As I stated in my last post, predicting home runs from fly ball data could be another component of how we compare home run hitting abilities of players. As you can see from the graph above, I plotted the fitted values from the model split by each hitter. Most of the fitted values tend to be at the extremes, which coincide with logistic model properties. As for comparing hitters, it looks like Adam Dunn has the most predicted fly balls becoming home runs, while Jason Bay is on the other side of the fence.

In case you were wondering, here are each player’s mean HR prediction for fly balls: Adam Dunn (~50.4%), Manny Ramirez (~39.2%) and Jason Bay (~34.0%). No surprises there really. The order of these hitter’s HR predictions coincide with their career HR/FB rates and our general notion of their hitting style. Dunn swings for the fences or strikes out otherwise, while Manny and Bay display more use of the entire field (though that may be an optimistic statement about Manny’s capabilities now). While Hit Tracker does an excellent job telling us how far home runs really went, and what park/weather factors impacted the ball’s real projection, we don’t really have an idea of what those factors had on non-HR fly balls. Though I am speculating, maybe this topic of research will increase once the data from Field F/X (previewed in THT’s 2011 Annual) is published. Only time will tell…

As you may remember, back in December I had to complete a couple of final projects. One idea that I didn’t use dealt with the concept that home runs are not always equal in displaying a player’s power or batting skills. We  equate overpowering shots to right-center field by Prince Fielder with balls that graze the more-than-generous right field wall of Yankee Stadium. What I mean is, there are more variables than just pure distance that go in to determining whether or not a fly ball becomes a home run. With this in mind, I can run a regression model to compute the probability that a flyball will turn in to a home run. I received a large data set (many thanks to Greg Rybarczyk at Hit Tracker) that spans the 2006-2008 seasons for three players (Adam Dunn, Manny Ramirez and Jason Bay). The data includes observational and calculated data (in the similar ways of Hit Tracker’s data – i.e. True Distance or Elevation Angle, etc.) on every long fly ball the players hit, totaling a tad over 700 observations. Included are variables such as what ballpark the ball was hit in, date & time, and the outcome of the play (single, double, home run, out, etc.)

As you can tell from the graph above, the outcome of the play isn’t so clear when only given the elevation angle and distance traveled summary of the ball. All the outcomes are generally scattered so that we cannot conclude any real correlation. I superimposed two boxes to easily show how similar balls can have different outcomes. In the case of the right-side box, a slightly different elevation angle could mean the difference between a home run and a fly ball.

In this next plot we’re seeing the outcomes of the play split into two events: a home run or no home run (the latter equating to zero, or the orange points). We see both smoothed curves have the same shape, with the home runs curve reaching further distances on average. However, the smoothed curves don’t show how the blue and orange points are still very much intermixed. The likelihood of a home run (based on knowing the ball’s angle and distance) is quite sporadic.

Now that I’ve convinced you of this issue, we can start modeling (yay!). For those who are statistically inclined, I used a logistic multiple regression model to find any pattern for predicting home runs. This model will essentially spit out a probability of a ball becoming a home run, given a bunch of variables. The equation used for this type of modeling is:

Prob(HR) = 1/1 + exp(-z)

Where z is a linear equation whose coefficients are estimated (later on)…

The variables I used include the true distance the ball reached, time in the air, speed off the bat, elevation angle, horizontal angle (imagine a baseball field where a larger angle equates to left field, etc.) and apex of the ball (highest vertical point the ball reached). After editing  the model to include only those that are statistically significant, the final coefficient confidence intervals looked like this:

2.5 %                              97.5 %

(Intercept)      -69.55676316           -48.86556510
True.Dist.          0.08764763              0.12669753
Time                  -9.12581512               -6.25056613
Elev  Angle       0.85324327              1.24073619
SOB                     0.16324949               0.33018947
Horiz  Angle   -0.03296355              -0.00181532

From this we’re seeing that Distance, Elevation Angle and Speed off the Bat are all positively associated with home runs, while hang time of the ball and horizontal angle are negatively associated. This is so-so new news to baseball fans; any physicist could probably come to the same conclusions. It may be a better use of time to focus on the more intangible affects on fly balls, such as temperature, winds, and elevation above the sea (i.e. – Coors Field affect). The next regression I use will consider all the fly ball variables and these other uncontrolled park variables. Running this regression surprisingly has all variables as statistically significant. Better yet the AIC (which measures how much error is in the model) from this model is lower than the original. Remarkable stuff!

I won’t go into more detail (for now), but maybe models like this can help us determine how good of a home run hitter a player really is. For example, if Manny has an average probability of a fly ball making it over the fence than Jason Bay, we should probably credit Manny as the better power hitter, despite possibly having lower home run totals (this is all hypothetical). Instead of looking at home run totals, there are probably better ways to discern power ability.

Another final report I wrote was based on MLB Free Agent contracts, and how or if we can model their outcomes based on prior years’ performance. The contract terms I used as response variables were contract length (in years) and average salary per season. I also focused on hitters and how metrics like Batting Average, On-Base Percentage, Home Runs, or even advanced ones like Wins Above Replacement (WAR) can help us see what the market is favoring and at what price. The reason to use different sources of metrics is to see what MLB Executives are listening to: traditional statistics or those advanced ones used by the Sabermetric community? Using models like this can also have some predictive powers.

Overall, I found there was a good mixture of metrics involved when fitting a best model to average salary and number of years. Average Salary was mostly related to Age of the Ballplayer, WAR, Batting Average, Slugging and Homeruns. Contract length was associated most with Age and WAR.

The final model I concluded with is a bit technical, but here are some interesting facts I found about FAs who signed after my project was completed, or haven’t yet this winter of 2010.

-According to the model, Carl Crawford should have received a $14.62 million average salary for 5 years. Instead he received a contract worth $20.3 million per year for 7 years from the “Boo”Sox.

-Adrian Beltre, who will likely receive way too many years in the real world, should get $17.9 million per year for 5 years if it were up to my model.

We see that the model underpaid Crawford, but in all likely events, Beltre will not receive that high of a salary. Some poor team may outreach and give him 5 years, however (I just really hope it’s not the A’s). Like all other linear models, we’re bound to get variation between predictions and the observations. But in general, the model was very good with lower end players: the ones that sign 2 or 3 year contracts worth less than $20 million. The true outliers, are the ones the media tends to only cover: the Cliff Lees or Derek Jeters. Don’t even get me started about how huge of an outlier Jeter was…it’s pretty sad. Although I will admit he has more than just baseball value to those Yanks.

Anyway, if you want to read the full report, feel free to do so. The link is below.

FA Salaries 08-10

PS – IceBat is fine! I was just overworking him with final everythings and holiday everythings.

Crazy schedule for me these next few weeks. I’ll try to stay active, I promise. If not, IceBat will take over, but I’m guessing he won’t say much (he’s pretty shy and likes to chill in the corner of my room). Anyways, I thought I’d share a recent report I did for my times series class. It’s about the general shift of runs scored per game (by one team) over the years of MLB’s existence. If you have some time (and enjoy a few technical terms) I’ve uploaded a link below. Happy December holidays!

R.G in MLB History

But who’s right here? Is there enough past history of Japanese pitchers coming to the American market to justify a $15+ million average salary? Or can the A’s justify giving Iwakuma the same salary he received in Japan because of the high cost of the negotiating bid? I’ve listed some recent Japanese pitchers who made the move to the big leagues, and some meaningful figures.

Daisuke Matsuzaka (Bos): $51 million bid, 6 years, $8.6 mn average salary, 2.55 average WAR per season

Kei Igawa (NYY): $26 million bid, 5 years, $4 mn average salary, -0.1 average WAR per season*

Hiroki Kuroda (LAD): 3 years, $12 mn average salary, 3.3 average WAR per season

Koji Uehara (Bal): 2 years, $5 mn average salary, 1.5 WAR per season

Kenshin Kawakami (Atl): 3 years, $7.5 mn average salary, 2.2 average WAR per season

*Igawa was stuck in the minor leagues for 2 of his 4 seasons with the Yankees

Some general trends from these five players (while I can discuss these trends, I by no means am inferring causation, or any regression type analysis, as the sample size is just too small):

Bidding: Looking at the players who went through the bid process, in no way did they receive a $10+ million average salary. It looks like teams can use the bidding process as a sort of leverage in negotiations. While Dice-K only got $52mn from Boston, adding in the bidding costs puts Boston at a little over $100 million.

WAR: Don’t expect crazy MVP type numbers from these players. The most a team got was an average of 3 WAR per season (the Dodgers from Kuroda). Even more against Iwakuma’s case that he deserves an 8-figure salary.

From this, I don’t think Iwakuma’s side can or should use past pitchers as a guideline, as its obvious Dice-K and Igawa have failed in many ways over the past 4 years. And while I’m certain Oakland is a bit lowballing the righty, Iwakuma has no leverage. But I think it would hurt the image of both sides if a deal isn’t made. Iwakuma will look like Iwa-crazy. From a fan point of view, Beane risks further detachment from the Oakland fanbase. There’s already rumors (or even claims) that free agents don’t want to come to Oakland for numerous reasons. This just adds fuel to the fire.

On that note, there are also reports Oakland bid on Iwakuma to keep other teams from negotiating with the pitcher, since if no contract is signed, Oakland gets to keep its money. This is an obvious negative externality, and the bidding process should negate this by forcing the team to still pay at least half the bid no matter the outcome of negotiations. It’s a loophole that should not exist. It hurts the credibility of MLB, and the pitcher’s desire to compete at the highest level.

Picture yourself as the umpire or catcher looking towards the mound and that is exactly what the above plot is showing us. Thus a right-handed batter will be on the left side of the graph, while a left-hander is on the right side. I also superimposed a strike-zone to show the strike-ball nature of each pitch.

Another important graph is to look at the total vertical/horizontal movement of pitches. Again, this is in perspective of the catcher or umpire. The movement of a pitch is the difference of a projected straight line from a pitcher’s release point and the actual location of the ball once it reaches home plate. An example is Braden’s slider movement (the purple points); it’s motion slides horizontally, away from a lefty, or towards a righty. The graph also tells us his fastball movement is going upwards as it approaches home plate.

You’ll also notice the cluster of red and blue points that tend to be inner mixed meaning two different types of pitches are having the same kind of movement. The two pitches are the change up (which deceives batters by having identical fastball movement, but its speed is drastically slower) and a two seam fastball. The only difference between these two pitches is their speeds.

From this plot we can see the speeds of each type of pitch. As I was stating earlier about the two nearly identical pitch movements, Braden’s change up (CH) was around the 65 MPH range, while his two-seam fastball (SI) was around the low-80s.

One question after looking at these plots may be how the system dictates or knows what kind of pitch is thrown. The F/X system uses algorithms to dictate types of pitches. Based on the history of pitches thrown, we have a general idea of how each type of pitch can be characterized. Sometimes the algorithms are wrong but in general, they seem to do a great job with assigning pitch types.

Something to take away from these graphs is that it looks like Braden worked to locate his pitches inside the strike zone (a 71% strike-thrown percentage) well. And if you find anything amazing about his change-up on May 9, it’s that it looked almost identical to his two-seam fastball, just slower by an average of 15 MPH. That will get you a bunch of misses or very field-able balls any day. I’m sure after the game, Braden partied a bit like CB (IceBat sure did):

I think it would be an understatement to say Pujols has been the most consistent hitter in baseball over the past 5+ years. He’s a sure bet to be in the MVP talks from the beginning of each season. I decided to look at his Win Probability Added per game (a plus WPA means he added towards winning the game, while a negative WPA suggests a player was detrimental to the winning cause) over the 2010 season.

I added a line at 0.0 WPA to easily compare a good or bad game produced by Pujols. More so than usual, Pujols was above the line, and you can see his highest WPA (at around 0.38) is double that of his lowest (about -0.20).

Just so I make myself clear, I’m not trying to take anything away from Pujols as a player. But as you can tell the series goes up and down very sporadically. If you had to predict Pujols’ next game performance by WPA you’d probably have a tough time. From a time series approach, we can try to find any sort of correlation between 2 games that are X lags apart (ie – knowing the outcome of game 50, what can we predict about the 55th game?). By doing so, a time series approach allows us to formulate an equation for predictions. But in this case, no model seems to fit, as the correlation isn’t convincing for one. Thus the best approach would be a white noise fit, meaning Pujols’ performance would be like predicting the Dow Jones’ price index on Monday morning.

As promised, I also looked at a pitcher’s performance: Roy Halladay’s Fielding Independent Pitching (FIP) metric over the past 5 seasons. For those who don’t know, FIP shows a runs allowed number (comparable to ERA) that is dependent only on home runs, walks and strikeouts (the three outcomes a pitcher has 100% control over, thus they are fielding independent).

The same looks to be happening for Halladay’s FIP over the years. I used the same methodology as before, and found no evidence for a time series model for predicting Halladay’s next start.

These two examples essentially tell us the day-to-day production of baseball players is very random. More so,  looking over a player’s success over a long period of time (ie – 162 games) is the better indicator of how good players are. It’s all about sample size folks. Thus, my version of an answer to the main question of this post is, “well…depends on over what period of time…per season? per game? per at-bat?”

NEW YORK (AP)—Seattle right fielder Ichiro Suzuki has won his 10th straight Gold Glove and New York Yankees shortstop Derek Jeter has won his fifth overall…

I find it a little hard to believe that Derek Jeter was able to win this award, for the second time in a row. All the news sources point to his efficiency with only 6 errors over the year. Well what about those balls that he couldn’t possibly get to, considering his limited range (meaning he just can’t get to balls that are farther away the way other start shortstops can)? Those balls get scored as hits rather than “Balls Jeter couldn’t get to”.

Also, any advanced defensive metric out there these days answer many questions that can lead us toward comparing fielders. Like how much ground is a shortstop able to cover? Is this due to great timing/instinct or great footwork? How accurate is his arm? How many runs can he save over the course of the year? In any of these metrics, you will find Derek Jeter at the bottom of the list. Guaranteed.

[Satisfied stretch] Much better. Oh wait…the agony didn’t stop there as one particular comment underneath the article made me gag:

Fielding percentage is not the only consideration. Reputation, history, along with intangibles such as really difficult throw outs, and really difficult catches. Outs are not rated on a scale. The runner is either out or safe. But the way a player sacrifices his body to make an out at times is huge and the way a fielder hustles and makes extra effort, although it cannot really be gauged, plays a huge factor in golden glove voting. . And that is how it should be.

Phew. Okay…deep breaths IceBat…it’s going to be alright. Here are some flaws I see in the “general fan’s” comment (I will now refer to him as “Worm”):

1. Jeter should not win this award off of reputation, or history. Let’s get this right Worm. You want to give Jeter this award because he has won it in the past? This award is designed to recognize a player’s season performance, not what he’s done pre-2010. Why does that matter?
   
2. Difficult ground balls and throws CAN be measured. Like I said earlier, we have metrics now that tell us how hard it was to successfully make a defensive play. Lawyered.
3. Sacrificing his body…hustling and the extra effort. If this should be included in the awards, then holy crap, I would have won. Heck, I work my ass off and make sure I’m the one getting my body beat. Should this count toward assessing how good a ball player I am? Essentially no, because otherwise I would have made it to the big leagues already. Boom. Roasted.

Okay I’m done ranting. But how do we fix this flawed system that is seemingly recognizing the wrong people? I think there’s one solution that would help. Currently, managers and coaches are the ones voting. Because managers get to see fielders play everyday, it’s hard to get those ‘flashy’ plays out of their heads. The spinning, diving and twirling can sway anyone. Thus, we should at least include some writers in the voting process. They vote for the MVP’s and Cy Young’s, why exclude them here? It would allow for at least some voters to base their opinions on numbers and metrics, rather than just video footage.

IceBat’s End of the Year Roster:

C – Carlos Ruiz (Phi)

1B – Joey Votto (Cin)

2B – Howie Kendrick (LAA)

3B – Scott Rolen (Cin)

SS – Elvis Andrus (Tex)

OF’s – Carlos Gonzalez (Col), Andrew McCutchen (Pit), Delmon Young (Min), Jay Bruce (Cin), Dominic Brown (Phi), Magglio Ordonez (Det)

SP – Ubaldo Jimenez (Col), Zack Greinke (Kan), Trevor Cahill (Oak), Justin Verlander (Det), J.A. Happ (Phi/Hou), Phil Hughes (NYY), Brian Matusz (Bal), Chad Billingsley (LAD)

RP – Rafael Soriano (TB), John Axford (Mil), Luke Gregerson (SD)

Thoughts on IceBat’s Roster:

I would say I had an OK year. Despite not making the playoffs, I managed to win all consolation playoff games, so that was kind of cool. While I did have players with great seasons (Votto, CarGo with MVP-caliber seasons), I just didn’t have enough to get it done, as all my players performed well during different parts of the season.

I would like to note one trade I consider season-defining. In early June, I traded for Ubaldo, Andrus and Cory Hart (terrible decision to drop afterwards), in replace of Ryan Braun, Marco Scutaro and Josh Beckett. At the time, I desperately needed to switch things up as I was getting pummeled in the standings. At the time, Ubaldo was on an historic ride, as he’d won his first 10 of 11 games. I second-guessed myself weeks after the trade, because I still wasn’t sure whether Ubaldo could sustain the level at which he was performing at. I felt like I had given up a lot in my first round pick Braun. But evidently, Braun had a down season, which made me feel better, while Ubaldo still had instances of spectacular but also struggled at times. In hindsight, both owners traded away depth for necessity, so I can’t really complain about the production nor the intangibles (I jumped on the Ubaldo bandwagon afterwards, changing my team name to “Ubaldo for Prez!!”). Also if you throw in the fact my trade partner gave away Hart, I would consider the trade’s positives outweighed the negatives.

Thoughts on Drafting and Confirmation Bias:

Examples of confirmation bias include the hot-hand fallacy in basketball (Something I hear too often – “Player X is on fire tonight”) or, after seeing 5 heads in a row, you’re more likely to see a tail on the 6th flip. These examples tend to show a person’s naive misunderstandings on the importance of independence. Thus, these perceptions cloud our analysis and judgement (ie – how Vegas is a bad idea). This has a lot to do with fantasy drafting, as often you will see owners over paying for players that had a recent break out season. I am guilty as charged, as I drafted Zack Greinke (coming off a Cy Young award season) waaaaay too early. Heck, I even did this in my NBA draft last year, taking Devin Harris way too early. And it’s clear Greinke couldn’t live up to expectation, especially with a non-productive team in Kansas City (7 straight losing seasons and counting), it was almost assured Greinke could not have great numbers twice in a year. On that same note, owners tend to underpay on those players coming out of down years. One season is just not indicative of how great a player is – in all sports, players can have down years, simple as that. Thus, look for Greinke to do better than 2010, especially if he’s moved by the Royal’s front office.

Besides this remark, I would say I’ve been consistent at how I’ve approach drafts over the years. I tend to over draft a certain field position (last year, first basemen; this year, outfielders), and also stock up on starting pitchers who’ve been consistent at one thing: innings pitched. All in all, don’t be afraid to over draft in a position, because you can always use them as trade bait later on. Trading depth away for necessity I think is a better strategy than drafting solely based on positional needs.