Mets all stood out as possible suitors while the Rangers, Yankees, Padres and Mariners also seemed like possible options. For the purposes of this article I’m only going to focus on the first three.

With a 2015 budget of about $76,622,575 million the Arizona Diamondbacks definitely have room to financially take on Tulo’s contract; the question is, is that where LaRussa and Dave Stewart want to take the team? None of us truly know but if the asking price is right, perhaps Randall Delgado and Ender Inciarte, maybe the thought of Tulo and Goldschmidt would fit their plans. They did spend $68.5 million for 6 years of Yasmany Tomas and with the emergence of David Peralta and A.J. Pollock, the Diamondbacks have outfielders to spare. If the trade were to go through the Blue Jays would gain about $18,487,000 giving them a total available amount of about $33,980,334. That would definitely be enough to sign Heyward to a 7-10 year deal (depending on what the market drives his year amount to) at anywhere from $20-$29 million per season. With the $36 million coming off the books in 2017, Toronto would have about $37 million to spend on the DH spot (Possibly Bautista) and SP or RP spot open (depending on how they handle Sanchez and Osuna). Compared to the $50 million amount they could have in 2017 minus whatever they pay for a starting pitcher this off season. In reality that $50 million would probably be more like $30-$35 million with two rotation spots available as well as the DH. If the Teheran trade and Heyward signing were to happen, here is what the 2016 and 2017 Blue Jays lineup would look like.

2016 Lineup                2017 Lineup

C = R. Martin                C = R. Martin
1B = E. Encarnacion    1B = C. Colabello
2B = D. Travis              2B = D. Travis
3B = J. Donaldson       3B = J. Donaldson
SS = R. Goins                SS = R. Goins
LF = B. Revere              LF = B. Revere
CF = K. Pillar                CF = K. Pillar
RF = J. Heyward         RF = J. Heyward
DH = J. Bautista          DH = ?

SP = R.A. Dickey                 SP = M. Stroman
SP = M. Stroman                 SP = J. Teheran
SP = J. Teheran                   SP = D. Hutchison
SP = D. Hutchison            SP = M. Estrada
SP = M. Estrada                   SP = ?

RP = R. Osuna                     RP = R. Osuna
RP = A. Sanchez                  RP = A. Sanchez
RP = L. Hendricks              RP = L. Hendricks
RP = B. Cecil                        RP = B. Cecil
RP = R. Delgado                  RP = R. Delgado
RP = S. Delabar                   RP = S. Delabar
RP = A. Loup                        RP = A. Loup

BN = E. Inciarte                   BN = E. Inciarte
BN = J. Thole                        BN = D. Pompey
BN = C. Colabello                 BN = ?
BN = D. Barney                     BN = ?

If Heyward’s contract was structured so that his first year was set at $20 million, the Jays would enter 2016 with about $13-$14 million left in the budget for any additional moves. It would also shore up right field a year before it’s an issue while upgrading the bullpen and perhaps leading the way for Sanchez or Ozuna to enter the rotation for 2017. The point is Toronto has money coming available next year but in order to get the player that best fits their future needs, they might have to make a move now instead of waiting till next year.

The next team I thought might make sense as a trade partner was the Chicago White Sox, who recently released long time SS, Alexi Ramirez. The White Sox had a budget of $118,860,487 in 2015 and were supposed to be contenders with the additions of Melky Cabrera, Jeff Samardzija, David Robertson and Adam LaRoche but instead fell way short and put together an all-around forgettable season. With the release of Ramirez, shortstop seems to be an area of need for Chicago, and Tulowitzki with Abreu, Cabrera and LaRoche would be a great fit on the south side.

Unlike the Diamondbacks however the White Sox don’t have as much potential new money available, so off-setting the cost of Tulo’s contract would have to be taken into account when thinking about a trade. Someone like Zach Duke, who is owed $5,000,000 over the next two years might be a good addition to the Toronto bullpen. If the Sox would somehow include often-injured Avisail Garcia, this trade might really swing in Toronto’s favor but really saving money for a Heyward run would be more important then any name on the back of a jersey.

For argument’s sake I’m going to use the Duke/Garcia for Tulowitzki trade as an example. The difference in salaries would be about $12.7 million and that added to the $15,493,334 left over after the Teheran trade, Toronto would have about $28,193,334 left over to make Heyward an offer. And again, if the contract was structured so that the first year paid Heyward $20 million, the Blue Jays would have about $8 million left over for additional offseason/mid-season upgrades.

The last team that I thought would make sense for a potential Tulo trade was a team that was linked to him while he was still in Colorado, the New York Mets. Coming off a spectacular run to the World Series, the Mets are set to lose Yoenis Cespedes and Daniel Murphy to free agency. In 2015 they had a payroll of $120,415,688 and Cespedes and Murphy combined for $11,729,508 of that total budget, over half of what Tulowitzki is owed going into 2016. For the Mets, their quality rotation is under team control or earlier arbititration for the next few years, so continuing the winning environment at a fraction of the cost is of utmost importance. The health of David Wright is suspect and with a nice young group in Conforto, d’Arnaud, Duda, and Lagares, trading for someone of Tulo’s caliber might help their development and continue the winning environment.

The Mets would be in the same situation that the White Sox are — they can’t add too much salary, so off-setting costs would play into the equation. If the Mets traded Jonathan Niese, who’s owed about $9 million in 2016, and Kirk Nieuwenhuis, they’d clear about $10,688,729. Add that with the money saved from letting Murphy and Cespedes walk and they could easily bring in Tulowitzki’s contract. The Blue Jays would have about $26 million to work with and again, if Heyward’s first year was set at $20 million, they’d have about $6,182,063 to work with for offseason/mid-season upgrades.

All of this is unauthorized speculation but I do think that the Blue Jays are in a unique situation where they can really make some moves that could set them up for years of success. Chasing the big-name starting pitchers may seem like the obvious move but taking advantage of other team’s situations could allow them to acquire elite talent for minimal cost and the money saved on starting pitching could be used to solve future needs that aren’t quite here yet. As always, thanks for reading and let me know what you think.

Since the Rockies have started playing baseball in Colorado, they’ve continually run into the same problem: pitching. We’re all familiar with the situation — the altitude and thin air create a hitter’s haven and a nightmare for pitchers, particularly starting pitchers. The Rockies have tried to remedy the situation in the past by bringing in top-tier starting pitchers, only to have them struggle. In 2012 and ’13 they tried a four-man rotation with a 75-pitch limit which led to a 64-98 record and a 5.22 team ERA. 2013 was a bit more successful, as they finished with a 74-88 record and a 4.44 team ERA. Still it wasn’t good enough to contend for a playoff spot and definitely not good enough to compete for a World Series title. In fact, in 2007 when the Rockies had their only World Series appearance, they carried a team ERA of 4.32. Only four teams since 2007, including the Rockies, have had a team ERA of over 4.00 and made it to the Fall Classic. The others were the 2009 New York Yankees and Philadelphia Phillies and the 2010 Texas Rangers. As the Mets and Royals have shown us this year, quality starting and relief pitching can take you pretty far in this game. My question is, with all the different strategies the Rockies have tried, what can they do differently to compete?

My suggestion is a slight tweak on an idea that Dave Fleming wrote about in 2009 called the 3-3-3 Rotation. In his article he describes the 3-3-3 Rotation as three pitchers, pitching three innings, every third day with a pitch limit of 40-60 pitches. By having a pitcher essentially go through the order one time, it allows them to give it all they have for a short time instead of conserving their energy for the later innings. In theory, this makes sense. Look at the Royals the past few years; they’ve turned a number of former starting pitchers into relievers and most, if not all have found success in their new roles. In his first year as a starter in 2008, Luke Hochevar had an opponents batting average of .243/.289/.319 the 1st, 2nd and 3rd time through the order. His last year as a starter in 2012 was a little bit better with a .288/.263/.294 BAA but his best season in the majors came as a reliever in 2013 when he held opponents to a .169 BAA.

This may hit a little too close to home for Rockies fans but last year Franklin Morales as a starter for Colorado had a split of .300/.337/.220; in his first year with the Royals out of the pen he held opponents to a .246 BAA. Staying with the Kansas City bullpen, we can look at Wade Davis, who actually had declining BAA numbers in his last year as a starter — .280/.251/.236 — but still posted a solid .151 BAA in his first season in relief. Andrew Miller had a split of .336/.261/.300 in his last year as a starter in 2011; his first year as a reliever in 2012 was significantly better with a .194 BAA. Zach Britton is a similar case with a .272/.266/.293 BAA split in his last year as a starter in 2011 and a .180 BAA in 2012 as a bullpen piece. The point is, generally speaking, when a major-league hitter has a chance to see a pitcher three times in one game, the advantage shifts to the hitter, and if a pitcher with quality stuff can face the order once, the advantage goes to the pitcher. This point is even more important for the Rockies who can’t afford to give their opponents any more advantages when playing in Colorado.

The Rockies have always struggled to attract top-tier starting pitching, since no one really wants to inflate their numbers by pitching half of their games at Coors Field. Colorado has tried to draft and develop power arms who rely on strikeouts and ground balls more so than fly-ball pitchers but still the results are the same ;; a sub-.500 team with an ERA over 5.00, which is not a recipe for success. The average major-league team has five starting pitchers and carries seven relievers in their bullpen. My tweak on Dave Fleming’s 3-3-3 rotation would be to split the 12 pitchers into four groups of three, all with a pitch count of 40-60 depending on effectiveness. In a perfect world every pitcher would go through the order once, throwing anywhere from 30-60 pitches and then turning the ball over to the next guy up who would hopefully do the same thing.

But we don’t live in a perfect world so by having four groups of three, each pitcher could be shifted around depending on the amount of pitches thrown in a week, meaning an effective pitcher could pitch as much as three to four times a week. The average starting pitcher in the majors pitches once maybe twice a week, each time throwing anywhere between 70-120+ pitches depending on the outing; by splitting up that workload they could see action three to four times a week. The average reliever definitely pitches less innings, around 70-80, and in turn throws less pitches but many major-league relievers spent time in the minors as starters, throwing 100+ innings a season. The workload is definitely something to monitor but in 2015 the Rockies used 29 different pitchers. The average amount of innings that a team played was 1,447, and the Rockies staff as a whole pitched 1,426.1 innings. So between the 29 different pitchers, you could keep arms fresh and put pitchers in a position to succeed.

Which brings me to my next point — putting pitchers in a position to succeed. When an offense has a strong 3 and 4 hitter, a manager may put a young player in the 2nd spot instead of lower in the order to ensure that the young player will see strikes. A pitcher never wants to walk someone in front of a player who can crush it out of the park. This leads to more balls seen in the strike zone, hopefully leading towards a positive result, Josh Donaldson is a great example of that this year. Joe Maddon has also implemented a strategy to set young Addison Russell up for success by having him bat 9th after the pitcher instead of 8th before the pitcher. The logic is the same — Russell will see more strikes because opposing pitchers don’t want to walk him and turn the lineup over to their heavy hitters.

I believe the 3-3-3 rotation does this for pitchers, especially pitchers in Colorado. The Rockies had a collective split of .298/.339/.351 the 1st, 2nd and 3rd time through the order in 2015. By having their pitchers face the opposing lineup once, it allows them to display all of the pitches right away. Instead of establishing your A and B pitches the first time through the order and showing your C and possibly D pitches through the second and third time, a pitcher can show all of them through the first three innings. This creates confusion for the hitters and also forces them to be more aggressive at the plate early, something that can be taken advantage of if properly executed. It’s also worth mentioning that some of the best offenses in the game do a tremendous job of communicating with their teammates about the pitcher and the pitches they’re seeing. Remember, the more familiar the pitcher is to the batter, the more advantage the batter has. If you can remove that advantage from the opposing offense, it further sets your pitching staff up for success. Opposing teams would have to have different game plans for each pitcher they see, and those quick adjustments aren’t the easiest to make throughout a 162-game season.

All in all it’s an experiment and besides Tony LaRussa trying something similar for a week in 1993, there hasn’t been another team to try this method. For many teams, the classic five-man rotation works and who am I to say they’re wrong but the Rockies have never really been able to figure it out and if any team is in a position to give it a shot, I believe it’s them.

Recently, Dave Cameron examined a planned back-pick by Russell Martin and the Blue Jays in Game 1 of the ALDS.  The play didn’t have a chance to happen because Delino DeShields put a 2-1 change up in play.  Not just in play, but on the ground to directly where the second baseman Ryan Goins would have been had he not been breaking for second in anticipation of the pick.  Dave wrote a great article that covered the play in depth, so feel free to go read it here.  In this article, I analyze the strategy of calling for a set pickoff attempt. What I found not only vindicates Martin and the Jays, but also questions one of my longest-held beliefs about pickoffs.

My strategy for evaluating the set pickoff was to calculate the break-even point (BEP) for a pickoff attempt using Run Expectancy (RE), similar to previous analyses on bunting and stealing. To calculate the BEP for a given pickoff attempt, I calculated the RE benefit (to the defense) of an out and the weighted RE cost of a safe call or an error.  This sounds simple enough, but calculating the RE after an error involved some guesswork.

Although errors can result in multiple outcomes, I chose to pick one outcome for each base to simplify the analysis. Thus, I assumed 2 bases for all runners on an errant throw to first, 1 base for all runners on an error to second, and, after much thought, 2 bases for runners on second and 1 base for runners on the corners on an error to third. If you have data that can replace these assumptions, please let me know.  Otherwise, be cognizant of my assumptions when you attempt to make use of the findings.  For example, if there is a slow runner on second, the BEP for a pickoff attempt to a corner will be overly conservative (inflated).  Additionally, I didn’t differentiate between pickoff attempts from the pitcher and the catcher.  The pitcher has a shorter, unobstructed throw, and favorable balk rules when picking to second or third, but still has to deal with the risk of a balk, especially to first, along with the added difficulty of throwing off the mound.  Finally, while calling for a back-pick from the catcher can put a defender out of position, I chose to ignore this factor because a) I assume it is rare for a hitter to find the vacated hole, and b) the defense can choose to avoid contact.

In order to weight the cost of a failed pickoff attempt appropriately, I had to estimate what the error rate would be on attempts.  While we do have data on pitcher error rates on pickoff attempts (around 0.95%), the data are only from throws to first.  Set pickoff plays are more challenging for the defense, so the error rate should be higher than on typical attempts to first.  My solution, in lieu of empirical data from actual set pickoff attempts, was to estimate catchers’ throwing error rates from the 2015 season.  I chose this strategy for two reasons: First, catchers are one of the primary players who can attempt a set pickoff, so it made sense to sample from their performance.  And second, catchers accumulate a large portion of their assists under similar conditions to the pickoff attempt (for example, in 2015 nearly 40% of all catcher assists came from caught stealing).  Thus, I expected catcher throwing error rates to approximate the error rates we would observe on set pickoff plays.

While not a perfect method, I estimated catcher throwing error rate as Throwing Errors / Assists + Throwing Errors + Stolen Bases.  The mean throwing error rate in a sample of catchers (n = 38) who played at least 500 innings in 2015 was 3.6%.  Do you accept that set pickoff plays will result in 3.8 times more errors than typical pickoff throws to first? If not, adjust your own estimates accordingly.

Using the estimated throwing error rate for catchers, the formula for estimating the BEP on a set pickoff attempt is RE cost / (RE cost – RE benefit). In this equation, RE benefit = RE after a pickoff – RE before a pickoff; RE cost = RE before a failed attempt – RE with a failed attempt, and RE with a failed attempt = (RE of a safe call *.964) + (RE of an error *.036).  Using the RE tables found here, I generated Table 1 below.

Table 1.  Success rate required to attempt a pick at each base.

Table 1 presents the BEP for the defense of (successful pickoffs / attempts) X 100.  In other words, Table 1 provides the minimum expectation of success required for the defense to attempt a set pickoff and it be a break-even strategy. Unfortunately, it is difficult to guess how successful set pickoff attempts typically are.  In Dan Malkiel’s study of pickoffs to first, he found that righties and lefties were successful about 2% and 4% of the time, respectively.  However, Malkiel’s study sampled situations with base-stealers on first, so the stolen-base rate was between 17% and 21%.  It’s impossible to know what percentage of successful pickoffs occurred when the runner intended to steal, but it’s safe to say 2% and 4% success rates are a little high if the runner on first isn’t planning on going. Set pickoffs usually work differently than throws to first, since neither the pickoff nor the steal are always expected. Therefore, the data on picks to first can only serve as a point of reference, helping to calibrate expectations rather than serving as predictions themselves.

One way to assess if teams are over- or under-utilizing set pickoffs is to compare their pickoff to error ratios with the BEPs for that metric. Unfortunately, I could only find data for one special case of the set pickoff: a catcher back-pick to first.  In the Malkiel study, successful back-picks were 96% of back-picks plus errors.  If we assume an error puts the runner on third, the BEP for pickoffs/pickoffs + errors is 50%, suggesting that catchers have room to get much more aggressive in attempting to pick runners off first.  Without more data, it’s difficult to comment further on current MLB behaviour regarding set pickoff plays. Nevertheless, the estimates in Table 1 provide interesting insights into the risks and rewards of pickoff plays. Below, I list six lessons that can be gleaned from Table 1.  At least two of these lessons fly directly in the face of my own long-held beliefs, and maybe yours too!

Lesson 1

If, at any time, the defense notices that it has better than a 15% chance of picking off a runner, they should attempt the pickoff.

Lesson 2

Pickoff attempts require greater confidence with two outs, with three exceptions.  Often, the required success rate is over 5%, requiring a fairly egregious mistake by the runner to warrant a throw. The exceptions to this rule are with a runner on first, a runner on second, or a pick to second with runners on first and second.

Lesson 3

A runner on second with no runner ahead of him should probably be targeted frequently.  The BEPs are consistently low for attempting the pickoff to second, while the runner is motivated to be aggressive by the chance to score a run or steal third. Even failed attempts have the favorable by-product of keeping the runner close, a factor not considered in Table 1.

Lesson 4

Throwing behind the runner on first with runners on first and second or the bases loaded is dangerous.  This doesn’t mean it’s a bad play if the runner on first opens the door, but the defense should be really confident to make the throw.

Now for the lessons that go against everything I thought I knew…

Lesson 5

Pitchers should throw over to third with runners on 1^st and 3^rd in a steal situation.  Ever since the MLB outlawed the fake-to-third move, pitchers haven’t been allowed to bluff the throw in hopes of catching the runner breaking from first.  Based on Table 1, it seems strange that pitchers ever faked the throw to begin with.  With no one out, the defense would only need to pick the runner off third 8 times per 1000 attempts, or nail the runner stealing second 3 times per 100 attempts, or a combination of the two to break even.  Additionally, if the runner on first breaks for second it’s an easier throw from third than from first, which was often the result with the fake-to-third move.  While many old-school baseball people will object to throwing over to third, the common refrain “he’s not going anywhere!” doesn’t necessarily apply to the 1^st and 3^rd steal situation.  The runner could be trying to get closer to home so he can steal on the catcher’s throw to second, making it the perfect time to throw over.  Although the third baseman’s positioning will sometimes make a true pickoff attempt at third difficult, the rules do not require the pitcher to throw directly to third.  Thus, teams can make legitimate efforts to get the runner on third when the situation allows it, while other times making throws away from the base solely to catch the runner on first breaking for second.

Lesson 6

The situation that requires the lowest probability of success to attempt a pickoff is when there is a runner on third with no one out.  The defence needs to nab merely 2 runners out of every 1000 attempts to break even. And get this, the BEP on pickoff attempts to third with 0 out is lower than the BEP for typical throws to first, even with the much lower error rate on throws to first (0.95%), and even after adjusting the assumed cost of an error to one base.  Holding probability of success constant, the pickoff attempt to get a runner on third with 0 out is the least risky pickoff attempt possible. The LEAST risky.

Of course, a runner who is on third with no one out should be taking no chances.  But that doesn’t mean a pickoff will never work…

The timeless struggle between pitcher and batter is one of dominance — who holds it and how. Both players use a repertoire of techniques to adapt to each other’s strategies in order to gain advantage, thereby winning the at-bat and, ultimately, the game.

These strategies can rely on everything from experience to data. In fact, baseball players rely heavily on data analytics in order to tell them how they’re swinging their bats, how well they’ll do in college, how they’ll perform at Wrigley versus Miller.

Big data has been used in baseball for decades — as early as the 60s. Bill James, however, was the first prominent sabermetrician, writing about the field in his Bill James Baseball Abstracts during the 80s. Sabermetrics are used to measure in-game performance and are often used by teams to prospect players.

Baseball fans familiar with sabermetrics, the A’s, and Brad Pitt have likely seen Moneyball, the Hollywood adaptation of Michael Lewis’ book. The book told the story of As manager Billy Beane’s use of sabermetrics to amass a winning team.

Sabermetrics is one way baseball teams use big data to leverage game theory in baseball — on a team-wide scale. However, by leveraging their data through the concepts of game theory on a smaller scale, baseball teams can help their men on mound out-duel those at the plate.

Game theory studies strategic decision making, not just in sports or games, but in any situation in which a decision must be made against another decision maker. In other words, it is the study of conflict.

Game theory uses mathematical models to analyze decisions. Most sports are zero-sum games, in which the decisions of one player (or team) will have a direct effect on the opposing player (or team). This creates an equilibrium which is known as the Nash equilibrium, named for the mathematician John Forbes Nash. What this means is that if a team scores a run, it is usually at the expense of the opposing team — likely based on an error by a fielder or a hit off a pitcher.

In the case of pitching, game theory — especially the use of the Nash equilibrium — can be used to predict pitch optimization for strategic purposes. Neil Paine of FiveThirtyEight advocates using big data and sabermetrics to analyze each pitch in a hurler’s armory, then cultivating the pitcher’s equilibrium — the perfect blend of pitches that will result in the highest number of strikeouts, etc.

Paine has gone so far as to create his own formula, the Nash Score, to predict which pitcher should throw which pitches in order to outwit batters.

In perfect game theory, the Nash equilibrium states that each game player uses a mix of strategies that is so effective, neither has incentive to change strategies. For pitchers, Paine’s Nash Score uses their data to find the optimal combination of pitches to combat batters, including frequency.

Paine does point out that creating this kind of equilibrium in baseball can be detrimental to a pitcher. He is, after all, playing against another human being who is just as capable of using game theory to adapt strategies to upset the equilibrium.

If a pitcher’s fastball is his best, and his Nash Score shows that he should be using it more often, savvy hitters are going to notice. “ . . . In time, the fastball will lose its effectiveness if it’s not balanced against, say, a change-up — even if the fastball is a far better pitch on paper,” writes Paine.

In this case, a mixed strategy is the best — in game theory, mixed strategies are best used when a player intends to keep his opponent guessing. Though pitch optimization using Paine’s Nash Score could lead to efficiency, allowing pitchers to throw fewer pitches for more innings, it could also lead to batters adapting much quicker to patterns, thus negating all the work.

Prior to the August, 2015, non-waiver trade deadline, the Toronto Blue Jays sent their leadoff hitter Jose Reyes to the Colorado Rockies for Troy Tulowitzki, a classic middle-of-the-order bat. Everyone assumed from his career power numbers that Tulowitzki would slot in the heart of the Jays order, but with Josh Donaldson, Jose Bautista, and Edward Encarnacion already comfortably set at 2-4 (over 200 RBIs between them at the time) they instead used him in the vacated leadoff spot. The move seemed to work as Tulo went 3 for 5 in his first game, and the Jays proceeded to rattle off a tidy 11-0 streak with their new top-of-the-order guy.

Troy Tulowitzki Shortstop B/T: R/R .297 / .370 / .510 29 HR 100 RBI 8 SB

José Reyes Shortstop B/T: B/R .290 / .339 / .432 12 HR 65 RBI 50 SB

One doesn’t mess with success, but everyone knows Tulowitzki is not an ideal leadoff hitter, never having batted there before in his 10-year MLB career, and with all of 3 stolen bases in the last 3 seasons. His above-average pop suggests a traditional run-producing spot: 29 HR and 100 RBI career numbers over an averaged 162-game season (Baseball-Reference.com), but with the Jays on a 22-5 tear, Tulo, touch wood, wasn’t moving anywhere.

A leadoff hitter naturally gets more at bats per season, one reason Jays manager John Gibbons gave for putting Tulowitzki at the top of the order, given his career .297 BA and .370 OBP. But tradition and common sense dictate that top RBI men are more valuable with men on base, impossible for a leadoff man in the first inning, and presumably sub-optimal afterwards. As Tulowitzki’s new teammate 3B Josh Donaldson noted in the midst of an August run that saw the Jays go from 6 back of the Yankees to 1 1/2 up in the AL East, “I feel like every time I’m coming up I have someone in scoring position or someone on base.” Exactly.

Fine-tuning a lineup is an argument for the ages, but can we determine where a power hitter should bat, where his numbers best fit 1 to 9? Should high-average batters hit before the sluggers, or should we just bat 1-9 in order of descending batting average (or OBP)? Can we calculate how to arrange a team’s lineup to maximize the optimum theoretical run production?

Enter Monte Carlo simulations, used to model the motion of nuclei in a DNA sequence, temperatures in a climate-change projection, even determine the best shape and size of a potato chip. In Do The Math!, Monte Carlo simulations were used to calculate where a Monopoly player will most likely land (Jail and Community Chest, followed by the three orange properties: St James, Tennessee, and New York), and whether to hit or stick in Black Jack against any dealer’s up card.

In some cases, algebraic probabilities are difficult (using Markov chains, a continuously iterative system with a finite countable sample space), whereas brute force computation does the trick over a large number of trials. If a picture is worth a thousand words, a simulation is worth a thousand pictures.

BOO V1 (Batting Order Optimization Version 1) is a Monte Carlo program written in Matlab that randomly selects a hit/out event over a 9-inning, 27-out game, averaged over a large number of games, e.g., 1 million. It uses a flat lineup where all hitters have a .333 OBP (roughly the Jays average), but doesn’t include errors, hit batsmen, sacrifices, double plays, stolen bases, etc., or opposing pitchers’ numbers. (In Part II, I will include the hitting stats of a real lineup: 1B, 2B, 3B, HR, BB, K, GO/AO.)

The mathematical guts are fairly simple, essentially a random number generator and some modulo math (think of leap-frogging 3 or more chairs at a time in a circle of 9), and elegantly captures some interesting trends, in particular, the distribution of end-game batters 1-9 and thus the most likely batter to end a game. From such a simulation, we can calculate where best to slot a team’s best hitter to maximize his chances of coming to the plate with the game on the line, another stated reason for putting Tulo in the Blue Jays number 1 spot.

Figure 1a shows the distribution of batters faced (BF) over 1,000,000 simulated BOO games, where the most likely end was 40 batters faced followed by 39 and 41 (the 3-5 hitters), as might be expected with a hard-wired OBP = .333 (binomial p = .33). It seems the custom of having your clutch hitters in the 3-5 slots matches the computational results.

Figure 1a: Distribution of # of batters faced   Figure 1b: Distribution of end-game batters

Interestingly, however, the leadoff hitter doesn’t end a game more often than a middle-order batter. Figure 1b shows the distribution of end-game batters (EGB) for a 1-9 lineup, and is perhaps counter-intuitive. In fact, the number 2 and 3 hitters are more likely to end a game than the leadoff hitter, while there is an obvious dip 3-7. Table 1 shows the frequency of end-game batters 1-9 (number and percentage).

Table 1: Number of games ended and percentage versus lineup position (OBP = .333)

Initially, I expected a constant drop-off from 1 to 9, or perhaps following some form of a Benford’s Law distribution, for example, in the wear pattern on a ATM pad or the leading digit in a collection of financial data (1 appears about 30%, 2 about 18%, 3 about 12%, 4 about 10%, . . . , and 9 about 5%). Note, if the data were randomly distributed, each number would appear 11.1% or 1/9. But the modulo aspect of a repeated baseball lineup creates another distribution, one that has a clear maximum after the leadoff spot and a mid-lineup dip at batter number 7.

Of course, the leadoff hitter will always have more plate appearances over an entire season, but somewhat surprisingly does not end a game more often. Table 2 shows the number of at bats 1-9 averaged over a 162-game season (I have assumed 8.5% of plate appearances are walks). As can be seen, the leadoff hitter gets about 130 more ABs than the number 9 hitter, or 21% more per season, reason enough to put your best hitter at the top of the order. From one batter to the next, however, the difference is only about 17 ABs (monotonically decreasing), about an extra AB every 10 games. Not that much difference one spot to the next.

Table 2: Number of ABs and percentage ABs over 162 games (OBP = .333)

Using BOO, we can also analyse how the EGB distribution changes for a good and a bad team, modelled using an OBP of .250 and .400. The results are shown in Figure 2 including our .333 OBP team. Here, it seems that the lineup order matters more on a bad team than a good team (a practically flat EGB). Indeed, it is often said that you can run any lineup out with a good team. Conversely, losing teams are always juggling their lineups to find the right mix.

Figure 2a: Distribution of # of batters faced   Figure 2b: Distribution of end-game batters (OBP = .250, .333. .400)

Of course, baseball is not just statistics over a large number of sample-sizes (or simulations). Baseball is played in bunches and hunches. It would take a little over 400 years to play 1,000,000 games in a 30-team, 162-game schedule. Matchups, streaks, situational hitting, and team chemistry may be more important than any theoretical trends. And, of course, a real, non-flat, batting lineup (which I’ll look at in Part II).

In an actual BF and EGB distribution for the 2014 Toronto Blue Jays and their opponents over a 162-game season, we see the small-sample versions of our super-sized theoretical distributions (Figure 3). The actual BF distribution is comparable to the theoretical binomial/Gaussian BF, though positively skewed, showing the effect of blowouts, not adequately covered in the hit/out simulation. The EGB distribution seems quite random, but late peaks may indicate the use of pinch hitters in the closing parts of a game. It is also interesting to note that BOO “throws” a perfect game about once every 10 seasons, a bit less than the official 23 over the last 135 years.

Figure 3a: Distribution of # of batters faced   Figure 3b: Distribution of end-game batters (2014 Toronto Blue Jays and opposition)

So do the calculations mean anything? According to the numbers, your best hitter should bat 2 or 3, that is, if you want him coming up more often with the game on the line. In “The Batting Order Evolution,” Sam Miller noted that “the anecdotal evidence is strong” to put your best hitter in the number 2 spot. The worst spot for heroics is number 7.

Furthermore, a classic run producer such as Troy Tulowitzki shouldn’t bat leadoff, something the Jays found out after he struck out 4 times, almost a month to the day after acquiring him. Dropping him to the number 5 spot, the manager John Gibbons stated, “Maybe this’ll jump-start him a little bit.” Or maybe, he saw the wisdom of inserting the 2014 NL hit leader and speedster Ben Revere in the leadoff spot and using Tulowitzki’s power in a proven RBI position.

Mind you, with a scorching hot lineup that has scored 100 more runs than the next-best hitting team, it may not matter who bats where. That is, if the game is on the line.

Do The Math! is available in paperback and Kindle versions from the publisher Sage Publications, on-line at Amazon.com, and on order at local book stores. Do The Math! (in 100 seconds) videos are on You Tube.

Classical baseball line-up construction involves putting your fastest player in the lead-off spot. This is due to the belief that speed generates runs (a la Rickey Henderson). In order to test this theory I went back to 1998 (since the last expansion) and looked at how may runs were scored in each season and then looked at 3 indicators, OBP, wOBA and stolen bases to test which indicator would be most useful in predicting runs. Although OBP and wOBA are very similar stats I decided to include both of them in the analysis because of differences in calculation. To put simply OBP gives a home run the same weight as a single and considers them equal (which they are not) while wOBA gives different types of hits more weight (see the OBP and wOBA pages for more information). I’ll admit that I am a huge fan of stolen bases, there is nothing like watching a player steal second or third to try and get a rally started. But the question is, can you expect to score more runs by being fast or by getting on base?

To get started I only looked at data from 2015 and pulled out the top 25 players from each stat category in order to define the “fast” players and the players who get on base the most. I also standardized runs scored to runs per game (RPG) to account for rest days and injuries which may have kept players out of the lineup for short periods of time. In the plot below it appears that the leaders in stolen bases have been scoring fewer runs per game than players who get on base more often. Based on the 95% confidence intervals of the top 25 players the difference was not significant, but the results are interesting nonetheless.

Now let’s look at some long-term data with how many runs were scored each year since 1998. In the plot below we can see that there was a large spike in runs scored in 1999 and 2000 before scoring evened out. The trend seemed to remain relatively stable from 2001 up until around 2006 or 2007 and then we see a dramatic decrease in runs scored up until last year. MLB started testing for steroids in 2003 and perhaps this is why we’ve begun to see that decrease in runs scored, but that is outside the scope of this article so let’s just focus on runs.

Runs are the most important aspect in baseball, whether that means scoring runs or preventing them. In the end, if your team can’t score any runs then you can’t win any games and unless a team have a titan of an offense you need to prevent runs as well. Here we are going to focus on run generation so we can forget about run prevention from here on out. Let’s look at the seasonal stats for our indicators and see how they look over time. I’m going to note here that OBP and wOBA shown in the plots are the league average, while the stolen bases are the league total for each season. A quick look tells us that OBP and wOBA are very closely related to the trend we saw in the second figure while stolen bases have a lot of variability over time. This seems to give a lot of evidence to getting on base, but let’s go one step further and see if we can develop a linear model to predict how each predictor affects the expected runs scored in a season.

In the final plot below I’ve put runs per game on the y axis and each stat on the x axis. In order to test how changes in league performance affects run scored I predicted the number of runs scored based on the 10%, 50% and 90% quantiles to see how many runs a player would generate over a 162-game season.

I’ve created a summary table for easy comparison of each stat and the thing that really jump out is that stolen bases doesn’t have any effect on runs scored. Based on the model, in a season where players steal almost 700 more bases collectively they generate less than 1 extra run.

In the end, getting on base is the most important (Thanks Moneyball!). For many the results should be unexpected, players who get on base more give their teams more opportunities to score runs. There doesn’t seem to be a significant advantage to using OBP or wOBA to predict runs, but based on advanced analytics people should probably consider wOBA more useful since singles, doubles, triple and home runs are all treated differently in the calculation.

Remember at the end of last season and before this season when we all foresaw an Indians rotation that could possibly feature somewhere between 2 and 5 really good, and possibly great, starting pitchers?  Don’t get bogged down on the slight exaggeration of that 1^st sentence – To recap what we were looking at coming into this season for the Indians’ rotation:  Corey Kluber won the 2014 AL Cy-Young; Carlos Carrasco had a string of starts to end 2014 in which he seemingly (finally) figured out how to harness all of his powers in a bid to ascend his name to an echelon where only Clayton Kershaw’s name resides; Danny Salazar has always had elite swing and miss stuff and was also excellent in the second half of 2014;  Trevor Bauer and his Costco-sized arsenal of pitches have made some of us incredulously, if not warily optimistic since he was taken 3^rd overall in 2011; and even T.J. House made us pause and take notice with his strong second half of 2014.

Then, like hype men with a special blend of Cleveland Kool-Aid being intravenously administered, Eno Sarris and Daniel Schwartz posted one of my favorite FanGraphs articles ever, Pitch Arsenal Score Part Deux, and the anticipation over the Indians’ rotation pulsated like a vein in the neck of John Rambo in the midst of fleeing from man-hunters.

The supporting cast, the lineup, looked poised to support the staff with plenty of runs.  Returning would be: break out star Michael Brantley; bounce-back candidate Jason Kipnis; now-full-time-first-basemen, Carlos Santana; a supposedly healthy Michael Bourn; an offense-first but totally-respectable-defensively, Yan Gomes; and an actually-not-that-horrible-in-2014, Lonnie Chisenhall.  Slugger Brandon Moss, and contact-happy-supposedly-glove-first Jose Ramirez had secured full-time spots as well in RF and SS respectively.  So even though it wasn’t without flaws, it seemed like they would allow the pitchers to rack up plenty of fantasy-relevant wins.

Note: This post isn’t about the disappointment of the Indians, though they have been disappointing; it’s more about what factors beyond luck have contributed to the numbers of the Indians’ starting rotation at various points throughout the year, and the disparity (big or small) between the pitchers’ rates and predictors at those points.

The Indians’ starting pitchers, or at least the top 4 (Kluber, Carrasco, Salazar, and Bauer) have, for the most part, been putting up good, albeit, inconsistent numbers all year despite posting some elite peripheral rates and ERA indicators.  A number of reasons have caused these numbers to grow apart (bad), come together, and then grow apart again (good).  Luck can work like a bit of a pendulum, swinging from one extreme, through the middle, and to the other extreme before evening out and that is at the core of what the Indians’ starting pitchers have experienced this year — although they have yet to experience the final stabilization phase.

We will examine plenty of numbers (Beginning of season to August 18th) based on this time frame: (Spoiler alert – this article is long and dense, and this timeline serves as a sort of cliff notes as to how the staff’s numbers have improved throughout the year – so if you’re the type of person who feels like looking at a bunch of data is superfluous when the bullet points are in front of your eyes, just read the timeline and be done with it.)

April 6^th – May 23rd/May 24th – June 15th

One week into the season, before it was evident that the team’s defense was very sub-par, Yan Gomes hurt his knee and hit the disabled list for over a month.  Roberto Perez filled in quite nicely, and looking at just a couple numbers, could be considered the more valuable catcher (1.4 WAR compared to 0.5 WAR for Gomes).  Brett Hayes (0.0 WAR) was called up and was the secondary catcher during this period.  Behold, a table from StatCorner:

Perez has had the least amount of pitches in the zone called balls and the most amounts of pitches out of the zone called strikes.  Overall, despite receiving fewer pitches than Gomes, he has saved more runs (4 DRS to Gomes’ 1) and their caught stealing rates are basically identical with a slight edge going to Perez – 38% to Gomes’ 35%.  Gomes was much better in terms of framing in 2014, and it’s possible the knee injury has limited his skills all around this season.  Anyways, from April 6th – May 23rd, the combined stats of Kluber, Salazar, Carrasco, and Bauer look like this:

Gomes returned as the primary catcher on 05/24, and from that point through June 15th, the cumulative numbers aren’t too different, although there is a dip in both K-BB% and GB% that we’ll have to look into.

So despite lower K-BB and ground ball percentages (leading to higher ERA predictors), the group’s ERA in the segment of the season when Gomes was reinstated is essentially exactly the same as from the first block of time with Perez.  Now, I am not a big believer in CERA because there is a high level of variation and too many unknown variables pertaining to how much of the responsibility/credit goes to the catcher, the coaching staff, or the pitcher; but I do think that it’s possible Gomes’ extra service time has enabled him to be more in tune with his staff as well as understand hitter tendencies better than Perez and Hayes.  I realize we’re getting into a gray area of intangibles, so I’ll reel it in with some results based on pitch usage%.

% Difference in Pitch Usage with Yan Gomes compared to Roberto Perez

Using BrooksBaseball Pitch f/x data, let’s painstakingly find out how different each pitcher’s pitch usage was in regards to different counts, or better known as Pitch Sequencing.  We’ll look at first pitches, batter ahead counts, even counts, pitcher ahead counts, and 2 strike count situations.  As good as pitch f/x is, the data still isn’t perfect.  There may be discrepancies if you look at usage at Brooks compared to the usage at FanGraphs, so for each pitcher we’ll split the pitches up into three categories: Fastballs (four-seam, sinkers, cutters), Breaking Balls (sliders, curve balls), and Change Ups (straight change/split finger) – I’m aware that splitters are “split fingered fastballs”, but I liken them to change ups more because of the decreased spin rate and generally lower velocity.

*Having a table for each pitcher in regards to pitch sequencing made this article quite messy, so I’ve included a downloadable Excel file, and briefly touched on each pitcher below.

Pitch Sequencing Excel Doc.

Corey Kluber

Looking at the data, Gomes stays hard with Kluber more than Perez until they get ahead in the count.  Perez swaps some early count fastballs for curve balls, but they both see his curve ball as a put-away pitch.  Gomes tends to trust Kluber’s change-up more than Perez later in counts and Perez likes it more earlier in counts.

Danny Salazar

Much like with KIuber, when Gomes catches Salazar, they have a tendency to stay hard early.  Gomes pulls out Salazar’s wipe out change up after they’re ahead whereas Perez will utilize it in hitter’s counts as well.

Carlos Carrasco

Carrasco has 5 good pitches and he’s pretty adept at throwing them for strikes in various counts which is why there is some pretty even usage across the board, at least in comparison to Kluber and Salazar.  There is quite a bit more usage of Carrasco’s secondary pitches in all counts and there are pretty similar patterns when Gomes and Perez are behind the plate.  With Hayes, it doesn’t look like there is much that changes in sequencing until there are two strikes on a hitter.

Trevor Bauer

Bauer is probably a difficult pitcher to catch because of the number of pitches he has and the constant tinkering in his game.  Side note: Gomes is the only catcher to have caught a game in which Bauer threw cutters, and in their last game together, Bauer threw absolutely no change-ups or splits.  Bauer’s highest level of success has come with Hayes behind the plate and perhaps that’s from their willingness to expand his repertoire in more counts than Gomes and Perez do, but there is no way I can be certain of that.

Pitch sequencing can effect the perceived quality of each pitch and therefore, can produce more favorable counts as well as induce higher O-Swing and SwStrk percentages (or less favorable and lower).  So despite the framing metrics favoring Perez, the group throws more strikes with Gomes and also induces more swings at pitches outside the zone – although, as previously noted, there is some regression with Gomes behind the dish in terms of SwStrk% and K-BB%.

**These graphs represent numbers through the entire season to garner a bigger sample size.

With lower line drive rates and more medium + soft contact, and (in the case of the Indian’s defense), more fly balls, a conclusion could be jumped to that the staff’s BABIP has trended downward since Gomes regained his role.  A look at BABIP throughout the course of the season:

Woah!  It was well above league average in April and then plateaued at just above league average through mid June, but has been plummeting ever since.  Obviously a catcher is not responsible for this dramatic of a swing in BABIP, so the Indians’ defense must have improved.

June 16th – August 18th

The rotations’ traditional stats look even better if you use June 16th as the starting point:

So let’s take a look at the Indians’ defensive alignment by month (Player listed is the player who received the most innings played at the position).

If you’ve paid attention to the Indians at all, you know they’ve made some trades and called up a couple prospects.  But just how different is the new defense?  Well, we only have a small sample with the current configuration, but it appears to be A LOT better. If BABIP wasn’t enough of an indicator, and it’s not, because there has to be some regression to the mean – it can’t stay that low – here are some numbers from the players who were playing the most in May compared to the players who are playing the most in August (again, numbers represent full-season stats):

What’s interesting is that the biggest difference in the infield is Francisco Lindor (Giovanny Urshela has been very solid, but Chisenhall was pretty similar this season at 3B).  I’m sure someone at FanGraphs could churn out a really cool article (if someone hasn’t already) that shows us a quantifiable difference an above average to well above average shortstop makes for a team even if you just keep the rest of the infield the same, as the control.  The 2015 Tigers come to mind – a healthy Jose Iglesias has made a difference for a team that still features Nick Castellanos at 3B and Miguel Cabrera at 1B.  Teams are willing to sacrifice offensive contributions if a SS has elite defensive skills (Pete Kozma, Andrelton Simmons, Zack Cozart to name a couple off the top of my head).  Lindor, to this point, has been an above average offensive player, too, so this could be special.

At this point the Indians are in last place and are out of contention.  Abraham Almonte is their starting center fielder and with Kipnis back from the DL, Jose Ramirez is not playing 2B, but is instead getting reps in left field while Michael Brantley DHs due to his ailing shoulder.  Perhaps all this means is that they don’t have better replacements; OR PERHAPS they’re planning to establish a more defense-oriented squad next year…

Now there’s no doubt that this research has led to some frustrating conclusions.  With Gomes behind the plate, the K rate and GB rate of the staff has trended in the wrong direction in regards to ERA indicators; so is the difference in the batted ball profile plus an improved defense enough to make up for these facts?  This small sample size thinks so, but it could 100% just be noise.  However, there are clubs that are succeeding by using similar tactics right now:

Granted, the Royals and Rays have the 1st and 2nd best defenses in baseball, and their home parks play differently than the Indians, but they also don’t boast the arms the Indians do.

The Indians have their noses deep in advanced metrics and having rid themselves of Swisher, Bourn, and Moss during 2015’s trading period has allowed them to deploy a better defensive unit which has amplified their biggest strength – their starting pitching.  Furthermore, their unwillingness to move any of their top 4 starting pitchers also leads me to believe they see next year as a time for them to compete.  I’m not going to speculate what moves the Indians will make in the offseason, but I hope they stick with this defense-oriented situation they have gone with recently because it’s been working (and because I own a lot of shares of Kluber, Carrasco, and Salazar in fantasy).

We’re officially in the dog days of summer, which means a few things of note: NFL is almost upon us; the fantasy baseball playoffs have begun for many; and finally, whether you’re in a roto league without playoffs or otherwise, you’re still looking to find value on your waiver wire.

I define value as something like: Players who produce counting stats (and/or average), who, for whatever reason, have low ownership rates and thus can be found on waivers for free, or in my case, for a few FAAB dollars (of which, I have zero remaining). The players I’m referring to are generally valuable in deeper mixed leagues or NL- or AL-only formats, but some, like Dexter Fowler, whom I’ve written about in the past, can offer solid numbers for leagues of any size/format.

I’ve recently written about guys like David Peralta, Fowler, and Jung-Ho Kang, and my advice on these players remains the same as it’s always been: pick them up ASAP. Their low ownership rates on ESPN continue to leave me flummoxed; E.g., David Peralta and his .294 average, 48 R, 13 HR, 66 RBI, and 5 SB is owned in just 70% of ESPN leagues. Go figure. Better yet: Go pick him up.

Here are a few more hitters I like who can help you down the stretch:

Yangervis Solarte: Solarte hit his tenth home run on August 21 and third in as many games. A switch-hitter, Solarte has multi-position eligibility (1B; 2B; 3B) and is owned in just 34% of ESPN leagues. With a triple-slash line of .269/.325/.425, Solarte has 47 R, 10 HR, and 49 RBI. Those stats play in most leagues, and while he is a bit streaky and on a power surge in August, his ambidexterity keeps him in the Friars’ lineup on a near-daily basis. Solarte has solid on-base skills (29:46 BB/K), hits for decent power, above league-average batting average, and the vast majority of his AB’s come in the leadoff or 2-holes in the lineup (110 and 142 AB, respectively).

That said, hitting in front of a hot Matt Kemp and a hopefully-getting-hot Justin Upton should help keep his run totals healthy, and he’s showing some nice HR power in August. His .283 BABIP is in line with career norms, so I don’t expect much regression in terms of batting average; if anything, that number seems somewhat low for a player who runs well, but ZiPS projects a BABIP of .280 the rest of the way. At any rate, you could certainly do a lot worse than Solarte, a player who might be finding his stride in the second half.

Colby Rasmus: In short, Rasmus is who he is: He hits for power and not much else. His power, particularly against righties, is the real deal: Rasmus owns a .451 slugging percentage and a solid .222 ISO in 2015 (with a career-norm .297 BABIP); his 17 HR and .750 OPS suggest he can help in AL-only or deeper mixed-leagues.

Owned in just 6.5% of ESPN leagues, Rasmus has 44 R, 17 HR, 44 RBI, and 2 SB to his credit (along with an unsightly .228 batting average), with the two most recent of his 17 Colby Jacks courtesy of Detroit lefty Matt Boyd. While he does sit against most LHP, Rasmus’ OPS against lefties in 2015 is a respectable .815 across 80 AB’s (compared to a .726 OPS vs. RHP over 244 AB). That said, you will see him in the lineup against a few soft-throwing lefties, but that will likely stop when Springer returns.

For perspective, consider Brandon Moss relative to Rasmus:

Moss is batting .211 with 38 R, 15 HR, and 51 RBI. He was recently ranked OF number 52 and 49 by two CBS analysts, whereas Rasmus is ranked 63 and 88. Although Rasmus’ power is less proven than that of Moss, Moss has been miserable since June and Rasmus has been steady, if unspectacular, effectively all season. But despite hitting more HR—and being projected to hit just 3 fewer HR than Moss (8 HR projected for Moss ROS seems totally absurd, incidentally)—Moss is owned in roughly 8 times more leagues than is Rasmus. In short: Colby is either massively under-owned, or Moss is hugely overvalued; or, I guess, both.

ZiPS has another 5 HR and 13 RBI projected for Rasmus rest of season, but those number seem a bit soft in the absence of Springer for a player hitting at Minute Maid Park. Rasmus won’t win a batting title anytime soon, but his solid OPS vs. lefties this year (an outlier, to be sure) and strong defense at all three OF positions keeps him in the lineup on a near-daily basis, especially given the recent, albeit short-term, demotion of Preston Tucker. Colby is a funk since his 2-HR game on 8/16, but like most power hitters, Rasmus is prone to streaks; my advice to you is exactly the same advice I took myself: pick him up and enjoy the HR power, but don’t expect him to suddenly become Bryce Harper.

Asdrubal Cabrera: Arguably the hottest hitter in baseball since he returned from the DL on July 28, Cabrera is hitting .404 with an OPS of 1.078 since the All-Star break. Those are not typos, though his numbers are propped up by a massively inflated BABIP. Also since the break, Cabby has 20 runs, 4 HR, 13 RBI, and 2 SB across 89 AB’s. He’s on fire, no two-ways about it.

What we’re seeing here, I think, are two things: 1) a player out-of-his-mind hot and 2) a veteran with proven, decent power and a solid hitter regressing to the mean. Currently batting .264 with 49 R, 9 HR, 35 RBI, and 5 SB (.730 OPS), Cabrera has hit at least 14 home runs every season since 2011 (career high of 25), and he’s on pace for roughly 12 this year. A career .267 hitter, Cabrera was miserable in April, May, and some of June, and while he’s hitting an unsustainable BABIP of .320, he was certainly due for a few bloopers to drop.

With dual 2B/SS eligibility, his ownership rate on ESPN has spiked from sub-20% in mid-August to 39% at the time of this writing. If you’re looking for help at a very weak SS position, or a possible Howie Kendrick replacement, Cabrera can certainly help you out; and as a switch-hitter, you’ll find him in the 5- or 6-hole in the Ray’s lineup on a daily basis.

I wish I knew why Jung-ho Kang and Ben Paulsen seem to get so little respect. It’s baffling. Regardless, people should be talking about these guys and their production — both have very legit numbers, yet few seem to have noticed. More to my point: fantasy baseball players should pick them up from the waiver wire ASAP. I mean, right this second.

Kang, recall, is the stud the Pirates signed from Korea. An unknown for the better part of the season, Kang is making his presence felt in the middle of the Pirates lineup, having just earned honors this July for NL Rookie of the Month. Kang, with dual SS/3B eligibility, is owned in just 57.9% of ESPN leagues and is slashing a highly productive .291/.365/.446 and, based on what he did in Korea, his .809 OPS could prove to be low in the long run.

Kang went through a bit of a power drought in June, but he caught fire in July. He’s now hitting .291 with 8 HR and 35 RBI. Consider that in the last week of July, Kang recorded multiple hits in five out of eight games with 6 R, 2 HR, and 3 RBI in that stretch. In his next game, on August 1, he hit his 8th home run of the season, a ball that traveled 412 feet. In 2014, Kang launched 40 home runs in 120 games in Korea, while also hitting .297. The kid can flat-out rake. With Jordy Mercer on the shelf (and not very good when healthy), Kang continues to occupy the 4–6 holes in Clint Hurdle’s lineup.

As many hitters have said before: As the summer heats up, so do they. I suspect we’re going to see Kang launch many more home runs before season’s end. If nothing else, even if the power is merely moderate, the fact that he hits for average, steals a few bases, and slots in the middle of a very potent Bucs lineup makes him worthy of a pickup in leagues of any size.

Ben Paulsen. What’s not to love about a guy who: 1) plays half his games at Coors Field; 2) made minor league pitching look like little league; 3) hits for both power and average; and 4) absolutely kills right-handed pitching? Answer: Nothing. His numbers aren’t dissimilar from those of Kang (in fact, they’re nearly identical), with a .300 average, 8 HR, and 34 RBI. His average is a bit buoyed by a .363 BABIP, though ZiPS projects a .333 BABIP the rest of the way. The only knocks against Paulsen are playing time and his ugly platoon splits, which are obviously related. But as with guys I’ve discussed before, who cares if he’s not an everyday starter; he’d just tank your average anyway. Instead, bench him against the few lefties he’s allowed to face, and you won’t be disappointed.

FanGraphs had this to say about him before the season started; it’s like these guys are clairvoyant or something. But they’re also very much wrong in the when they say that Paulsen’s game is made for just NL-only leagues. It’s much better than that (keep reading). Per FanGraphs:

The Quick Opinion: If Morneau starts the year on the disabled list as he recovers from knee surgery, Paulsen could be a sneaky short-term option in NL-only leagues, but that’s about it.

Paulsen, actually, is now effectively an everyday starter in the mercurial Walt Weiss’ lineup, thanks to the demotion of Wilin “Baby Bull” Rosario. Justin Morneau’s concussion symptoms are persisting, and he may have played his final game in the big leagues. Thus, the gig is Paulsen’s to lose, and with Corey Dickerson on the DL again, Paulsen has also been playing some corner outfield when called upon.

And when the 27-year old Paulsen is called upon, the numbers are a thing of beauty — against RHP, anyway, who he’s torturing to the tune of a .308/.361/.535 triple slash. Paulsen’s OPS of .896 isn’t just ‘productive,’ it’s downright fantastic. Frankly, it’s more than a little weird that just 19.7% of ESPN players own him. I’m happy to say I’m one of them, though I missed out on Kang, much to my dismay (and totally because of my stupidity).

There will be more blogs to follow, with similar themes in mind: finding value where there seemingly is none. There always is, you just have to look hard enough.

The importance of getting ahead of hitters is stressed to pitchers from the first time they play in a non-coach-pitch league.  It’s not what happens on the pitch immediately following a first pitch strike, it’s because the numbers for the rest of the at bat sway dramatically in the pitcher’s favor.

These are league averages, but for the most part they apply to individual hitters as well.  Paul Goldschmidt is not a “league average” hitter, in fact, he is at least in the conversation when discussing the best hitter in baseball right now (2015) – and I only say at least because I’m too afraid of the backlash I might receive if I declared him the best.  But regardless if a pitcher is facing an average hitter or an elite hitter, the law of getting ahead applies –  even if the numbers for Goldschmidt do look a bit different from the table of above.

Paul Goldschimdt is just so strong, and so adept at making hard contact to all parts of the field that, even at his worst, he’s still so much better than other professional hitters.  The results clearly show that he’s a lesser version of himself throughout the duration of an at-bat that starts with a first-pitch strike, but here’s the thing: getting a first-pitch strike on Goldschmidt isn’t easy.  Not only is he discerning, but he is so devastatingly destructive when he sees something he likes.  Pitchers have gotten a first pitch strike against Goldschmidt 56.7% this season (league average is 61.1%).  In 471 PA, Paul Goldschmidt has only swung 126 times at first pitches, or 26.8%.  It could be said that Paul Goldschmidt “goes to bat with a plan”.  But it’s not like pitchers’ game plans will stand idle while Goldschmidt continues to pummel them; they will make adjustments, and one adjustment they have made, because the pay-off is so dramatic, lies in figuring out how to get ahead of him.

First, let’s consider two samples from Goldschmidt’s 2015 – through July 3^rd of this year Paul Goldschmidt put up MVP numbers:

April 6 – July 3:

Since then, however, he has hit like someone who just might be mortal:

July 4 – August 4:

So what course of action have pitchers taken to get ahead of him in the count?  The answer lies in the conveniently bolded numbers featured in the CB% column of the table below.

Numbers represent the usage of pitches in all first-pitch situations to Paul Goldschmidt.

Obviously there’s been an uptick of a larger percentage in split fingers for first pitches, but a hell of a lot more pitchers throw curveballs than splitters, so that value is not really important.  What is important is that 119.5% increase in first-pitch curveballs, because Paul Goldschmidt SPITS at first pitch curveballs.  He saw twenty-eight, 1^st pitch curveballs in the sample size concluding July 3^rd and swung at a grand total of 1 of them.  Since then, in a month, he’s seen 20, first-pitch curveballs and has swung at exactly 0 of them.

Goldschmidt is looking for something hard-ish (fastball/slider/change-up; league average change up velo is 83.3 compared to 77.7 for curveballs and 84.2 for sliders) that he can drive on the first pitch, and knows he can lay off curveballs to sacrifice a first-pitch strike and still be an above-average hitter.  For the record, it’s not like Goldschmidt is bad against curveballs; he owns a 3.31 wCB/C in 2015 (3.79 through July 3^rd, and 2.16 after), it’s just that he’s committed to his plan.  Pitchers – or analysts – have noticed his disregard for curveballs as first pitches, and the pitchers – not the analysts – have twirled curveballs in to Goldschmidt on the first pitch at a much higher rate over the last month – again, that number is 119.5% more often.  While the strike percentage of these curveballs has only been 45%, that’s still up from the 28% of curveballs for first-pitch strikes through July 3^rd.

Conjecture alert:  Perhaps expecting more first-pitch curveballs, Paul Goldschmidt has readied himself to not swing at the first pitch, as he has swung at just 25.3% of non-curveball first pitches since July 4^th, compared to 32.9% through July 3^rd.  Pitchers have been able to sneak their first pitch strike percentage up against Goldy from 55.9% to 59.5% in this past month – that’s a 6.4% increase.  So it seems as though the best way to beat Paul Goldschmidt is to try to find some way to make him swing the bat less, because when he does, bad things happen to baseballs.  For clarification, I’m talking about throwing him more first pitch curveballs, not walking him every time up.

Paul Goldschmidt is so good that he will probably adjust to this new approach fairly quickly.  I said earlier, “he knows he can lay off curveballs to sacrifice a first-pitch strike and still be an above-average hitter” – Paul Goldschmidt’s aim is not to be a player who is an above-average hitter – he’s a force at the plate and he will adjust.  Health permitting, Goldschmidt will likely finish the season with at least a .300 AVG, 100 R scored, 30 HR, 100 RBI, and 20 SB – a line we haven’t seen from a first baseman since Jeff Bagwell did it in 1999.

So as Goldschmidt adjusts to this new attack from pitchers, maybe the real number to take away from this research is that Goldschmidt is partying like it’s 1999.