RotoGraphs, in addition to several Community writers, have been posting about an “x” category of metrics for quite some time. They include things like Andrew Dominijanni’s xISO, Andrew Perpetua’s xBABIP, and more. The clear purpose of developing those statistical indicators was to measure and predict fantasy-baseball success, something we all aspire to in our hopefully low-priced leagues (although you probably found that using x-stats is a lot like overstudying for a test because the amount of effort you put into preparing yields diminishing returns, and you “over-Xed” the players).

One of the most prominent of the x-stats trotted out at the beginning of every season is xHR/FB, developed by Mike Podhorzer, and always accompanied by an amusing “leaders and laggards” piece. His version of xHR/FB is quite good, with a .649 R-squared value. In his regression analysis, Mr. Podhorzer utilizes somewhat exclusive metrics (hopefully public at some point), such as average absolute angle. Overall, it’s a pretty good predictor, and it becomes doubly understandable to the layman when it gets multiplied by fly balls to produce an expected home-run value.

The only real issue I have with HR/FB (and its prediction) is that it is HR/FB. While it is more stable for hitters than for pitchers, it still isn’t quite as stable as a stat I’d like to use for fantasy baseball. For my 1000 player-season sample from 2009-2015, HR/FB had a year-to-year R-squared value of .49. It isn’t terribly difficult to figure out why. There are numerous reasons, including weather changes, team changes, opponent changes, player development, and more. Moreover, it doesn’t take a very good picture of a hitter’s overall profile because it only looks at how many home runs a player hits per fly ball. A player might have a high HR/FB, but he may not hit enough fly balls for the metric to accurately describe his power (i.e. whether he actually hit a lot of home runs). On the other hand, it’s important to note that a high HR/FB generally goes with a higher FB%.

Perhaps a better metric for evaluating a player in the greater context of his hitting profile is HR/BBE. Home runs per batted-ball event is just HR/(AB+SF+SH-SO). It has a slightly higher year-to-year R-squared of .56 (from my sample), in large part because it takes into account more variables than does HR/FB. Under the umbrella of BBE fall not only fly balls, but line drives (and there can be line-drive home runs), and ground balls. In case you’re wondering why I included sacrifice hits, it’s because they tell a little bit about what kind of hitter a player is. Most modern managers are far more likely to ask a Ben Revere to lay down a sacrifice bunt than they are a Kris Bryant.

And so I thought it might be useful to run a linear regression analysis to develop an xHR/BBE (and from there, xHR). I’m a statistical autodidact, so I tried to keep things simple. Additionally, I thought it would be best if I utilized accessible variables like FB% so that a moderately literate sabermetrician could use it. After testing myriad variables, I came up with four that I’d use — average FBLDEV (Statcast), wFB/C, SLAVG, and FB%.

• AVG FBLDEV – Average fly ball/line-drive exit velocity. The idea is that the higher this value is, the harder the player is hitting the ball, and so he will hit more home runs.
• wFB/C – A rather obscure metric buried in the FanGraphs glossary, wFB/C is weighted fastball run values per 100 pitches. I use it because most home runs come off some form of a fastball, and home-run-hitter types are typically good fastball hitters.
• SLAVG – “Slap” average, a metric of my own invention (although someone else has probably thought of it – I just haven’t seen it before), is singles divided by at-bats. It’s a bit like ISO in that it tells you about a player’s power distribution (or lack thereof). I figure that this is inversely correlated with power because the more singles a player hits, the fewer home runs he’s likely to hit.
• FB% – Fly ball percentage obviously figures pretty heavily into a power hitter’s profile. It’s awfully difficult to hit a lot of home runs without hitting a plethora of fly balls.

It seems like a decent list of predictors in that they are understandable and accessible to the average fan, in addition to having a good relation to home-run hitters. I used all players that had at least 100 batted-ball events in 2015 and 2016 (Statcast only has data going back to 2015), which turns out to be close to 500 player-seasons. So let’s throw them into the Microsoft Excel Regression grinder and see what it spits out:

Note: To be clear, the end goal is not necessarily xHR/BBE, but rather xHR. xHR/BBE is just the best path to xHR because HR/BBE is a rate stat, meaning that it will have a better year-to-year correlation than home runs because that’s a counting stat. So if a player gets injured and only plays half a season, his HR/BBE would probably be similar to his career values, but his home-run numbers would not be.

The primary thing to recognize here is the R-squared value: a pretty good .78272. To the uninitiated, this simply means that the model explains 78% of the HR variance. If you’re interested (and you really ought to be), here are the coefficients for the variables and the overall formula:

xHR= (.114557524*FB% – .183885205*SLAVG + .006658976*wFB/C + .004075449*FBLDEV -.343193723) * BBE

With this information, it isn’t terribly difficult to look up a few pieces of data on FanGraphs and Statcast to see how many home runs a player “should” have hit. In case you’re wondering about its predictive value relative to that of HR/BBE, xHR/BBE has an R-square value that’s six points higher (.61). Nevertheless, it’s important to note that, based on the graph, the model struggles to predict home-run numbers for the players on the extremes – the Jose Bautistas of the world. Because the linear regression tends to underestimate rather than overestimate at the top, it’s likely that a quadratic regression would fit better. It’s something to look into, but this’ll do for now. Moreover, while there are some really crazy outliers, like Jose Bautista being predicted to hit 12 fewer home runs (Steamer does have him on pace for only 26 this year!), the model does work reasonably well for more average players.

Keep in mind that numerous improvements will be made. If anyone wants access to data or has a question, then just let me know. If not, then enjoy the tool and use it for fantasy, even though it’s getting a bit late for that. Maybe next year.

Over the weekend, the Atlanta Braves swapped their bad infielder embroiled in a domestic violence incident, Hector Olivera, for nice-guy outfielder Matt Kemp. The deal was largely panned within the industry, and many felt the Padres benefited most by ridding themselves of Kemp while he still had value. Olivera’s involvement in the deal was a purely financial exchange, as he was immediately designated for assignment, and he may never play in the majors again amid the stink of mediocrity and domestic violence. But the complex financials of the deal effectively mean that to land Kemp, the Braves’ bank account will be light just $30M or so over the next three years. Forgetting for a moment the enormous misstep the Braves made in acquiring Olivera in the first place, this Kemp acquisition is unbelievably impressive considering the price other teams are paying for defensively-challenged power-hitting outfielders.

Take Jay Bruce. One of the hottest names on the hot stove this July, he got moved on Monday for Dilson Herrera and Max Wotell. The interesting thing here is that Bruce is due $13M and signed only through next season, and the Mets had to give up real talent to acquire him. Herrera, the headliner going back to the Reds for Bruce, is a 22-year-old second baseman with a .790 OPS in AAA. But the kicker here is that Bruce isn’t good. He’s been worth six wins below average over the last three years.

Consider:

• Matt Kemp 2015/16: .263/.301/.460, 46 HR and an OPS+ of 109
• Jay Bruce 2015/16: .240/.301/.481, 51 HR and an OPS+ of 108

Undoubtedly, Bruce has been the better player this year. His OPS+ is 20 points higher than Kemp’s, meaning he’s been about 20% better than Kemp. But let’s consider what that means for a moment. Purely in terms of slugging, it’s about 25 total bases over the course of 400 at bats. That’s an extra base every four games, or twice a week. I realize that baseball is made up of all those little differences — and that those differences are what separate the contenders and the pretenders — but we’re talking about a whole lot of luck when we’re talking about two extra bases a week.

So why does “the industry” value one of these guys so much more highly than the other? Perception. The Reds have spent the greater part of the last year building up Jay Bruce as a potential difference-maker for a playoff team desperate for power. They’ve subtly leaked rumors of his availability to the press. They’ve reminded everyone that he’s clocked 233 homers in his career, and they had to smile as Yoenis Cespedes proved last year that flawed players can bring teams over the hump.

But is Kemp really all that different from Bruce? Was Kemp available for 3/$30M to everyone? Do you realize what 3/$30M means in today’s baseball? Last offseason, Joakim Soria signed for 3/$25M while Gerardo Parra got 3/$27.5M. That type of money goes to 7th-inning relievers and 4th outfielders. Kemp doesn’t even have to be good to be worth that type of money; merely average.

But Sean, the Defense!

Eh. They’re both pretty bad at defense. Whether one guy is worth -20 runs while the other is worth -15 really doesn’t matter to me. Maybe it should, but it really doesn’t. That type of difference is similar to the white noise to which one can ascribe that one extra base per week.

So really, it comes down to a simple proposition. It’s not as glamorous as trying to pick between Nolan Arenado, Manny Machado, or any other young superstar.  You’ve got two guys. Both are power hitters and play bad defense. One might be better than the other this season, but he was way worse last year. That one costs a solid prospect, and is signed for one year at $13M. The other costs zero prospects, and is effectively signed through 2019 at ~$10M per.

Who do you take?

In this post, I take a look at the 2016 Chicago Cubs though their first 100 games. I’ll start out by focusing on the Cubs’ run differential (Runs Scored – Runs Allowed). After a historic start, they reached their pinnacle after the 67th game of the year against the Pirates. At this point, the Cubs were 47-20 and had outscored opponents by 171 runs! Since then, the ball club is 13-20 and their current run differential is at +153.

Still, the Cubs’ +153 mark is 42 runs better than the next-closest team (Washington Nationals). The Cubs and Nationals are the only clubs to have a run differential that is greater than +100. The second-place Cardinals rank third in the league at +95 right now. While the Cubs dominate the top end of the spectrum, the Reds and Braves are running away with the worst run differentials in the league. The Reds have a -143 mark, largely due to the thrashings they have taken at the hands of the Cubs so far in 2016. The Braves have the second-to-worst differential at -134 runs.

Projected Runs to Wins

In another place, I introduced the “Pythagorean Theorem’s of Baseball” which basically tries to determine the number of games a team will win based on their number of runs scored and number of runs allowed. Here are the formulas for six of the most common win-percentage projection formulas:

I added up the Cubs’ total runs scored and total runs allowed after each game this year and compared their actual number of wins to the projected number of wins based on each formula. These charts visualize the differences between those numbers.

This matrix summarizes how accurate each of the projection formulas has been in predicting the Cubs’ winning percentage and total number of wins so far in 2016. The most accurate formulas was the James_1.83 followed by the James_2 and Soolman. Four of the six formulas were very good predictors, but the Cook and Kross formulas overforecasted the number of wins that they expected the Cubs to have. Notice that at one point this year, each of those formulas projected the Cubs to have over 15 more wins than they actually had. The R^2 value (coefficient of determination) is indicative of how well the projected win percentage matched up to the actual win percentage after each game this season.

All in all, the Cubs have should have at least six more wins this year based on these formulas. Scoring as many runs as they have (4th most in the MLB) and allowing as few runs as they have (T-1st in the MLB) should result in an even better record than 60-40. We knew it was unlikely that they would keep up their record-setting start in the run-differential category, but it will be interesting to see how these numbers match up as the season progresses.

Well, here we are: Over 100 games into the season and Bryce Harper has yet to break out of his slump. When Bryce came to the Majors back in 2012 he was one of the most hyped prospects since Alex Rodriguez broke into the bigs as a 19-year-old shortstop. The pressure, I’m sure, was immense, and through his first three seasons Harper had put up good numbers, but had yet to establish himself as the superstar we all thought he’d be. Something clicked in 2015 though, as he posted an amazing 9.5 WAR, 197 wRC+, and 0.461 wOBA, all best in the MLB by a fair margin. We all thought he’d done it, he had exceeded expectations and was ready to join Mike Trout as one of the most exciting, talented, and productive players in the game. His 1.5 WAR, 180 wRC+, and 0.443 wOBA through April of 2016 merely affirmed this sentiment.

Here we are. 2.8 WAR, 115 wRC+, and 0.346 wOBA. To be fair, these are by no means terrible numbers. He is still creating runs at a decently better rate than the average MLB player, with much of the credit going towards his MLB-leading 18.2 BB% and his 0.214 ISO. His defense has also been very good this year, helping to raise his WAR to 41st in the MLB. No, I am not saying Harper is a bad player, I’m just saying he is worse than the Bryce Harper we saw in 2015. We were all ready to call him a superstar (heck, we even voted him into a starting spot at this year’s All-Star Game), but now he’s taken this step back and we have no choice now but to start questioning his superstar status. Let’s take a look both at what might be causing this slump, and what Bryce could do to bust out of it (if anything at all).

The stat that jumps out at me most is his BABIP. The MLB average is exactly 0.300 this year, and Bryce has a career mark of 0.317. Bryce isn’t too far into his career, and while it’s possible that his 0.369 BABIP last season was an anomaly, it’s certainly safe to say that Bryce is definitively above average in this area. This season his BABIP has dipped down to 0.234, good enough for second to last in the MLB, ahead of only Todd Frazier (0.203). BABIP has a great degree of luck involved, in that some hitters with higher BABIPs might just get lucky (e.g. hit a little bloop into shallow right field that drops for a hit), or might be playing poor defenses (e.g. Jason Heyward would have caught that little bloop, but Jose Bautista was in right field and missed it by a foot). I believe, though, that going from 0.369 in 2015 to 0.234 in 2016 is enough of a differential to at least form the hypothesis that Bryce is struggling beyond just facing better defenses and getting less breaks.

One of the keys to figuring out this drop in production is figuring out what has changed from last year. Obviously his BABIP has declined, but why? For the  most part, pitchers are throwing him the same types of pitches at the same rates, and are throwing pitches in/out of the zone at the same rates as well. He has almost the exact same swing% on pitches outside the zone, but there’s about a 5% decrease in his swing% on pitches in the zone; nothing monumental, but something we ought take note of. The greatest changes that may be observed are in his batted ball numbers, shown here:

We can almost construct a narrative from these numbers: He’s hitting balls soft significantly more often, and he’s also hitting less line drives. Soft ground balls and fly balls are easier to convert into outs, and his infield fly ball% increase implies that he is hitting fly balls with less power. This explains why his home run rate is down. Where he was previously hitting hard line drives and grounders, and turning fly balls into home runs, he is now hitting softer, more easily-fielded grounders and popups, resulting in a steep decline in BABIP.

But this isn’t a cause, it’s a symptom. Again, we are forced to ask why it is that Bryce isn’t hitting balls as hard, and why he’s hitting less line drives? Bryce has been known for having great plate discipline, something that generally hasn’t changed over the last two years. At the surface, we see that he still has a very high walk rate, lays off pitches outside of the zone, and is one of the more patient hitters in baseball. However, one stat that caught my eye was his contact% on pitches outside the zone (and even inside the zone). His O-contact% went from 60.9% to 67.4%, and even his Z-contact% increased from 84.4% to 87.7%. This can be visualized here:

For the 2015 season

And for the 2016 season

There are two ways to look at this: The types of pitches Bryce is seeing, and the counts he’s getting himself into. All of this revolves around where pitchers are throwing pitches, where he’s swinging, and where he’s making contact. As you can clearly see, Bryce has been making a tangibly higher amount of contact this season. Logically, it makes sense to say that he is taking more pitches in the zone, and making weak contact where he used to just swing and miss. But that can’t be the whole story, can it? In attempting to find differences between this season and last, I merely found that regardless of what the count was, Harper was always making more contact; it didn’t matter if he was ahead, behind, or even. He was also making more contact regardless of what pitches were being thrown.

Let’s start with the types of pitches Bryce sees. We’ll split it up into fastballs (which includes 4-seamers, 2-seamers, and cutters), and secondary pitches (curveballs, sliders, and changeups). With secondary pitches, pitchers have begun to come into the zone a bit more than they used to. These charts show where pitchers are throwing Bryce non-fastballs:

2015

2016

It is by no means a huge difference, but it’s still there. Obviously, pitchers are still mostly throwing him non-heaters down and away, they’re just getting them in the zone more frequently. How does Bryce respond to this change? Well, he’s been laying off the low pitch a bit more, and instead has attempted to hit the inside pitch. These are his swing percentages on secondary pitches:

2015

2016

This also means that those non-fastballs are being called as strikes more frequently (assuming that umpires are generally going to call pitches in the zone as strikes). As we can see in his contact% charts, this season Bryce has been making contact at an extremely high rate on those high and inside pitches, and softer pitches have been absolutely no exception. In fact, he’s been making contact with the high and inside non-heaters more than he is with high and inside fastballs. What are the implications of this? Let’s look at his slugging% against secondary pitches:

2015

2016

Slugging% is by no means a perfect measure of a hitter’s ability. Yet, in this case, it gives us a decent idea of which locations a hitter is making solid contact. In his 2015 campaign he was able to get his arms extended and drive curveballs with great power. This season he is attempting to pull the ball more, and it’s resulting in weaker contact. While he is able to drive the inside breaking ball at a pretty decent rate, I suspect that he’s opening up his stance, which can occasionally result in a hard-hit ball, but will often result in a weak fly ball to the opposite field, or a weak grounder to the pull side. The fact that he’s swinging so much more frequently at inside pitches would also be reason to guess that as he’s swinging at breaking balls out over the plate he is still attempting to pull them, as opposed to going with the pitch. Further evidence of this comes from looking at how he hits breaking balls from lefties (curving away from him), versus how he hits them from righties (curving towards him).

2015

He even seems to do better against lefties. Against both of them, however, he clearly is able to see the pitch that will eventually break across the middle/outer half of the plate, and drive it with power. Let’s head over to 2016:

While his production has decreased against both righties and lefties, it is clear that the disparity is much larger when it comes to lefties. This is because Bryce is able to get away with trying to pull the ball against righties, as the ball is curving towards him. This makes pulling the ball a much more natural motion. Against lefties, the only breaking balls he is hitting are the ones that start inside and break right to the inside part of the plate, and the pitches that break to be right down the middle. It is the non-fastballs that are low and on the outer part of the plate that he is unable to drive, especially the ones being thrown by lefties. He’s opening up more, which also explains why his pull% hasn’t gone up (in fact it’s gone down). When he’s open, it’s hard to drive the outside pitch even if you make contact with it intending to hit it to the opposite field. Instead, he’s making that weak contact that results in outs.

Looking solely at secondary pitches, the narrative becomes: Bryce is taking the pitches that are out over the plate, and is instead swinging at pitches that are high and inside. He has a tendency to attempt to open up to the ball, and while he can sometimes get away with it against righties, lefties have been able to essentially shut him down. He is also making much more contact with all of these pitches, meaning that he’s putting more balls in play, yes, but they are weak balls that are easy to field, and are thus resulting in outs. With this mindset, even trying to hit the ball to the opposite field becomes more difficult, and all of this culminates in a lower BABIP.

Next, let’s look at how he’s handling fastballs. One thing that quickly becomes evident is the fact that Harper has been swinging at fastballs a lot less this year, especially ones up in the zone.

2015

2016

His swing% on fastballs in other areas of the zone is roughly the same; it’s really just those high and down-the-middle fastballs that he’s suddenly laying off of more. And yet, just as with non-fastballs, Harper still has been managing to make more contact this year, especially on pitches high and inside, as well as pitches low and out of the zone. How has that translated in terms of his slugging%?

2015

2016

What immediately jumps out at you is the large hole in the top part of the zone this year where Bryce is generating virtually no production. His production on low fastballs is closer to on par with last season, but up in the zone (the same area where he isn’t swinging nearly as often) he can’t get anything going. Why is this? With fastballs it’s a little more simple than with breaking balls in some aspects: For whatever reason he’s laying off fastballs in the zone, and he’s making weak contact with fastballs both high and inside, and down and away (which is where pitchers throw him fastballs most frequently). He’s giving pitchers more opportunities to throw fastballs out of the zone too. The big question mark comes at why he can’t do anything with those high fastballs specifically?

The answer isn’t too straightforward, but I do think that a large part of it is what types of pitches Bryce swings at in which counts. See, there is a very large differential in Bryce’s swing% in counts with no strikes between last year and this year, whereas in two-strike counts his swing% is about the same. He is taking more pitches when he has no strikes against him, especially the high fastball:

2015

2016

He seems to be swinging at less pitches overall, and his focus has shifted from the top of the zone to the inside part of the zone. It should be noted, too, that he is swinging significantly less at breaking pitches with no strikes as well, which highlights something that’s a little less tangible. With fastballs the narrative becomes this: Bryce is taking more fastballs early in the count, which means he isn’t capitalizing on those fastballs. Once he has two strikes on him, it would reason to guess that he would have more trouble making square contact, right? Well, not quite…

Against fastballs in two-strike counts Bryce is actually hitting decently, but he’s still missing the ones across the middle of the plate. One thing I noticed is that, in two-strike counts, he’s getting thrown more breaking pitches than before, and less fastballs. In 2015, 258 out of 719 two-strike pitches were breaking balls (36%). In 2016, the mark has been 189 out of 448 (42%). With two-strike pitches in 2015, 383 out of 719 were fastballs (53%), whereas 2016 has only seen 220 out of 448 (49%). Bryce has become more aware of the outside pitches, both fastballs and breaking balls, and this has something to do with it.

With two strikes, Bryce is swinging at around the same rate in 2016 as he was in 2015. The pitches he is hitting successfully are: High and inside fastballs, away fastballs, away breaking pitches from righties, all breaking pitches in the middle of the plate, and high and inside breaking pitches from lefties. Ok, that’s pretty tedious. Let’s show all of that visually, looking just at 2016:

First, fastballs with two strikes

Again, he’s gearing up for away pitches, and he’s swinging at almost anything, so he has success against away fastballs. We know that he’s been very keen on high and inside pitches of all kinds and in all counts this year, and that is also the easiest pitch to see. He has a reactionary eye for that pitch, and is able to catch up and drive it. High fastballs out over the plate can be somewhat easy to react to but he a) isn’t as keen on hitting them, b) isn’t seeing them that often in two-strike counts anyways, and c) isn’t expecting them. Thus, he’s most likely popping them up, which explains his high increased infield fly ball%. This is supported by the fact that his ground-ball rates on high fastballs with two strikes is quite low:

Next, let’s look at slugging% against breaking pitches from righties with two strikes

Again, it appears that because the ball is curving towards him it’s going to be easier to drive. He is then able to pull the breaking pitches that are up and out over the plate, and is able to drive the low and outside pitches with authority. His lack of success on up and away pitches is a little perplexing, but could be attributed to anything from bad luck, to him possibly not seeing that exact pitch as well, to the fact that the sample size here is pretty small and he hasn’t seen a ton of pitches in that area.

Finally, let’s check out breaking pitches from lefties

Nothing monumental in this aspect, especially as it’s not too different from how he hits breaking pitches against lefties in all counts. Regardless, it still fits our narrative as the up and inside pitches are right in his wheelhouse, and the pitches that breaking out over the plate are easier to hit than any other breaking pitch coming from a lefty.

Whew. That is a lot of heat maps to take in. Let’s review a bit: Bryce has a tendency to take more pitches early in the count, something he hasn’t done before. He’s also opening up, which makes him susceptible to breaking pitches and causing him to make weaker contact. The fact that he’s making more contact on pitches outside of the zone doesn’t help much either. He’s taking more fastballs as well, and once he has two strikes on him he’s seeing less of them, and is most likely expecting them less. He then begins to swing much more frequently, which actually reaps pretty good rewards, though there are some holes in his swing against certain pitches. He can’t get the high fastball, and struggles with breaking pitches against lefties. The result of all of this? Lower BABIP, lower wRC+, lower wOBA, you name it.

Obviously there are factors involved with this that go far beyond what heat maps and stats can show us. Baseball is an incredibly mental game, and once you realize you’re in a slump it can sometimes just drive you deeper into that slump. Statistics also can almost never tell the whole story, and as I mentioned earlier the sample size here is small enough that none of this is much of a predictor for future behavior. There’s a good chance that, on many of the situations mentioned above, Bryce has just gotten unlucky (or heck, maybe even lucky) and thus the heat map doesn’t reveal much. Overall though, when looking at everything in a holistic manner it allows us to construct an idea as to why Bryce is failing where he previously succeeded. We can never know everything for sure, but we know more than we did.

I’ve been hearing for months now that Bryce will be just fine, slumps happen to everyone, he will soon return to form, etc., and I’m not here to disagree with that. Although, I will ask (and I ought add that I am a big supporter of Bryce’s): What if he doesn’t break out of it? Odds are his 2015 will be one of the best seasons of his career, and 2016 (if it continues like this) will be one of his worst, and he will find himself somewhere in between for the rest of his career. It’s just that the deeper he drives himself into this rut the more compelled I am to find the source of problem as best I can, from a purely analytical standpoint.

Love him or hate him, the more that Bryce (and the many young superstars like him) thrives, the more baseball thrives.

(Note: All statistics and heat maps taken from Bryce’s page on FanGraphs.com)