As a Yankees fan (albeit one that has only witnessed their 2009 World Series), I have never been more excited about the team’s present and future. With the MLB roster slowly filling with good, young talent, and with even more stirring circumstances in the minors, the Yankees have the potential to be another powerhouse team.

The Team

Right now, the Yankees are in the midst of a revolution. Out with the old (A-Rod and Teixeira) and in with the new (Sanchez, Judge and Austin). Despite missing out on the playoffs, they will feature a well-rounded lineup at the start of next year.

It’s safe to say that Gary Sanchez won’t enjoy quite the success he did in the last two months of this season. Actually, he won’t come close. This isn’t to say he will play poorly, it’s just that he played so well that he can’t come back to those levels. However, Sanchez will no doubt still be one of the better-hitting catchers in the MLB with average to plus defense behind the dish, so they will already be better in that position in 2017 than they were in 2016.

The Yankees infield is the most likely to change the least with only Greg Bird slotting in at first base. Didi Gregorious, Starlin Castro and Chase Headley are each under team control until at least 2018, and there isn’t anyone challenging them for their spots at the moment. At first base, though, I say it is most likely that Bird gets the spot because it is possible that Tyler Austin beats him out in spring training. Austin is more likely to be used as a quasi-utility player as he can play at first, in right field and DH.

In the outfield everything could remain the same as the end of the season with Hicks or Judge in right, Ellsbury in center and Gardner in left. It could also see some changes. Gardner and Ellsbury both have the potential to be traded over the offseason with Gardner the more likely of the two. There are options to fill those gaps if trades do happen. Mason Williams could fill in until Clint Frazier is (hopefully) ready later in the season. Hicks, Austin and Judge could also fill the holes if needed.

The Yankees pitching is the most worrisome issue. The starting pitching, that is. Masahiro Tanaka performed well in 2016, so there is no reason to think otherwise for the next year. Beyond that, though, are question marks. Nate Eovaldi will probably be a non-tender after his Tommy John surgery. Pineda had his usual ups and downs. Sabathia is still getting older. Then there are numerous options in Luis Severino, Chad Green, Luis Cessa and Bryan Mitchell. Severino will be given the longest look because of his end to the 2015 season, but it’s a toss-up from there.

The bullpen in New York is still a quality one despite trading away Aroldis Chapman and Andrew Miller. Dellin Betances is one of the best in the game, so that’s a good start. Tyler Clippard, Adam Warren and whoever misses out on the rotation gig will presumably fill in the rest with a lefty thrown in.

The Minors

Now comes the most exciting part of the Yankees. With a system that starts with four top-30 prospects despite Sanchez already graduating, the Bombers are on their way to a good future. Frazier is in AAA and still needs to put up good at-bats before he gets the call to the majors, but that time will come soon enough. Gleyber Torres and Jorge Mateo will likely start the year in AA, so they won’t be seen until 2018 most likely, especially with the likes of Gregorious and Castro blocking them. Beyond their top three guys, the Yankees still have plenty of players who could make a major-league impact once it’s their time. Simply, there is a lot to be excited about when it comes to the team’s future.

The Yankees will have the 17th overall pick in next year’s draft, so they will be in familiar position after having the 16th and 18th picks in the two previous years. Their first-round picks in recent years have both been ones that I personally like, but who wouldn’t? James Kaprielian is shining in the Arizona Fall League and Blake Rutherford looks like a steal at the 18th pick, especially after his hot start to his pro career. This year will hopefully prove to be another that produces some good picks.

The Offseason

With the Yankees pretty much set with position players, there’s no reason to add any pricey free agents. It also wouldn’t be wise to block some of their young players out to prove themselves or ones that are close to ready in the minors. Pitching is another story.

As I stated before, their starting pitching has question marks when it comes to Sabathia’s age, Pineda’s consistency and Severino bouncing back. There also aren’t many pitchers on the free-agent market that stand out. Overpaying for Rich Hill would be contradictory to what the Yankees are trying to do in becoming younger, but his dominance when healthy is something that can’t be questioned. It wouldn’t be a bad move to sign him, but it would add yet another question mark to their rotation due to his injury history. Signing him also wouldn’t help any towards getting under the luxury tax, which Steinbrenner would like to do.

The only free-agent acquisition that I would like to see is a top-notch reliever, which means one of Chapman, Kenley Jansen or Mark Melancon. Jansen is likely going back to the Dodgers and Melancon would be yet another righty for the bullpen. A reunion with Chapman would be the best move. Pairing him with Betances again would put the bullpen in great shape. It’s just that it will cost a lot.

In terms of trading, I am one that is all for trading Gardner, Ellsbury and/or Brian McCann. Ellsbury’s contract probably means he’s staying, but Gardner will be easy to move if Brian Cashman can get the right return. Some reports have said that a swap of him for a middle-of-the-rotation pitcher could work, and that would be just what the Yankees need. McCann will have high demand this offseason with multiple teams needing catchers and not enough free agents to go around. The Yankees will have to eat a good chunk of his contract to get anything of value in return, but it shouldn’t be a problem as they’d be shedding a good portion of his $17-million-per-year contract. It would also give younger players like Bird, Austin and Judge a chance to DH.

The Braves have been said to want a reunion with McCann but won’t trade Mike Foltynewicz for him. The Yankees will do well if they can eat about half of his contract and get a couple middling prospects with some upside.

With such a deep farm, the Yankees also have the ability to trade for a front-of-the-rotation starter. Landing one of the top guys on the trade market probably isn’t in their best interests, though. To get one of Chris Sale, Chris Archer or Sonny Gray will cost a good portion of what the Yankees were able to get for Chapman and Miller. Instead, they should look to trade from depth for a guy that is a step down from the others. With Torres looking like the better middle-infield prospect, trading Mateo as the headliner of a package for a starter would be a good move and won’t impact the team’s future too much.

In Summary

In an ideal scenario, the Yankees will sign one of the top relievers to pair with Betances, stand pat on other free agents and see how Cashman can work the trade market for a third straight offseason. The Yankees likely aren’t a top contender next season, but the potential is there. If things break right with Judge, Bird, Sanchez and the rotation, they could find themselves at the top of the A.L. East. Right now, though, they should look to continue development of their top-three farm system and look at 2018 as the year to really contend.

In Part I, one of the major observations was that a group of smaller-statured players seemed to be using backspin as a distance tool. I was curious how the increase in home runs would look when broken down by physical size. In addition to using Statcast data from Baseball Savant, I downloaded player heights and weights from MLB rosters and created size quintiles. While I expected to see significant contribution from smaller-sized players, the magnitude of what is occurring was quite surprising:

Note: Size based on height * weight. Since pitchers skewed the quintiles due to their above-average size, they were excluded in making the quintile groups; however, their HRs are included in order to tie back to HR totals.

Now that is democratization of power! While interesting, the obvious question is: How are the smaller players hitting all the additional home runs? Is it more distance through exit velocity (EV) and/or launch angle (LA), more pulled balls, more fly balls, or just better-hit fly balls? Let’s take a look:

Distance, EV and LA

Note: Balls hit at Coors Field excluded

Although the data above would support a slight increase in homers overall, there is no smoking gun as to what might be happening within the smaller player groups. If smaller players are not hitting the ball that much harder or further, maybe it could be that they are hitting more homers to the pull side.

Pulled HR and Hits

Although the location mix of homers did not change significantly from the prior year, smaller players in both years hit a much higher percentage of their homers to the pull side than average. The more important metric to consider with respect with the pull factor is what is happening to the mix of well-hit fly balls.

Again, more data supporting a slight overall increase in homers – More well-hit fly balls hit to the pull side and more of those balls going for homers. No real support here for what might be happening with the smaller players. What about well-hit fly balls in general:

Now we’re getting somewhere! Smaller players experienced a significant increase in well-hit fly balls in 2016. What about fly balls in general, not just those of the well-hit variety:

The last two charts kind of sum it up – smaller players are hitting more fly balls in general as well as more well-hit fly balls that are going for homers. Before closing, I’d like to show two other tables which I believe are meaningful for both the home-run question as well as hitting in general. In a certain respect, it appears hitters are making better contact. The following chart shows the volatility (via standard deviation) for EV, LA, and Distance.

Since EV is up in terms of MPH but down in terms of volatility, this would indicate players in general are making better contact. The same is true for distance – higher average distance but lower volatility. However, the increase in volatility of launch angle would seem to indicate quite the opposite – that players are using a lower ball-contact point in order to achieve the higher number of fly balls. Take a look at pop-ups over the past two seasons:

While not up across the board, it is very interesting that there is a significant increase in pop-ups in the group responsible for the largest increase in homers.

After considering the data above, I was curious how the homers looked broken down by age. The increase in homers of the younger players was equally surprising:

I checked for the obvious relationship between size and age; however, the 24-26 age group was reasonably well distributed in terms of size so there is likely something additional going on with the younger players. Whether it is a power focus earlier in their development, a selection bias through the draft or some other factor I’m not sure. Maybe I’ll get into that another time.

Summary

This is a very interesting issue to consider and while I’m sure there will be much more written on the topic, it certainly takes some possibilities such as a juiced ball completely out of consideration. Now that would be a conspiracy! That umpires are throwing out juiced balls for the little guys! Except that the balls would have to be so stealthy that they don’t get hit significantly harder or further – they just hit bats of the smaller players for well-hit fly balls more often.

For me, the really interesting part is the underpinning driver – that advanced metrics have changed the market which values the players. Whether consciously or not, players are changing to align with the market to maximize their value. Even more interesting is what the future holds – what is the cost of the hyper-focus on power and loft and what are the unintended consequences that have yet to come to light?  As far as the home-run issue, at least in terms of player size and age, less certainly has been more.

Any fan that is somewhat invested in the game of baseball understands the importance of putting both a good team on the field at the MLB level while also sustaining an adequate farm system. The Angels have done neither.

This is a hard thing to do when the best player in baseball plays for you, but Arte Moreno and the Angels have managed to do that. Let’s take a look at how they ended up in this dire situation.

MLB Team

One thing the Angels do have (sorta) is a good core of players. They have Mike Trout, Kole Calhoun, Andrelton Simmons and Garrett Richards. Trout and Simmons play at premium positions, Calhoun is a good two-way player and Richards has ace potential (given his arm doesn’t snap). They even have quality players in Yunel Escobar and C.J. Cron who are quietly productive. With the exception of Escobar, each of those players are controllable for the next several years. The team isn’t devoid of talent behind Mike Trout like some believe. They also have a few starting pitchers who have either shown success or are promising in Matt Shoemaker, Tyler Skaggs, and Andrew Heaney. The only problem is that Heaney is done for next year already and Skaggs may be too if his stem-cell therapy doesn’t work.

The holes in the team are at second base, left field, starting pitching spots that aren’t guaranteed and the bullpen. Especially the bullpen. The only true bright spot of their bullpen is Cam Bedrosian while everyone else is expendable at best (unless Huston Street can return to form).

Now that we’ve looked at their roster heading into next season, how can they fix it?

Win-Now Options

Moreno has to let Billy Eppler spend some money this offseason. He isn’t paying Jered Weaver or C.J. Wilson anymore. That leaves them with roughly $30 million to spend before hitting the luxury tax, which Moreno has made clear he won’t go over. One thing this offseason is sure to provide is offense.

Obvious fixes would be to sign Yoenis Cespedes and one of Justin Turner — which would move either him or Escobar to second — or Neil Walker. The Angels can’t go another year with below-replacement-level players at those positions if they truly want to win. The smart route for them would be to avoid what are likely to be excessive bidding wars for Cespedes and Turner. Walker is a great fit at second for them. He offers good offense from the left side to couple with their righty-heavy lineup as well as average defense to a team that has seen paltry turnouts at the position.

As for left field, their are plenty of corner outfielders on the market. However, instead of paying too much for a reunion with Mark Trumbo, the Angels should look at Ian Desmond, Dexter Fowler and Carlos Gomez. Desmond and Fowler failed to garner much interest last offseason, so an offense-heavy free-agent class should keep their price tags down. As for Gomez, he was DFA’d by the Astros before playing somewhat better with the Rangers. Gomez is the higher risk/reward player while Fowler is the closest to a sure bet to perform consistently. Desmond is a wild card since he just converted to the outfield and profiled as below average in center. Shifting him to left with Trout in center could improve his defense, so he is also a viable option. The Angels took huge risks in the past that didn’t turn out well, so Fowler is probably their best option. Plus he adds another lefty bat against righties.

If the Angels can manage to add both Walker and Fowler, their offense would actually fill the basic requirements for a successful team. They would have a leadoff hitter in Fowler, and a number two in Calhoun, with Trout in the three slot. Either Cron or Pujols will bat fourth and fifth with Walker behind them. Then some mix of Escobar, Simmons and their catcher in the 7-9 spots.

As for fixing the rotation, that will be much harder, and they might just have to wait out the storm or go over the luxury tax. Overpaying for Jeremy Hellickson or Ivan Nova would be a bad move and Rich Hill isn’t a good fit for a fairly old roster that already has its risks. Henderson Alvarez could be a good bounce-back candidate after missing 2016 following a shoulder surgery. Andrew Cashner could be an option in a pitcher-friendly park in Anaheim, though the one in San Diego didn’t do him much good. Going into the season with Richards, Shoemaker, Skaggs, Nolasco and one of Alex Meyer, Nate Smith or Daniel Wright isn’t the end of the world. It just has its risks.

What about the farm?

Minor Leagues

According to RosterResource.com, the Angels have 11 home-grown players on their 40-man roster. That’s definitely on the lighter side compared to most teams, but it isn’t quite as extreme as the Padres’ six. They also only have six free-agent signings, which isn’t too large of an amount. The part of their roster that stands out is their eight waiver claims. The fact is that the Angels didn’t have the depth to fill their own roster with players already within their organization.

Going back to the team’s free-agent signings, six isn’t a large amount as I stated before. However, some of their more recent signings have been very costly (both in terms of monetary and baseball value). In the offseason prior to the 2012 and 2013 regular seasons, they signed Albert Pujols, C.J. Wilson and Josh Hamilton. Each of these players cost north of $15 million per season. Each also cost the team draft picks. They lost two first-round picks and a second-round pick.

The teams’ most recent top picks most likely aren’t going to make an impact with the MLB team. For one, Sean Newcomb definitely won’t since he’s on the Braves now. Taylor Ward and Matt Thaiss were both very weak first-round picks. Ward won’t hit and Thaiss is basically limited to first base.

This isn’t to say the Angels have nothing in the minors. Jahmai Jones is promising but very young and a few of their other 2016 picks could develop into good MLB players, including Brandon Marsh and Nonie Williams. Their farm isn’t deep enough to trade for any key pieces though, and they shouldn’t do that even if they did have the pieces. Eppler has a chance to use a top-10 pick this year as well as future picks to try and build the strong farm that the Angels have lacked for so long, so he can’t waste that opportunity on a middling team.

In Summary

I feel that I’ve laid out the best-case scenario for the Angels next year with potential signings of Walker and Fowler, who would fit in very nicely with their current lineup. Any team with Mike Trout has a chance to be successful after all. They will need to sign those two players first, and then the rotation needs to have luck on its side with the injury situations. The bullpen is a clear gap in the roster, so safe signings over the offseason could complement Bedrosian and possibly Street. Their farm system is also a clear work in progress, but it isn’t empty in terms of talent. That talent is just a little ways off at the moment. Overall the future of the Angels seems dreadful, but if things break right they can be a contender next year. Their overall run differential was only 18 apart from the first-place Rangers, so they at least played in close games. Now all that needs to be done is execution by the players and by the front office to bring a winner back to Anaheim.

Among the astounding phenomena abundant throughout calculus, linearization remains one of the least glamorous. It’s incredibly simple, taught in less than a day, and a more precise (and more complicated) method can often be substituted for it. On the other hand, it’s an incredibly powerful tool and one with weighty implications for fantasy baseball. Because of the concept’s relative simplicity, a reader with even the most basic inkling of what calculus actually is should be able to understand the idea of it, so don’t let a fear of mathematics deter you.

First, let’s think about graphs, functions, and derivatives. Put simply, continuous functions, whether they’re linear, quadratic, or exponential, will generally experience some rate of change — slope. Think of it as the change in the y direction per unit change in the x direction between two points. This is considered a secant line, or the average rate of change between two points. More interesting, however, is the concept of the tangent line, or the instantaneous rate of change at a given point. Note that the tangent line only touches the function at one point rather than two, meaning that we can easily evaluate and analyze the rate of change when comparing two points on a curve. Importantly, the magnitude of the slope of the tangent line tells us the rate by which the function is increasing or decreasing. So the greater the slope, the faster it is increasing (perhaps indicating an exponential function), and the lesser the slope, the more it is decreasing (a negative quadratic).

In calculus, the formula for linearization is:

L(x) = f(a) – f'(a)(x – a)

Here, given some value of a, we get a y-value, or f(a). From there, we subtract the product of the derivative of f(a) and the difference between the value we are estimating, x, and the value we already have, a. This gives the linear approximation and we get a pretty good estimate.

When rendered down to its most basic essence, linearization is a glorified form of estimation that gives credence to gut instinct through a formula. Using the tangent line at a certain point, one can make very incremental estimations, but it’s important to note that they must be very small. The farther from the initial point a that one travels to find an approximation of y, the less accurate the result will be.

It seems that this would have little application to baseball, but that’s incorrect. Recently, I started toying with a couple of formulas that could actually have some importance in the realm of amateur fantasy baseball with the usage of a regression line for an entire player’s career in pretty much any statistic.

L(x) = f(k) – f'(a)(x – a)

Here, f(k) is the actual value at the known point (k), f'(a) is the derivative of the predicted point on the regression line, x is the point for which we are predicting the value, and a is the value we start from.

L(x) = f(a) – f'(a)(x – a)

Differing here, f(a) is the predicted value at the regression line, f'(a) is the derivative of the predicted point on the regression line, x is the point for which we are predicting the value, and a is the value we start from.

I don’t know which would work best, but my guess is that first formula would be most accurate due to its mix of actual and predicted values. Neither of them would be terribly precise, but it’s a heck of a lot better than relying on what you feel might be best.

Regardless of which formula you might prefer, the implications of the linearization idea as applied to fantasy baseball are apparent. Probably best used for 10-day predictions, linearization mixes short-term performance with long-term talent to assess how well a player might perform for a short period of time — whether he’s likely to continue streaking, slumping, or somewhere in between. Rather than having to rely on gut instinct or dated and/or biased statistical analysis, a fantasy player could rely on some concrete math to make short-term decisions. This would be especially helpful in leagues that play for only a month, or can only alter their rosters once a week, or even at the end of a highly competitive season (perhaps making the risky move of dropping a slumping MVP for the streaking rookie).

It’s understandable if it’s unclear how to use one of the formulas at this point. To simplify matters, let’s use formula 1 to demonstrate how this might work in regard to something as simple as batting average. So what you might have is a regression line for a player of rolling 10-game predicted batting averages plotted along with actual values. In this case, x-values are 10-game rolling averages by each 0.01 (the intervals are arbitrary). So 1.1 is the x-value at 110 games played, while 1.2 is the x-value at 120 games. Let’s just say for simplicity that the player has played 110 games in his career, had an actual average of .264 during the last 10-game stretch, and the derivative of the regression line at this point is 0.12. We want to guess his average for the next 10 games, up to career game number 120.

L(1.2) = .264 – (0.12)(1.2 – 1.1)

L(1.2) = .254

We’d expect him to hit .254 over the next 10 games. Hopefully that makes some sense. Obviously it’s still in development and I haven’t done a whole lot of research yet, but expect some to come out later along with some clarifying material if necessary. Confusion is to be expected, but with some explanation applied linearization could potentially help a lot of people out next season in fantasy.

I’ve watched many a baseball game over my lifetime (that’s 50+ years), and I’ve cringed every time I see a National League manager send his starting pitcher up to bat any time prior to the seventh inning. Especially with runners on base! Doesn’t he know that pitchers can’t hit? Doesn’t he know that if he would just pinch-hit for the lame-batting starter he’d improve his team’s chances of winning?

So, after years of pondering this problem for five seconds at a time every couple of days, I decided to see if I could build a solid quantitative case for never letting a pitcher come to the plate for a National League team (obviously this is not an issue for the American League with their designated hitters). How would this change the look of the team’s pitching staff? And more importantly, how many more games would a team expect to win in a season if they adopted a “pitchers never bat” strategy?

The answer to the first question is pretty easy. The staff would “look” different. There were would be no more “starting pitchers.” A team’s pitching staff would consist only of “relievers.” Sure, one of the “relievers” would throw the first pitch of the game and could technically be called a “starter,” but given that he’ll be taken out of the game as soon as his spot in the batting line-up comes up, he’s effectively a “reliever,” just like the other 10 or 11 guys on the staff.

Now, the conventional wisdom would say that the current starting pitchers, especially the “aces,” get in a groove, and can give you six or seven solid innings. Why would anyone take them out the game in the second or third inning? Well, let’s do a “cost-benefit” analysis and see if we can make a case for “The Pitchers Never Bat” strategy.

Key Components of the Case:

The two primary components of the analysis are 1) how many more runs would a team expect to score in a season by pinch-hitting for every pitcher, and 2) how many more runs would a team expect to give up in a season because their starting pitchers are no longer going six, seven, or more innings in an outing? Or, maybe the team adopting such a strategy would actually give up FEWER runs per year by giving up on the century-old strategy of planning for the starting pitcher to pitch deep into the game.

A third component of the analysis could include the benefit of being able to choose from any of the team’s entire staff (probably 11 or 12 pitchers) and use only the ones that look like they’ve got their “stuff” while warming up before the game, instead of sticking with the “starter” who is scheduled to pitch today because it’s his turn in the “rotation.”

A fourth component of the analysis could include the benefit a team could achieve because the other team can no longer stack their starting batting order with a lot of lefties (to face a right-handed starter), or with lot of righties (to face a left-handed starter), because the team with no “starters” will pinch-hit for their first pitcher after one, two, or three innings. So, in total, the “handedness battle” tilts slightly more in favor of the team implementing the new strategy.

A fifth component could include the cost (or benefit) of reducing the size of the pitching staff by one or two, and adding one or two more everyday players, who would be needed to pinch-hit in the early innings.

A sixth component could be an added benefit that batters will not be able to get “used to” a pitcher by seeing them multiple times in a single game. Under the new strategy batters will see each pitcher once, or, at most, twice in a game.

I’m going to focus on the two primary components above, and let the lessor components alone for now. Perhaps others can weigh in on how to quantify the potential impacts of these changes.

Component #1: How much more offense will the “Pitchers Never Bat” strategy create?

This is the easiest of the components to quantify. I will use the wOBA (weighted On Base Average) statistic as defined and measured by FanGraphs to evaluate this component. Let’s start with some basic information and rules-of-thumb.

Using data from the National League for the 2015 season I find that pinch-hitters have a wOBA of .275 across the entire league, while pitchers, when batting, had a wOBA of just .148 across the entire league. The difference in wOBA between pinch-hitters and pitchers is .127 (that’s .275 minus .148.) Note that all position players in the NL combined for an average wOBA of .318 in 2015. I’m assuming that our new pinch-hitters won’t get anywhere near that figure, but will be comparable to the 2015 pinch-hitters, who came in way lower, at .275.

Now, let’s assume we can replace every pitcher’s plate appearance (PA) with a pinch-hitter. This improvement of .127 in wOBA needs to be applied 336 times per season, because that was the average number of times that a National League team sent their pitchers up to the plate in 2015. And lastly, we need to know two rules of thumb from FanGraphs that are needed to complete the analysis of the first component: 1) every additional 20 points in wOBA is expected to result in an additional 10 runs per 600 plate appearances, and 2) every 10 additional runs a team expects to score in season translates into one additional win per year. OK – so, let’s do the math:

If 20 additional points of wOBA translates into 10 runs per 600 PA, then our new pinch-hitters who are now batting for pitchers will provide the team with 63.5 incremental runs per 600 PA (which equals 127/20 * 10.) And since these pinch-hitters will be coming to the plate 336 times, not 600 times, we need to reduce the 63.5 incremental runs per season down to 35.6 incremental runs per season (which is 336 / 600 * 63.5).

Finally, the last step is to take our 35.6 incremental runs per season and translate that into incremental wins per year using the rule-of-thumb that ten runs equates to one win. Therefore, our 35.6 extra runs results in an expected 3.6 incremental wins per year. That’s a decent-sized pick-up in expected wins.

OK, so now, what about the pitching staff? Will replacing the conventional pitching staff with a staff consisting of no starters and all relievers cause the runs allowed to increase, and if so, by how much? Enough to offset our 3.6 extra wins that we just picked up on offense?

Component #2: How many more runs will pitchers give up using the “Pitchers Never Bat” strategy?

Imagine, for the moment, that a GM is to build his pitching staff from scratch. (We’ll worry about how to transition from a conventional staff to an all-reliever staff later.) And let’s just assume he’ll pick just 11 pitchers. (Most NL teams use 12-man staffs while some use 13, so that will give the team one or two additional position players.) Currently, starting pitchers typically throw 160-200 innings per season, and relievers tend to throw 50-80 innings per season. But with the new all-reliever strategy, and using only 11 pitchers, each of our new guys will need to average around 130 innings each, with perhaps some pitching as much as 160, and some as low as 100 innings per year. So, the GM is looking for 11 guys who can each contribute 100-160 innings per season. Each outing will be for about one to three innings for each pitcher. How will they fare?

Let’s look at the National League’s pitchers for 2015. Starting pitchers had an aggregate WHIP (Walks Plus Hits per Inning Pitched) of 1.299, while relievers, in total, recorded an identical WHIP of 1.299. So my takeaway from this is that the average starter was equally as good (or bad) as the average reliever. From this, I am going to take a leap of faith, and assume that a staff of 11 new-style relievers could be expected to perform equivalently. (And that doesn’t even factor in some of the lesser elements of the new strategy, as mentioned above, such as Components 3 and 4 of the analysis.)

From this, albeit simplified, evaluation of Component #2, I estimate that a team moving to an all-reliever pitching staff will have an expected change in Runs Allowed of zero, and therefore the change will neither offset, nor supplement, the offensive benefit evaluated in Component #1.

Conclusion and Final Thoughts

In summary, using the two primary components of my analysis, I estimate that adopting a “Pitchers Never Bat” strategy in the National League (a.k.a. an “All Reliever Pitching Staff” strategy) will improve a team’s offense by an expected 36 runs per year, which will increase the team’s expected win total by 3.6 games. I estimate that the impact on runs allowed will be near zero. Some lesser elements, Components #3 through #6, could also add some additional value to the strategy.

Implementing the strategy does not necessarily need to be a complete, 100% adoption of the “pitchers never bat” rule. Modifications can be made. Perhaps a pitcher is doing well through two innings and comes to bat with two out and no one on base. In this case the manager could let the pitcher bat, so that he can stay in and pitch another two or three innings. This would change the name of the strategy to something like the “Pitchers Very, Very Rarely Bat” strategy.

As far as transitioning to an all-reliever staff from a conventional staff, it could be done over time, or only in part, such that a team could maintain, say, its two top aces, and complement them with eight or nine relievers. This way, the aces could pitch as they do now, going six-plus innings, every fifth day, while limiting the “Pitchers Never Bat” strategy to the three out of the five days when the two starters are resting.

Finally, let’s try to put a dollar value on this new strategy. The guys at FanGraphs, and other places, have tried to estimate how much teams are willing to pay for each additional win. Without going into all the various estimates and approaches at trying to answer that question, let’s just go with a simple $8 million per win. I’m sure it could be argued to be more or less, but let’s just put $8 million out there as a base case. If that’s true, a 3.6-win strategy, such as the “Pitchers Never Bat” strategy, is worth about $29 million per year. Go ahead and implement the strategy now, and, if it takes, say, three years before any of the other NL teams catch on, you’ve just picked up a cool $87 million (3 * 29 million).

And if the other components of the analysis (#3 through #6) are quantified and it can be determined that they add another 0.5 wins per year, which I think is quite doable, then we can get the total up to 4.1 wins per year, for a value of $33 million per year, or just around a cool $100 million over the first three years. And that’s how you make $100 million without really trying!

With the special attention pitchers receive today, such as pitch counts, innings limits, as well as the host of PITCHf/x data that can notify teams of when a pitcher is fatigued, it seems like they days of 300-game winners have come and passed. And for the most part, some of this is true. We’ve seen pitchers be shut down during their earlier years to prevent injuries, such as the Nationals keeping a close eye on Stephen Strasburg. When we think of 300 wins, the math isn’t that hard. It’s some combination of 15+ seasons of 15+ wins over an entire career. Let’s dive in to what further breaks down these pitchers.

I gathered data on pitchers who finished their careers after 1980 as well as pitchers younger than that; I did this to avoid looking at pitchers such as Cy Young who are a little tough to compare to the modern day, with rule changes and the different run-scoring environments. In my query, I looked at pitchers with at least 250 wins. This gave me more data, and since 250-win pitchers are reasonably close to 300, it will allow me to get at what exactly creates a pitcher of this caliber.

My list included 19 names:

Greg Maddux

Roger Clemens

Steve Carlton

Nolan Ryan

Don Sutton

Phil Niekro

Gaylord Perry

Tom Seaver

Tom Glavine

Randy Johnson

Tommy John

Bert Blyleven

Fergie Jenkins

Jim Kaat

Mike Mussina

Jamie Moyer

Jim Palmer

Andy Pettitte

Some of these guys were absolute iron men, pitching over 5000 innings in their career. Maddux did this, as well as Carlton, Ryan, and Sutton. Most of this group barely reached 12 wins per season, showing that they reached the 300-club with longevity, not necessarily dominance. The other guys on this list, by default, either had higher win totals or pitched forever, but without racking up a ton of innings (Kaat, Moyer). Surprisingly, or perhaps not, only four of the 19 pitchers did not pitch for 20 seasons, so again, dominance might not be the key factor — instead, longevity.

I then looked at where these pitchers were at when they were 30 years old. Thirty years seems to be about a halfway point, but the data indicates otherwise. In fact, only three of these 19 pitchers had at least 150 wins at 30. This again drives home the point that these pitchers do not necessarily have to be untouchable every single year they pitched; it just means they have to be pitchers that stay healthy and can pitch for a long, long time. At the same time, the average pitcher on this list had 115 wins at 30, so they did need to have a productive youth in terms of racking up wins.

Here is a table displaying the careers of our 19 pitchers:

The amazing part, at least in my opinion, is that these pitchers almost seemed to get better with age, at least in terms of wins. I know that wins is not a good stat for tracking the effectiveness of pitchers, but since we are talking the 300-win club, it is what we have in front of us. Anyways, 17 of these 19 pitchers had more wins after 30 than they did before. Again, this hammers home the idea that longevity and durability is more important than complete dominance. Yes, you have to be a good, if not great, pitcher, but you also have to stay healthy.

So when looking at current pitchers that possibly have a chance at 300, I filtered through active pitchers fulfilling a few different qualifications. First, the pitcher must have at least 190 innings pitcher per year, including years of injuries (this helps get at longevity and durability). Also, the pitcher must also average at least 12 wins per year. I came up with a group of pitchers who where close to matching these requirements. From this list of 14 pitchers, I think eight or so have the best chance of eclipsing 300.

Here is a table of possible contenders:

This list includes: Clayton Kershaw, Chris Sale, Justin Verlander, Madison Bumgarner, David Price, Rick Porcello, Jon Lester, and Felix Hernandez. CC Sabathia, although at 223 career wins, does not make this list, since I don’t think he has 5-8 more seasons of decent pitching in front of him. I will go into each pitcher in more detail to describe what each pitcher needs to do to have a chance.

I’m going to start with Lester. Lester is currently at 146 wins, with 2003 regular-season innings pitched. He has been great through his first 11 seasons, in nine of which he was a full-time starter. In those nine seasons, he failed to pitch 200 innings just once, when he posted 191.2 innings pitched. He has been an iron man, and at age 32, the recipe is simple. He just needs to stay healthy and he needs his game to age well. This is going to be a repetitive theme, but to be honest, that’s what we would expect. Things helping Lester? Well, playing for the Cubs is one. Not only do they have a great defense, but they also create great run support, which can help Lester pick up a lot of wins. He was 19-5 this past year, matching his career high in Boston in 2010.

Now on to Justin Verlander. After an injury-riddled 2015, Verlander was great this year, posting a 16-9 record and an ERA of 3.04 (FIP of 3.48). Currently, he sits at 173 wins and is 33 years old. I mentioned his injury struggles in 2015. He only pitched 133 innings. In his 11 years as a full-time starter, that was the only the second time he failed to reach 200 innings pitched. People may worry that Verlander is starting to lose his velocity, which could mitigate his effectiveness, but in 2016, he struck out batters at a career-high rate and also had a career-best strikeout to walk ratio. Verlander is back with the elite, and if he can avoid injury trouble, he deserves to be in the discussion for a possible 300-win flirtation.

I’ll now move on to Clayton Kershaw. Kershaw has been the best pitcher in baseball for the past five years, and has only struggled with injuries for this past year, when he hit the DL with back issues. He still picked up 12 wins, and looked like peak Kershaw when he came back. Kershaw continues to strike out hitters and not allow walks, and in his shortened 2016, he posted a career-best FIP. Kershaw currently sits at 126 wins, and is 28 years old, in the middle of his prime. I think there are two factors that could keep Kershaw from getting close. The first one is his back. The Dodgers shut Kershaw down for half the year, and hopefully it heals, but if it is one of those lingering injuries that can also affect his timing a delivery as well as his overall health, he won’t be able to age his game to the necessary limits needed to hit 300. Also, he should get more wins. I’m not sure this will be a big factor now that the Dodgers have Andrew Friedman at the helm, but if he cannot get the run support he needs, that could lead to two or three fewer wins every year.

Chris Sale is next. Sale sits at 74 wins and is 27. He has some work to do. He has been relatively healthy, however, over his five full years as a starter. I think the best bet for Sale is to get out of Chicago, or at least the White Sox, and get on a team that can give him some good defense and offense. His win totals just aren’t high enough, but he is young enough where if he finds a new team and can age well, he might be able to hit 250.

I’ll do Bumgarner next. He really hasn’t had any injury trouble in his six years as a full-time starter. He is 27 and has 100 wins. He is a little harder to project, but I would say he’s got a better shot than Sale. I mean, he is already at 100 and only 27. Kershaw might have a leg up on him, but MadBum has been able to stay healthy. To be honest, Kershaw had been healthy too before this year, which somewhat shows that pitching 20 full seasons does not happen to often. Anyways, Bumgarner hasn’t quite been as dominant as some of the other names on this list, but he has been very good, and has stayed healthy. He is on a solid team with a good defense. The conditions are correct, he just needs to age well and stay healthy. I still like Kershaw’s odds a little more, but Bumgarner’s are not far behind.

Now I’ll move on to David Price. Price is 31, has 121 wins, and has pitched relatively healthy for seven full seasons. He is on the Red Sox now, which — although their poor defense won’t help some of his pitching metrics, they should give him the run support he needs. He wasn’t terrible this year; I have a feeling people think he fell off the map. He had 17 wins, and a ERA of 3.99 and a FIP of 3.60. His ERA and FIP were at career highs, but the FIP really wasn’t too far off what we’d expect. I’d credit the higher ERA to playing in Fenway with not the best defense behind him. Price may not be as dominant as he once was, but the Red Sox should give him support. He might be a little behind pace, but he could be the next CC Sabathia or Mike Mussina, where upon retirement, we say, “I didn’t realize he had 260 wins!” For the record, I doubt CC gets there, but the point is that if Price can stay healthy and moderately effective on a team that will support him, he may be able to move up in the wins chart. Will he hit 300? I don’t see it, but realistically, I’m not sure any of these guys will.

Now I’ll move on to the other Red Sox pitcher on this list: Rick Porcello. Porcello had a modest beginning in Detroit, but his FIP always seemed to outperform his ERA, so he has that going for him. Porcello is only 27 and somehow has 107 wins already. Although he is on the Red Sox, who can support him, Porcello really hasn’t been able to stay healthy over his career, and only eclipsed 200 innings pitched in a season twice: 2014 in Detroit, and this past season in Boston. Still, he is young, and if he can hang around awhile, he might be able to pick up 100 wins or more if he can stay decent on an offensive team. Again, he doesn’t need to contend for the Cy Young, but he has to stay relatively effective, so he keeps his starting spot and racks up wins.

Finally, I move on to my dark horse, King Felix Hernandez. Felix is only 30, but has been a full-time starter for 11 years. He sits at 154 wins. I feel like as a baseball community, we tend to forget about Felix. He has been very durable, although he hit the DL this past season by injuring his calf when celebrating a win. But hey, forgive the guy; he plays in Seattle, who hadn’t given him much help until recently. He is my dark horse on the list. He now plays on a good Seattle team, so he should be able to pick up wins. He might not be as good as he once was, but if he can stay effective, he has the best chance of anyone on this list. He can age well, he has stayed healthy, and he now plays on a winning team. The conditions are there, and I think he has the best shot of anyone on this list.

Realistically, if I had to choose between none of them winning 300 or one of them winning, that would be a much harder choice than picking one out of the group. Realistically, do I think any of these guys have a shot? Sure, but a shot is a lot different than actually getting there. Who knows, maybe one of these guys will age well and will stay healthy. Your guess may be as good as mine.

In “Hardball Retrospective: Evaluating Scouting and Development Outcomes for the Modern-Era Franchises”, I placed every ballplayer in the modern era (from 1901-present) on their original team. I calculated revised standings for every season based entirely on the performance of each team’s “original” players. I discuss every team’s “original” players and seasons at length along with organizational performance with respect to the Amateur Draft (or First-Year Player Draft), amateur free agent signings and other methods of player acquisition.  Season standings, WAR and Win Shares totals for the “original” teams are compared against the “actual” team results to assess each franchise’s scouting, development and general management skills.

Expanding on my research for the book, the following series of articles will reveal the teams with the biggest single-season difference in the WAR and Win Shares for the “Original” vs. “Actual” rosters for every Major League organization. “Hardball Retrospective” is available in digital format on Amazon, Barnes and Noble, GooglePlay, iTunes and KoboBooks. The paperback edition is available on Amazon, Barnes and Noble and CreateSpace. Supplemental Statistics, Charts and Graphs along with a discussion forum are offered at TuataraSoftware.com.

Don Daglow (Intellivision World Series Major League Baseball, Earl Weaver Baseball, Tony LaRussa Baseball) contributed the foreword for Hardball Retrospective. The foreword and preview of my book are accessible here.

Terminology

OWAR – Wins Above Replacement for players on “original” teams

OWS – Win Shares for players on “original” teams

OPW% – Pythagorean Won-Loss record for the “original” teams

AWAR – Wins Above Replacement for players on “actual” teams

AWS – Win Shares for players on “actual” teams

APW% – Pythagorean Won-Loss record for the “actual” teams

Assessment

The 1902 Chicago Orphans 

OWAR: 37.4     OWS: 280     OPW%: .527     (74-66)

AWAR: 29.9      AWS: 203     APW%: .496     (68-69)

WARdiff: 7.5                        WSdiff: 77  

The 1902 “Original” Orphans finished in third place, ten games behind the Reds. Bill Bradley (.340/11/77) thrived against opposing hurlers, notching career-bests in base hits (187), runs scored (104), doubles (39), home runs and batting average. “Bad” Bill Dahlen drilled 25 two-baggers and swiped 20 bags. Danny Green delivered a .302 BA and pilfered 35 bases. Jimmy “Pony” Ryan slashed 32 two-base knocks and produced a .320 BA. Johnny “Noisy” Kling succeeded on 25 stolen base attempts. Jimmy “Rabbit” Slagle executed 41 thefts and supplied a .315 BA for the “Actual” Orphans.

Bill Dahlen rated twenty-first among shortstops in the “The New Bill James Historical Baseball Abstract” top 100 player rankings. “Original” Orphans teammates registered in the “NBJHBA” top 100 rankings include Frank Chance (25^th-1B), Johnny Evers (25^th-2B), Jimmy Ryan (26^th-CF), Joe Tinker (33^rd-SS), Bill Bradley (46^th-3B), Johnny Kling (48^th-C) and Tom Daly (55^th-2B). “Actuals” second-sacker Bobby Lowe placed fifty-sixth.

  Original 1902 Orphans                          Actual 1902 Orphans

Jack W. Taylor (23-11, 1.29) paced the National League in ERA, shutouts (8) and WHIP (0.953). Mal “Kid” Eason contributed 10 victories with a 2.76 ERA and Carl Lundgren (9-9, 1.97) completed 17 of 18 starts during his rookie campaign. Jock Menefee (12-10, 2.42) and Pop Williams (11-16, 2.49) rounded out the rotation for the “Actuals”.

  Original 1902 Orphans                         Actual 1902 Orphans

Notable Transactions

Bill Bradley 

Before 1901 Season: Jumped from the Chicago Orphans to the Cleveland Blues. 

Bill Dahlen 

January 25, 1899: Traded by the Chicago Orphans to the Baltimore Orioles for Gene DeMontreville.

March 11, 1899: Assigned to the Brooklyn Superbas by the Baltimore Orioles. 

Danny Green 

Before 1902 Season: Jumped from the Chicago Orphans to the Chicago White Sox. 

Jimmy Ryan

Before 1902 Season: To the Washington Senators in unknown transaction.

Charlie Irwin

July 11, 1901: Released by the Cincinnati Reds.

July 12, 1901: Signed as a Free Agent with the Brooklyn Superbas.

Honorable Mention

The 1966 Chicago Cubs 

OWAR: 43.3     OWS: 235     OPW%: .510     (83-79)

AWAR: 27.1       AWS: 176      APW%: .364    (59-103)

WARdiff: 16.2                        WSdiff: 59

The “Original” 1966 Cubs placed fourth with a record north of .500 yet fifteen games off the pace of the Giants. Ron Santo (.312/30/94) merited Gold Glove honors for the third straight season and paced the circuit with 95 bases on balls and a .412 OBP. Lou Brock aka “The Franchise” tallied 94 runs and topped the National League with 74 stolen bases. “Sweet Swingin’” Billy L. Williams socked 29 long balls and registered 100 runs scored. Al “Red” Worthington (2.46, 16 SV) fashioned a 1.018 WHIP and secured the late-inning leads. Ernie “Mr. Cub” Banks contributed 23 two-baggers and a .272 BA. Ken Holtzman collected 11 victories while furnishing an ERA of 3.79 in his inaugural season.

On Deck

What Might Have Been – The “Original” 1921 Tigers

References and Resources

Baseball America – Executive Database

Baseball-Reference

James, Bill. The New Bill James Historical Baseball Abstract. New York, NY.: The Free Press, 2001. Print.

James, Bill, with Jim Henzler. Win Shares. Morton Grove, Ill.: STATS, 2002. Print.

Retrosheet – Transactions Database

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org”.

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

The FanGraphs Twitter page tweeted out a bingo card for Game One of the ALCS. As I looked through it, I thought it was a terrific idea by Michelle Jay and a fun way to follow the game that night. I was going to play along, but then I had another idea. Some slots were much more likely to happen, such as the “Pitcher v hitter stats are mentioned” slot. I figured I would let somebody else receive a t-shirt and just count up exactly how many times the TBS broadcast team mentioned batter vs. pitcher stats. We all know announcers love doing this, and we all know that it’s pretty useless for predicting the outcome of that particular at-bat. I just thought it would be cool to experiment and see how many times they actually mentioned these stats.

First, I’ll just go over the final numbers for batter vs. pitcher stats. There were 65 batters in this game, and batter vs. pitcher stats were either mentioned by the announcers or shown on a graphic for eight of those batters.  There were two separate times where they showed a graphic and then mentioned the stats later in the plate appearance, or vice versa. Four of the eight instances occurred when the Jays were hitting against Corey Kluber, three of the eight came when Andrew Miller was pitching, and the last one came when Marco Estrada was on the mound. It’s interesting that they would mention those stats more often when a reliever is pitching, considering the sample size is sure to be even smaller against relievers, rather than starters.

For fun, I marked each occurrence and tried to quickly type out how the announcer mentioned these stats:

1. Top 1, Josh Donaldson vs. Corey Kluber: “He’s got some pretty good numbers, 6 for 16 with a jack, so he sees him well” -Cal Ripken
2. Top 1, Russell Martin vs. Corey Kluber: “Martin is only 2 for 10 in his career against Kluber, both home runs…in fact, two of his last seven off Kluber have been home runs” -Ernie Johnson (graphic added later in the plate appearance reading “2 for last 7 off Kluber with 2 HR”
3. Top 2, Michael Saunders vs. Corey Kluber: “Saunders steps in, he’s 3 for 8 in his career against Kluber, and he fouls it off” -Ernie Johnson
4. Top 6, Michael Saunders vs. Corey Kluber: “Saunders with his two hits, now 5 for 10 off Kluber” -Ron Darling
5. Bottom 6, Jason Kipnis vs. Marco Estrada: graphic shown reading “0 for 7 4 K VS ESTRADA”
6. Top 7, Melvin Upton Jr. vs. Andrew Miller: “Upton’s got some numbers against Miller, 5 for 12 with three home runs” -Ron Darling (“That is some numbers” -Cal Ripken)
7. Top 8, Edwin Encarnacion vs. Andrew Miller: “Encarnacion in his last six at-bats against Miller a couple of home runs and a double” -Ernie Johnson
8. Top 8, Jose Bautista vs. Andrew Miller: graphic shown reading “.286 (2 for 7) 1 HR 2 BB VS MILLER” (later in the plate appearance: “One of the two hits that Bautista has off Miller…long ball” -Ron Darling

I’m not trying to knock these announcers by saying that they’re not good at what they do or anything. I would be a terrible announcer. I just think these stats are pretty useless and it was interesting to see how many times they actually mentioned them during a game. Mike Petriello pointed out on Twitter an example of why these numbers aren’t good to look at.

This would be kind of fun to track during the regular season for the really good ones, such as “so and so: 1 for 2 (.500), single career vs. so and so.” Maybe this can be a new metric or something, bpBAAR (batter pitcher Baseball Announcer Above Replacement).

At any point, feel free to scroll down to the bottom to see some of the tables of pitcher clusters.

Clustering Pitches

Clustering individual pitches using data from PITCHf/x is a fairly simple task. All you need to do is pick out the important attributes that you believe define a pitch (velocity, movement, etc.) and use a clustering algorithm, such as K-Means clustering.

With K-Means clustering, you decide what K (the number of clusters) should be. For my analysis, I chose K to be 500 (rather arbitrarily). Different pitch clusters can represent the same type of pitch (i.e. fastball) but with varying attributes. For example, clusters 50 and 100 might both correspond to fastballs, but cluster 50 might be a typical Chris Young fastball whereas cluster 100 might be a typical Aroldis Chapman fastball.

One important point to remember is that you, the analyst, must decide what the clusters represent. By looking at attributes of the pitches in a given cluster, you might identity the cluster as “lefty changeups” or “submariner fastballs” (which is actually a category you will discover).

The Problem of Clustering Pitchers

We can identify every pitch that a pitcher throws as belonging to a cluster from 1 to 500. Therefore, we know the distribution of pitch clusters for a given pitcher. The difficult problem, however, is how do we compare two pitchers using this information? Let’s say we have two pitchers:

• Pitcher A’s pitches are 50% from cluster 1 and 50% from cluster 200.
• Pitcher B’s pitches are 33% from cluster 1, 33% from cluster 300, and 33% from cluster 139.

The question remains, are Pitcher A and Pitcher B similar pitchers?

The problem of clustering pitchers is a more complicated one than clustering pitches because we now have a collection of pitches instead of just individual pitches to compare. In order to cluster pitchers, I use a model that is typically used for topic modeling called Latent Dirichlet Allocation (LDA).

An Aside on LDA

In LDA for topic modeling, our data is a collection of documents.

Let’s imagine that our collection of documents is articles from the New York Times. There are global topics that govern how these articles are generated. For example, if you think of a newspaper, the topics might be sports, finance, health, politics, etc. Additionally, each article can be a mixture of these topics. We might imagine there is an article in the sports section titled, “Yankees payroll exceeds $300 million”, which our algorithm may discover is 50% about sports and 50% about finance.

Similar to what is mentioned above, the analyst must figure out what the topics actually are. You do not tell the algorithm that there is a sports topic. You discover that the topic is sports by observing that the most probable words are “baseball”, “Jeter”, “LeBron”, “touchdown”, etc. The algorithm will tell you that a particular document is 50% about topic 1 and 50% about topic 20, but you must ultimately infer what topics 1 and topics 20 are.

I am harping on this point mainly just to mention that there is no magic to these clustering algorithms. An algorithm can cluster data, but it cannot tell you what these clusters mean.

Relevance of LDA to Pitchers

Anyway, how can this model be used to analyze pitchers? We just need to use our imagination. Instead of a collection of documents, we now have a collection of pitcher seasons. Whereas each document is made up of a collection of words, each pitcher season is made up of a collection of pitches. We have already discretized each pitch using K-Means clustering in order to create our own “dictionary” of pitches. In our baseball model, we imagine that each pitcher is a mixture of repertoires, whereas in topic modeling, each document was a mixture of topics. We can then cluster pitchers together by figuring out who has the most similar repertoires.

Nitty Gritty Details

If you are not interested in getting into the nitty gritty details, feel free to skip ahead to the next section to just see the cluster groupings.

• Data used is from 2007-2014.
• The dictionary of pitches (500 clusters) was created by running K-Means using all of the pitches from 2014. The choice of 2014 is arbitrary, but I used just one year’s worth of data because I thought it might be a sufficient amount and it was much quicker to run K-Means.
• The PITCHf/x attributes that were used to cluster pitches were start_speed, pfx_x/pfx_z (horizontal/vertical movement), px/pz (horizontal/vertical location), vx0/vz0 (components of velocity).
• For each pitcher from 2007-2014, each pitch was assigned to its closest cluster (determined by distance to the cluster center). I filtered out pitcher seasons in which the pitcher threw fewer than 500 pitches.
• I then ran LDA on pitcher seasons, choosing the number of repertoires (topics) to be 5.
• I used the method from this paper to get a vector representation of each pitcher season. I could have used the inferred repertoire proportions as my vector representations, but for various reasons, this did not produce as nice of clusters.
• Finally, I ran K-Means (K=100) on these vectors to get clusters of pitchers.
• Whereas in topic modeling, it is often interesting to interpret what the global topics actually are, I am not really interested in what the global “repertoires” are for the model. I am really using LDA as a dimensionality reduction technique to produce smaller vectors (5 vs. 500) that can be clustered together.

Some Observations

The actual clusters along with some relevant FanGraphs statistics are provided below. Each table is sortable. For brevity, I have only included clusters in which there are 10 or fewer pitchers. Only the first cluster shown (cluster 3) has more than 10 pitchers, which I simply included to demonstrate that a cluster could be quite big.

• As is probably expected, clusters are almost always entirely righties or lefties even though this is not an input to the model.
• Guys with similar numbers of batters faced cluster together. This is by design, as the way I determined the repertoire proportions accounts for the number of times a particular pitch is thrown.
• Sometimes weird clusters can form, such as Cluster 37, which contains both Chapman and Wakefield. Cluster 37 is mostly cohesive with hard-throwing left-handers and I believe Wakefield ends up here simply because he did not fit well into any cluster.
• This is not to say that the algorithm cannot find clusters of knuckleballers. Cluster 14 is all R.A. Dickey from years 2011-2014.
• There are also other clusters that contain exclusively one (or almost one) pitcher. Cluster 8 is 5 Kershaw years and one Hamels year. Cluster 68 is 5 Verlander years. I believe these clusters form partially because their stuff is so good. There are other pitchers who fall into almost exclusively one cluster but who are joined by many other pitchers. Another factor is that they might be able to repeat their mechanics so well that they remain in the same cluster because they are always throwing the same pitch types.
• Clusters of individual pitchers also happens if a pitcher has an incredibly unique style. Justin Masterson has his own cluster because he is such an extreme ground-ball pitcher. Josh Collmenter does as well due to the extreme rise he generates on his “fastball”.
• Cluster 29 contains just Kershaw’s 2014 season and J.A. Happ’s 2009 season. If you do a Ctrl-F for J.A. Happ, he finds himself in some pretty flattering clusters. This is especially interesting because from 2007-2014, he does not have particularly good seasons, but he has been quite good the last two years. This is not to suggest that these clusters can uncover hidden gems, but it’s not fully out of the realm of possibility.
• Most clusters produce quite similar ground-ball percentages. One of the factors that goes into clustering pitches (and therefore pitchers) is horizontal and vertical movement, which play a huge factor in a pitcher’s ability to produce ground-balls.
• Submarine pitchers always end up together. Check out Clusters 9, 60, and 92.

Overall, I think this is pretty interesting stuff. I was honestly surprised that the clusters turned out to be as cohesive as they were. Additionally, besides being a descriptive tool, I have to wonder whether this information can be used for predictive purposes. For example, we often talk about regression to the mean when discussing a player’s performance, whether it be a pitcher of a batter. It is possible that the appropriate mean for many pitchers is the cluster mean that they happen to fall into.

For the type of baseball fan I’ve become — one who follows the sport as a whole rather than focuses on a particular team — 2016 was the season of Statcast. Even for those who watch the hometown team’s broadcast on a nightly basis, exit velocity and launch angle have probably become familiar terms. While Statcast was around last season, it seems fans and commentators alike have really embraced it in 2016.

Personally, I commend MLB for democratizing Statcast data, at least partially, especially when they are under no apparent obligation to do so. I’ve enjoyed the Statcast Podcast this season, but most of all, I’ve benefited from the tools available at Baseball Savant. For it is that tool which has allowed me to explore xISO. I first introduced an attempt to incorporate exit velocity into a player’s expected isolated slugging (xISO). I subsequently updated the model and discussed some notable first half players. Alex Chamberlain was kind enough to include my version of xISO in the RotoGraphs x-stats Omnibus, and I’ve been maintaining a daily updated xISO resource ever since.

Happily for science, all of my 2016 first half “Overperformers” saw ISO declines in the second half, while most of my first half “Underperformers” saw large drops in second half playing time. Rather than focus on individuals, though, let’s try to estimate the predictive value of xISO in 2016.

Yuck. This plot shows how well first-half ISO predicted second-half ISO, compared to how well first-half xISO predicted the same, for 2016 first AND second-half qualified hitters. Both of these are calculated using the model as it was at the All-Star break. There are two takeaways: First-half ISO was a pretty bad predictor of second-half ISO, and first-half xISO was also a pretty bad predictor of second-half ISO. Mercifully though, first-half xISO was a bit better than ISO at predicting future ISO. This is consistent with the findings in my first article, and a basic requirement I set out to satisfy.

Now, an interesting thing happened recently. After weeks of hinting, Mike Petriello unveiled “Barrels”. Put simply, Barrels are meant to be a classification of the best kind of batted balls. Shortly thereafter, Baseball Savant began tabulating total Barrels, Barrels per batted ball (Brls/BBE), and Barrels per plate appearance (Brls/PA). In a way, this is similar to Andrew Perpetua’s approach to using granular batted-ball data to track expected outcomes for each batted ball, except that the Statcast folks have taken only a slice of launch angles and exit velocities to report as Barrels.

By definition, these angles and velocities are those for which the expected slugging percentage is over 1.500, so it would appear that this stat could be a direct replacement for my xISO. Not so fast! First of all, because ISO is on a per at-bat (AB) basis, we definitely need to calculate Brls/AB from Brls/PA. This is not so hard if we export a quick FanGraphs leaderboard. Let’s check how well Brls/AB works in a single-predictor linear model for ISO:

Not too bad. The plot reports both R-squared and adjusted R-squared, for comparison with multiple regression models. I won’t show it, but this is almost exactly the coefficient of determination that my original xISO achieves with the same training data. I still notice a hint of nonlinearity, and I bet we can do better.

Hey now, that’s nice. In terms of adjusted R-squared, we’ve picked up about 0.06, which is not insignificant. The correlation plot also looks better to my eye. So what did I do? As is my way, I added a second-order term, and sprinkled in FB% and GB% as predictors. The latter two are perhaps controversial inclusions. FB% and/or GB% might be suspected to be strongly correlated with Brls/AB, introducing some undesired multicollinearity. While I won’t show the plots, it doesn’t actually turn out to be a big problem in this case. Both FB% and GB% have Pearson correlation coefficients close to 0.5 with Brls/AB (negative correlation in the case of GB%). Here’s the functional form of the multiple regression model plotted above, which was trained on all 2016 qualified hitters:

To be honest, there is something about my first model that I liked better. This version, using Barrels, feels like a bit of a half-measure between Andrew Perpetua’s bucketed approach and my previous philosophy of using only average exit-velocity values and batted-ball mix. My original intent was to create a metric that could be easily calculated from readily available resources, so in that sense, I’m still succeeding. Going forward, I will be calculating both versions on my spreadsheet. I’m excited to see which version serves the community better heading into 2017!

As always, I’m happy to entertain comments, questions, or criticisms.