# The Best Players in Baseball to Lead Off Your Team’s Inning

Timing in baseball is everything, it comes up again and again in different areas of the game. One area in which it is particularly important is the batting order, and which hitters come to the plate at various points in the game.

The effect of how the lineup is set has been well-documented, like herehere, and here, along with many other articles since then. But after the first inning or two, the order largely gets jumbled, and different players come to the plate at different points in the game with different leverages. With this in mind, which players have been the best this year at leading off an inning for their team(s)?

# The Blue Jays Quietly Have One of the League’s Best Rotations

Through August 13th, the Toronto Blue Jays’ rotation has performed at a high level, ranking 1st in innings pitched, 5th in groundball percentage, 3rd in GB/FB ratio, 4th in ERA, 12th in FIP, 9th in xFIP, and 5th in WAR. The collective of Marcus Stroman, R.A. Dickey, Marco Estrada, Aaron Sanchez, and J.A. Happ have even done this while posting league-average K% and BB% and laboring through innings (only the Reds and Orioles throw more than Toronto’s 17.1 pitches per inning). They also go after hitters at a league-average rate (i.e., they throw an average number of strikes), and yet they have the second lowest BABIP in the league at .273. What about Toronto’s rotation makes their results so special, when their peripherals seem so average? The short answer is their individual fastballs.

## The Blue Jays Have Among the Most Valuable Set of Fastballs

The Blue Jays starter’s draw a very high amount of value from their fastballs, of each the four-seam, two-seam, and cut varieties. Despite only 4 teams using four-seams less than the Blue Jays, they are second only to the Nationals in total value from the four-seam. In other words, Toronto uses the four-seam sparingly, but derive immense value from it. Unsurprisingly, per 100 pitches, their PITCHf/x values rank 1st, 3rd, and 6th for the four-seam, two-seam, and cut fastballs, respectively. Their four-seams have far below average velocity (likely due to Dickey’s 82mph fastball), but their two-seams rank 4th in the MLB at 93.2mph. But what is particularly impressive about their fastballs is the uniquely extreme movement each starter generates.

## Toronto’s Rotation Generates Extreme Levels of Fastball Movement (or Lack Thereof)

So far in 2016, there have been 271 pitchers that have started a game. Of these 271, 263 throw a four-seam fastball, 174 throw a two-seam fastball, and only 95 throw a cutter. Below is a chart highlighting some of the extreme rankings the Blue Jays’s starters have relative to the rest of the league. When looking at horizontal movement, the rankings are relative to the handedness of the pitcher (Happ is the only lefty). When looking at vertical movement, it is relative to movement up (i.e. a higher ranking means less downward movement and vice versa).

As above, each pitcher ranks in a fairly extreme position (either high amounts of movement or little amounts of movement) in one of the varieties of fastball. Stroman in particular generates very little movement (horizontal or vertical) on any of his fastballs, relative to the league. Dickey’s four-seam moves (far) away from righties, while not sinking much at all. Sanchez generates a fair amount of movement away from righties on both his four-seam and two-seam, with Happ having his respective pitches do the same to lefties.

## Marco Estrada’s “Cue Ball” Fastball Has Special Movement

Estrada, however, is the pitcher with the most interesting profile. As detailed here by MLB.com’s Mike Petriello, both Estrada’s four-seam and cutter generate very little downward vertical movement, and almost seemingly (and impossibly) have a rising effect. Estrada himself has deemed this effect the “cue ball”, as he feels that “[i]t’s just a perfect white ball. I notice my four-seamers are straight right up and down”.

It’s also interesting to note that Estrada has generally fallen in the rotation immediately after Dickey and/or Stroman, who generate the most vertical movement downward. Of the three, only Estrada generates higher than average numbers of strikeouts. But, both Dickey and Estrada generate lots of soft contact, and have low BABIP to show for it. Of the 160 starters with at least 50 IP, Estrada is 1st in the league at .217 and Dickey is 32nd at .270 (for good measure, Happ is 31st, also at .270, and Sanchez is 46th at .278). It’s interesting to wonder if each of their individual successes has something to do with the vastly different movement their fastballs display, and if this affects their opponents day-to-day timing. If a batter faces Dickey’s low sinking fastball in the first game of a series, and then Estrada’s cue ball the next day, would their timing be thrown off, even slightly?

## Blue Jays Starters Hammer the Zone with Fastballs

Further adding to this possibility is the fact that all Toronto starters use their fastballs similarly. The MLB average heatmap for fastballs looks like this (courtesy of Fangraphs). Each of Stroman, Dickey, Estrada, Sanchez, and Happ hammer the zone with their fastball at an above-average rate. These graphs also support the charts above, where Stroman and Dickey keep fastballs down in the zone, Estrada leaves his higher, and Sanchez and Happ pitch inside to same-handed batters.

The Blue Jays starters all get similar, stellar results, even though their peripheral stats may not suggest it. They do this by collectively using a wide range of movement on their fastballs, and attacking the zone with them. This has helped them maintain one of the lowest BABIPs in the league, and generate the highest values on their fastballs both individually, and as a group. Marco Estrada in particular has generated a prolifically low BABIP, and should he continue this level of performance, it would not be shocking to see him garner AL Cy Young votes. While their success has not been heavily covered this year, the Toronto Blue Jays rotation is poised to help them make a deep playoff run this MLB Postseason.

Readers, what do you think? Does the Blue Jays’s rotation deserve more recognition? What do you think is the key component to their success? Which starters, if any, deserve discussion for the AL Cy Young Award? Leave your thoughts in the comments below or on Twitter @SaberBallBlog. Don’t forget to subscribe to SaberBallBlog by clicking the green “Follow” button in the menu, and follow on Twitter for all of the latest updates on the MLB!

# Analyzing the Yankees 2016 MLB Trade Deadline by Prospect Surplus Value

The New York Yankees were far and away the busiest team at the August 1st trade deadline, and their decision to “sell” surprised many. As detailed here by MLBTradeRumors, the Yankees traded away 4 active players and a prospect, and received back 10 prospects, 2 major leaguers, and 2 players-to-be-named-later (PTBNL). While the Bronx Bombers are only 5.5 games back of the second wild card spot as of August 3, their decision to sell off aging players and retool for the future is a tried and true strategy that they hope will pay off.

# The MLB Postseason Effects of Regular Season Performance Against Top of the Rotation Starters

In the ensuing discussion of Review of First Half Rotation Matchup Luck, Reddit user /u/JustTrynaChill posited the question of the effect of regular season success against top-of-the-rotation starters on playoff success. This certainly was an intriguing question, and so using similar parameters, we’ll investigate the query.

To examine this effect, we’ll look at the 40 playoff teams from 2012 to 2015, the beginning of the expanded Wild Card era. During each individual season, we’ll investigate the performance of the team versus the top two quintiles of MLB starters by FIP. We’ll limit these starters to ensure that they have at least 80 IP as a starter (approximately half a season), to guarantee that they had a significant enough effect on their team’s season to qualify.

# Reviewing First Half Rotation Matchup Luck

Now that the unofficial second half of the MLB season is underway, every team looks to reassess its approach as the non-waiver trade deadline nears. Underperforming teams look to become “sellers”, while teams confident in their playoff chances seek new infusion of talent as “buyers”. Part of a team’s prospective outlook is its remaining strength of schedule. Teams that over or under performed their talent due to the MLB schedule in the first half may look to benefit in the second half.

Having poor luck with the scheduling can cause an MLB team to underperform, but in addition to this there the luck involved with rotation scheduling. For instance, on two separate occasions, the Braves had to face a stretch of 4 #1 caliber pitchers in a row, and one of these occurred in a stretch of games where 10 of the 12 opposing starters were #1 caliber. Similar “luck” has also occurred for the Phillies and Diamondbacks so far this year. While in some instances the team handled it well, in others it caused extended overall down turns.

This luck applies to both the rotation scheduling of the other team, but also your own, and the disparity between the two. Let’s evaluate the relative strength of rotations that each team has faced over the first half of the season, and the disparity in the quality of their starter versus that of the opposing team. Continue reading Reviewing First Half Rotation Matchup Luck

# Which Teams Use Their Bullpens Optimally?

Earlier this week, Casey Boguslaw posted an excellent article over at Baseball Essential regarding Lineup Optimization. The premise of his argument revolved around comparing a team’s wRC+ and their run production per game. In theory, a team with a low wRC+ but high R/G implies that the lineup has been optimized, i.e. they are squeezing every run out of which they are capable out of the lineup. Conversely, a team with a high wRC+ but low run production is suboptimal, and not scoring as much as they should.

Let’s apply this concept to bullpen use. Each team has a certain number of relievers they are able to use in different situations. Similar to the lineup, different points in the game are more or less crucial. This is tracked by the leverage index (pLi). In a few words, a game situation of average leverage has a pLi of 1, with more intense game situations greater than 1, while less intense situations are less than 1. For a bullpen to be optimized, as the leverage increases incrementally, better and better relievers must be used, i.e. the relationship is roughly linear.

# Probability: Why Hitting Streaks are Impressive (And Why They’re Not)

As it seems to happen every year, baseball was recently aflutter with a hitting streak chasing Joe DiMaggio‘s legendary 56 game streak. This time, it was Jackie Bradley Jr.‘s 29 game hitting streak, between April 24 and May 25. During this stretch, Bradley collected 44 hits, including 20 XBHs to triple-slash .415/.488/.783 and raised his batting average for the season from .222 to .350.

Then, his teammate Xander Bogaerts followed it up with a 26 game hitting streak of his own from May 6 to June 2. During this time, Bogaerts collected 45 hits, 13 of which were XBHs, and triple-slashed .385/.419/.581.

## Past Hitting Streaks of 25 Games or More

Using Baseball-Reference’s Play Index, Bradley and Bogaerts are two of the 39 batters to achieve 25+ game hit streaks since 2000, and were the first pair of teammates to have a hitting streak of that length start and end in the same season since Luis Castillo and Kevin Millar did it for the 2002 Marlins. Remarkably, they are also the 7th and 8th Red Sox players to achieve a hitting streak of at least 25 games since 2000, joining Nomar Garciaparra (26 games, 2003), Johnny Damon (29 games, 2005), Manny Ramirez (27 games, 2006), Victor Martinez (25 games, 2009), Dustin Pedroia (25 games, 2011), and David Ortiz (27 games, 2012-2013). Long streaks don’t just seem to happen in baseball every year; they seem to happen for the Red Sox alone that often!

A large part of the compulsion to watch hitting streaks is how invested fans become in the chase of DiMaggio’s streak. There is breakaway coverage and live look-ins to at-bats, constant updates on where the batter is in the lineup, or in which inning he collects the most hits. Another part of the interest comes from the sheer skill needed to amass such a streak.

## Determining the Probability of a Hitting Streak

Long streaks seem to indicate that a player is “locked in at the plate” or “seeing the ball well”. And that is likely true, to some extent. Just as players go through slumps when they’re hurt, they may be equally likely to have particularly good conditioning for a stretch, or face pitchers that they match up against well. There is conflicting evidence as to whether or not a “hot-hand effect” truly exists, or not. But one thing is certain: regardless of whether or not a player is “hot” or if that effect exists, the probability of a hitting streak is quite low the longer it goes on.

To build a model of hitting streak probability, let us first imagine a simple coin flip. When flipping the coin there are two possibilities, heads and tails, each with equal likelihood. If we were to flip the coin four times, there would be a certain probability that at least one flip out of the four was heads (we’ll call this a “head series”). If we did this series of 4 flips 162 times (that is, 648 times total, looked at in sets of 4), there would be a certain probability that there would be a long stretch of consecutive head series.

To adapt this model to baseball, we’ll change the “flips” to “plate appearances”, the “series” to “games”, and set the probability to “hitting average”.

It is important to note the difference in “hitting average” and “batting average“. While batting average is an actual statistic that gets tracked, hitting average is a statistic that we’ve developed for the purpose of this model. A player is very likely to get at least 4 plate appearances in a game, but if they earn a walk in 2 of them, then they will only be credited with 2 at-bats, the statistic that gets used to calculate batting average. In other words, batting average tracks the probability a player will get a hit when they are trying to get a hit, where as hitting average tracks the probability that a player will get a hit within a certain plate appearance, regardless of game context. To give context, the hitting average for the 4367 separate player-seasons since 2000 that had at least 300 PAs in a season is .243 (the corresponding batting average is .270).

From here, we will determine the probability that a player gets at least one hit in any one game. To do this, we subtract the probability that they will get no hits in 4 plate appearances from 1. For example, if a player had a .250 hitting average, the probability that they will get 0 hits in 4 plate appearances is the probability of not getting a hit $(1 - 0.250 = 0.750)$ to the fourth power: $0.750^{4} \approx 0.6836$. This means that this player has a 68.36% chance of getting at least one hit in any one game.

What we want to figure out is the probability that they will get a long stretch of hits over a season. It is reasonable to note, however, that hitting streaks are not season sensitive. For instance, Ortiz’s 27 game streak occurred almost equally between the end of his 2012 season and the beginning of 2013. The longest recent streak, by Jimmy Rollins at 38 games, occurred mostly in 2005 and extended into 2006. But in the scope of modeling how likely it is to happen each year, we will limit the calculations to a 162 game stretch.

To determine the probability that a 25 game hitting streak will occur during a 162 game season is different from estimating the probability that a player will get a hit in 25 consecutive games. To use the analogy from before, the probability of 25 consecutive heads in 25 flips is different than the probability of a stretch of 25 consecutive heads amongst a total of 162 flips. Knowing this, we will use the work of French mathematician Abraham de Moivre from 1738 and used here (before the invention of baseball, but it still applies!).

# Charting the Probability of Hitting Streaks by Average

By running different hitting averages and streak lengths through the calculation, we can chart the data to see how likely it is for a player to get a hit streak of a certain length. To make this chart compatible with the more common batting average, simply take the batting average and subtract around 0.030 (30 points) of batting average to estimate the hitting average.

Interesting things to note from the chart:

1. A player with a .200 hitting average is more likely to go an entire season without a hit (0.9997 probability of a hitting streak of at least 1 means 0.0003 of no hits) than Joe DiMaggio was to get a 56 game hitting streak (.289 hitting average translates to < 0.0000 probability)
2. After about 20 games, it becomes substantially more unlikely for the streak to continue, and this accelerates after 25 games. This bears out what we observe in the fanbase and media attention to streaks.
3. Medium length streaks (~15 games) are much more likely and common than we probably realize as fans.

# Why Hitting Streaks are Impressive

## Analyzing Jackie Bradley Jr.’s Hitting Streak

With this chart, we see how improbable Jackie Bradley Jr.’s hitting streak really was. Even considering the fact that the streak greatly increased both his batting and hitting averages, his career hitting average through a little more than 1000 PAs since his debut in 2013 is only .209. Consulting our chart, we can see that there is approximately a 1-in-33,333 (0.003%) chance of a hitting streak of this length for someone of that profile. In real world terms, this is like flipping a coin 15 times and getting all heads.

However, in fairness to Bradley, his true talent may be much higher than this number. Throughout his minor league career, Bradley maintained a .249 hitting average. To split the difference, we’ll combine his minor league and major league stats to put his hitting average at .233. This changes the odds to about 1-in-4,750 (0.021%), or about 7 times more likely. Again, in real world terms, the probability of getting struck by lightning at some point in your life is 1-in-3,000, or 1.5x times as likely. In some ways then, Bradley’s streak was like catching lightning in a bottle!

## Analyzing Xander Bogaerts’s Hitting Streak

Almost completely counter to the Bradley example, however, Xander Bogaerts’s streak was pretty unsurprising. Bogaerts’s career hitting average is .271. A 26 game hitting streak with this hitting average has a probability of 0.6%, or 1-in-160. In real world terms, this is only three times less likely than correctly guessing the face value and suit of a card randomly drawn from a standard 52 card deck.

Since 2000, there have been 1477 player-seasons with a player having a hitting average of at least .270. Of these, only 5 have contained hitting streaks of at least 26 games, for a percentage of 0.34%. If we extend this to hitting averages of at least .260 (since Bogaerts’s is currently a little higher due to the streak itself), we see that the percentages line up almost exactly, with 10 instances, coming to 0.64%.

Essentially, a hitting streak like Xander Bogaerts’s seems to happen almost every year because at any time there are about 100 players with similar hitting averages to his in the league and we expect almost one of them to have a 26 game hitting streak, probabilistically.

# Why Hitting Streaks Aren’t Impressive

A case for the unlikeliness of hitting streaks like Jackie Bradley Jr.’s simultaneously shows both why hitting streaks are impressive and why they are not. For someone like Bradley to have a hitting streak that long against such great odds, it would seem to require great skill. But the very fact that he does not possess great (relative) skill is what makes the odds so long. To see this easily, looking at someone like Xander Bogaerts and the much greater likelihood of his hitting streak diminishes the impressiveness of the feat.

The case most frequently used against hitting streaks states that a hitter could amass a streak (of any length) simply by triple-slashing .200/.200/.200. This would obviously hurt his team, but the hitting streak would be maintained. While this argument is valid, nothing quite close to it has happened in recent memory.

Since 2000, the worst batting average over a streak of at least 25 games was Casey Blake‘s .317, the worst OBP was Nolan Arenado‘s .383, and the worst SLG was Willy Taveras‘s .426. On their own, each of these are more than acceptable production from any level of player, so the argument that the player can hurt their team during a hitting streak, while true, doesn’t hold up to the evidence.

The argument that does hold weight, however, is that a hitting streak does not imply that the team itself is performing well, even though the player might be. The aggregate record across the 39 instances is 587-493, for a .544 winning percentage. This prorates to about 88 wins for the team in a year, certainly a respectable season. But this number is skewed by some very good stretches from team’s, including the 2016 Red Sox. In a little over a third of the cases (15/39), the team had a .500 record or less. These include some of the more high profile streaks, such as Chase Utley‘s 35 game streak in 2006 (the Phillies went 17-18), or Andre Ethier‘s 30 game streak in 2011 (the Dodgers went 13-17). So even in some of the hitting streaks with the most media attention, team success is not a guarantee. This could be due to any number of reasons, including opposing teams overexerting to stop the team in question, good players playing on bad teams, etc.

# Hitting Streaks: the Ultimate Verdict

Summing it all up, there still remains conflicting evidence as to whether or not hitting streaks are statistically impressive or not. On the one hand, they are probabilistically difficult for any one hitter to accomplish. But simultaneously, there can be over 100 active players at any one time ready to go on a long streak. When players like Jackie Bradley Jr. go on long streaks, it causes us to re-evaluate what their baseline skills are. But if a player like Bradley can go on such a long tear, doesn’t this also mean that it might not be that impressive? Finally, how does the team’s outcome during the stretch matter? There are plenty of teams that have fallen on their face despite the success of an individual.

Ultimately, it seems that this will be a debate that will continue indefinitely. There are too many variables to definitively state whether or not the hitting streak is a statistically impressive feat.

Readers, what do you think? Is the hitting streak statistically impressive, or just a stretch of good luck? What factors do you use to make your decision? Which hitting streaks of the past few years have been your favorite to watch? Which player do you think is likely to pull off the next long streak? Leave your thoughts in the comments below or on Twitter @SaberBallBlog. Don’t forget to subscribe to SaberBallBlog by clicking the green “Follow” button in the menu, and follow on Twitter for all of the latest updates on the MLB!

# AL Midseason Debuts: Prospects Looking to Make an Impact – #1 Blake Snell

With the 2016 season underway, each team looks to compete immediately with the pickups they made in the offseason. But as we saw around the MLB in the 2015, the midseason callups can have as big of an impact as the players obtained in free agency. This series will detail the 5 prospects in the AL looking to make the biggest impact on their respective teams this season.

For the purposes of this series, we will set a few baseline criteria:

1. The prospect cannot have any previous Major League experience prior to the 2016 season.
2. The prospect must already be reasonably close to the MLB.
3. The prospect must play a position of need for his big-league squad, and this need cannot be due to injury.

Be sure to check out the impact cases for the prospects previously covered:

#5 – Sean Manaea, OAK, LHP

#4 – Tim Anderson, CHW, SS

#3 – José Berríos, MIN, RHP

#2 – A.J. Reed, HOU, 1B

# AL Midseason Debuts: Prospects Looking to Make an Impact – #2 A.J. Reed

With the 2016 season underway, each team looks to compete immediately with the pickups they made in the offseason. But as we saw around the MLB in the 2015, the midseason callups can have as big of an impact as the players obtained in free agency. This series will detail the 5 prospects in the AL looking to make the biggest impact on their respective teams this season.

For the purposes of this series, we will set a few baseline criteria:

1. The prospect cannot have any previous Major League experience prior to the 2016 season.
2. The prospect must already be reasonably close to the MLB.
3. The prospect must play a position of need for his big-league squad, and this need cannot be due to injury.

Be sure to check out the impact cases for the prospects previously covered:

#5 – Sean Manaea, OAK, LHP

#4 – Tim Anderson, CHW, SS

#3 – José Berríos, MIN, RHP

# AL Midseason Debuts: Prospects Looking to Make an Impact – #3 José Berríos

With the 2016 season underway, each team looks to compete immediately with the pickups they made in the offseason. But as we saw around the MLB in the 2015, the midseason callups can have as big of an impact as the players obtained in free agency. This series will detail the 5 prospects in the AL looking to make the biggest impact on their respective teams this season.

For the purposes of this series, we will set a few baseline criteria:

1. The prospect cannot have any previous Major League experience prior to the 2016 season.
2. The prospect must already be reasonably close to the MLB.
3. The prospect must play a position of need for his big-league squad, and this need cannot be due to injury.

Be sure to check out the impact cases for the prospects previously covered:

#5 – Sean Manaea, OAK, LHP

#4 – Tim Anderson, CHW, SS