Archive for December, 2017

Overcoming Imperfect Information

When a team trades a veteran for a package of prospects, only minor-league data and the keen eye of scouts can be used to assess the likely future major-league contributions from those particular players. Teams have accurately relied on the trained eyes of scouts for generations, but of course the analytics community wants its foot in the game too. Developments such as Chris Mitchell’s KATOH systems make some strides, as it is helpful to compare historical information. Does prospects rank on’s or Baseball America’s top-prospect list really indicate how productive a player will be in the major leagues? Of course, baseball players are human, and production will always vary due to the result of numerous factors that could potentially change the course of someone’s career. Perhaps a player meets a coach that dramatically changes his game around, or a pitcher discovers a new-found talent for an impressive curveball that jumps him from low fringe prospect to MLB ready. The dilemma of imperfect information will always be present, so team must use the best resources available to them to tackle the problem.

To start my analysis of imperfect information, I look at the top 100 position prospects from 2009 using data from I break up the prospects into three groups based on their prospect ranking, which are position players ranked 1-10, 11-20 and 21-100. I then look at the value that those prospects contributed in their first six seasons in the major leagues, as well as their to-date total contributions using fWAR. I choose to look at the first six seasons of a player’s career because that is how long a player is under team control before reaching free agency. This study does not take into account any contract extensions that may have been given before a player reached free agent-eligibility. For players who have not been in the MLB for six full seasons, I look at their total contributions so far. The general idea for this study was inspired by a 2008 article by Victor Wang that looked at imperfect prospect information.

I convert the prospects’ production into monetary value based on the relative WAR values that were commanded in the free-agent market that year. I use fWAR to encompass the best measure of total value. When teams trade for prospects, they understand that they are trading wins today for wins in the future. Since baseball is a business and teams care about their performance on the field each year, I need to account for that fact in my analysis. In order to do that, I assume all else equal, a win today is more valuable than a win in the future. I apply an 8% discount rate to each prospect’s WAR value and create a discounted WAR value (dWAR). The value of the discount rate can be debated, but the 8% rate seems appropriate for the time framed looked at.

From here, I break up the prospects into a few different subgroups based on their average WAR contributed over their first six seasons in the major leagues. I follow some of the guidelines laid out in other studies with some slight modifications. Players with 0 or negative WAR per year are labeled as busts. Players with slightly above 0-2 WAR are contributors. Players with 2-4 WAR are starters and players with 4+ WAR are stars. Like described previously, I estimate the players’ monetary savings to their team by taking their monetary value based on WAR performance and comparing it to what similar production would command in the free-agent market for that year. There seems to be some debate on the value of one WAR in the free-agent market, however my calculations show that about $7 million bought one WAR leading up to the 2009 season. Victor Wang suggests that the price for one WAR had about a 10% inflation rate from year to year. I find the present value of each player’s WAR, then divide it by the $7 million dollars per WAR that would have been commanded in the free-agent market in order to find a player’s effective savings to their team based on production.

Position Prospects Ranked 1-10

Bust Contributor Starters Star AVG WAR/Y
1 2 5 2 2.83
10.00% 20.00% 50.00% 20.00%


Bust Contributor Starters Star
WAR/Y 0.43 1.53 2.73 5.17
Probability 10.00% 20.00% 50.00% 20.00%
PV Savings/y (in millions) 1.88 8.46 10.91 27.98

Interestingly enough, this prospect class panned out quite well compared to some other recent draft classes. The only bust in terms of discounted WAR turned out to be Travis Snider of Toronto, who was ranked the sixth-best prospect in 2009 but only managed to accumulate a cumulative WAR slightly above 0 in his first six seasons. Though the top 10 position-player prospects from this class feature names such as Jason Heyward and Mike Moustakas, the player that contributed the greatest WAR over his first six seasons from the top 10 ranking was Buster Posey of San Francisco, who posted nearly 6 WAR a year. It is important to understand that the savings a player gives to his team based on his production does not indicate any “deserved” salary for that player. Instead, it merely indicates the amount of money the team would have had to spend in the free-agent market to acquire that exact same production. The top 10 position-player prospects from this prospect class turned very productive to their respective teams, having a 70% chance of being either a contributor or star.

Position Prospects Ranked 11-20

Bust Contributor Starters Star AVG WAR/Y
5 2 1 2 2.158950617
50.00% 20.00% 10.00% 20.00%


Bust Contributor Starters Star
WAR/Y 0.67 1.6 3.56 5.71
Probability 50.00% 20.00% 10.00% 20.00%
PV Savings/y (in millions) 3.21 8.36 19.10 30.90

The next group is the 11-20 ranked position players. As perhaps expected, there are more busts in this group of ranked prospects. The variation of the small is sample is spread through the rest of the categories. Giancarlo Stanton, the 16th ranked prospect, and Andrew McCutchen, the 33rd ranked prospect, turned out to the be the two stars from the list. As the chart shows, the probability of getting a bust at this ranking of prospects is much higher than the 1-10 rankings. The variance does show, however, that player outcomes expectancy can also be promising at this ranking level. There was an identical chance of player becoming a star in this group compared to the first group, and a 50% chance of them being at least a contributor. In total, four of the top 20 prospects from 2009 turned out to be stars to this point in their careers, though not all have reached six full service years in the majors.

Position Prospects Ranked 21-100

Bust Contributor Starters Star
12 7 3 1
38.71% 22.58% 9.68% 3.23%


Bust Contributor Starters Star
WAR/Y 0.35 1.46 3.22 3.87
Probability 38.71% 22.58% 9.68% 3.23%
PV Savings/y 1.48 7.52 17.18 20.80


The next group of charts shows the rest of the top 100 ranked position players. The chart shows there is much more potential for busts to be found in this ranking; however, we must keep in mind that the variance will be different in this group automatically because of the larger sample size than the first two groups. Nearly 40% of position players ranked 21-100 turned out to be busts. In addition, only Freddie Freeman of Atlanta managed to get above the 4+ dWAR/year threshold to qualify as a star. In fact, the most common category of these ranked position players is a bust. When drafting a player, a team never knows for certain the production that the pick will produce in the major leagues, no matter the pick number of the draft pick. In addition, prospect rankings based on minor-league performance is still not a completely accurate indicator of future MLB productivity. Higher-ranked prospects in 2009 did have higher probability of contributing more to their major-league club, though rankings are understandably volatile. A variety of factors play into the volatile nature of prospect outcomes and the prospect risk premium. Part of the reason I chose to only look at position players is because they are traditionally safer from injury than pitchers, and therefore carry slightly less of a risk premium.

Looking at the variance of dWAR for the prospect group, the distribution is skewed left, which is to be expected because not all prospects will turn out to be as equally strong, and most will not become stars. It also makes sense because in any given year, only a few top prospects will become very strong players, while most will hover around average. We also see that the inner quartile range is about from 0.5 dWAR per year to slightly above 2.5 dWAR per year. Therefore, it could be expected that a team get production in that range from a given prospect ranked 1-100, varying sightly in what rank group they are in. A useful analysis would be to make a distribution chart of each rank group, but in the interest of brevity, I do not do that here.

New ways of evaluating both minor league and amateur players to relieve some of the prospect-risk premium is useful, although risk will always be present. In the next part of this study, I will try to discover statistically significant correlations between college and major-league performance in order to try to reduce the noise of prospect-risk premium. One of the great things about the baseball player development structure is that it allows players with the right work ethic and dedication, as well as others who were overlooked in high rounds of the draft, to prove themselves in the minor leagues. That can seldom be said it other professional sports. The famous example of this was Mike Piazza, who was one of the last overall picks in his draft class and worked his way to a Hall of Fame career. With perfect information, the graph would be perfectly skewed left, with each ranked prospect achieving a higher dWAR than the next ranked prospect. Some may attribute the imperfect information dilemma to drafting or the evaluation of minor-league performance, and some may attribute it to differences in player-development systems. Some may also rationally say that both the players and the scouts are humans and will not be perfect. Prospects rankings for a given year are based on several factors, including a player’s proximity to contributing on the major-league level. The most talented minor-league players could be at a lower ranking in a given year because of their age or development level, which could cause some unwanted variance in the data. Looking at the just the 100 top prospects helps somewhat eliminate this problem, but will not make the problem completely disappear. It is difficult to know when teams plan on calling up prospects anyway, and it really depends on the needs of the team. Some make the jump at 20, while others make the jump at 25, or even later.

This type of analysis could be useful for things like estimating opportunity cost of a trade involving prospects for both financial trade-offs and present versus future on-field production. A lot of factors play into the success of a prospect. When evaluating any player, things such as makeup and work ethic are just as big of factors as measurable statistics. Evaluating college and high-school players for the annual Rule 4 draft can be especially difficult because of the limited statistical information that are accessible. Team scouts work very hard to accurately evaluate the top amateur players in the United States and around the world in order to put their team in a good position for the draft. Despite the immense baseball knowledge that scouts bring to player evaluation, statistical analysis on college players is still explored and used to complement traditional scouting reports. Prospect-risk premium will always be something teams must deal with, but efficiently allocating players into a major-league pipeline is essential for every front office.

There have been a few other articles on sites such as FanGraphs and The Hardball Times on statistical analysis of college players. Cubs president Theo Epstein told writer Tom Verducci that the Cubs analytics team has developed a specific algorithm for evaluating college players. The process involved sending interns to photocopy old stat sheets on college players from before the data was recorded electronically.

Though I do not doubt the Cubs have a very accurate and useful algorithm for such a goal, the algorithm is not publicly available for review, and understandably so. However, for the several articles which tackle this question on other baseball statistical websites, I think there is some room for improvement. First, the multiple of different complex statistical analysis techniques to compare college versus MLB statistics yield about the same disappointing results as the other, meaning that some of the models are probably unnecessarily complicated. Second, though the authors may imply it by default, statistical models in no way account for the character and makeup of a college player and prospect. Even in the age of advanced analytics, the human and leadership elements of the game still hold great value. Therefore, statistical rankings should not be taken as precise recommended draft order. In addition, they do not take into account injury history and risk of a player. Teams can increase their odds of adding a future starter or star over a player’s first six seasons by drafting position players, who have been historically shown to be safer bets than pitchers due to a lesser injury risk.

The model in this post attempts to find statistically significant correlations between players’ college stats and a player’s stats for his first six seasons in the MLB. Six seasons is the amount of time a team has a drafted player under control until they reach free agency and the player is granted negotiating powers with any team, like we’ve gone over. However, the relationship between college batting statistics and MLB fWAR can only go so far because of the lack of fielding and other data for college players.

The first thing I did was merge databases of Division I college players for years 2002-2007 with their statistics for their first six years in the MLB. There is some noise in the model since some payers in the MLB who were drafted in later years in my sample have not spent six years in the MLB, which is accounted for. I only look at the first 100 players drafted each year. I then calculate each player’s college career wOBA per the methods recommended by Victor Wang in his 2009 article on a similar topic. However, since wOBA weights are not recorded for college players, the statistic is more of an arbitrary wOBA that uses the weights from the 2013 MLB season. Since wOBA weights do not vary heavily from year to year, it will do the trick for the purpose of this analysis. For MLB players, wOBA compared to wRC and wRC+ have a 97% correlation (varying slightly on the size of the sample) so I did not feel it was necessary to calculate wRC in addition to wOBA. In fact, when using ordinary least squares and multiple least squares regression techniques, I would have experienced problems with pairwise collinearity, so calculating both statistics would have proved pointless. Along with an ordinary least squares regression technique, I also use multiple least squares and change the functional form to double logarithmic. (A future study I hope to tackle soon is to use logistic regression techniques to calculate the odds of a college player ending up each of the four WAR groups for their first six season in the majors.)

Due to the limitations in the data as well as the restrictions on the amount of top 100 picks that actually make it to the MLB, the analysis is somewhat limited, yet still produces some valuable results. Interestingly, though perhaps unsurprisingly, my calculated wOBA for each player’s college career showed a strong and statistically significantly relationship with wOBA produced in the MLB. To a lesser extent, college wOBA also indicates a statistically significant relationship with MLB-produced WAR, even though this study does not take into account defense, baserunning, etc. Looking at a collinearity matrix, I find that college wOBA and MLB wOBA have about a 25% pairwise collinearity. In addition, the matrix shows a similar pairwise collinearity of about 25% between college wOBA and MLB WAR, though at a lower level of confidence. Using an ordinary least squares regression, I use different functional forms to further evaluate the strength of the relationship between college and MLB statistics.

The first model confirms a fairly strong and statistically significant relationship at the 1% level between college and MLB wOBA with a correlation coefficient of about .25. College strikeout to walk ratio is also statistically significant at the 1% level albeit without a strong correlation coefficient. Even so, looking back at the matrix indicated that players who are less prone to the strikeout in college, on average, see better success in the MLB. Interestingly enough, college wOBA and strikeout to walk ratio are about the only two statistically significant statistics that I can find by running several models with different functional forms. Per the model, we can also say that it is likely that college hitters with extra-base-hit ability have better prospects in the majors. The R-square for model one is about .20, which is not terrible, but certainty not enough information to provide a set-in stone model. The constant in the regressions seem to capture noise that is difficult to replicate, lending insight to the extreme variance and unpredictability of the draft.

For model 2, I use a double logarithmic functional form with a multiple least squares linear regression in order to see the variance in MLB wOBA with college wOBA and strikeout to walk ratio. The results of this regression are slightly stronger and look a bit more promising to the conclusion that the calculated college wOBA is a strong predictor of MLB wOBA.

According to the results of the double log model, a one percent increase in MLB wOBA corresponds to about 36% increase in college wOBA, all else equal. (Since the model is in double log form, the interpretation is done by percent and percentage points.) We can more simply interpret this that a player, on average and all else equal, will have a one percent higher wOBA in MLB for every 36% increase to their college wOBA compared to other players. The coefficient is significant at the one percent level. In addition, a one percent increase in MLB wOBA corresponds to about a six percent decrease in college strikeout to walk ratio. Again, I get about a R-squared of about 0.20.

Perhaps the most interesting thing that these regressions have shown is that college batting average has almost no correlation with MLB success. This may be a little misleading because hitters who get drafted in high rounds and who do well in the MLB will likely have high college batting averages, but the regressions show that there are other things teams should look for in their draft picks besides a good batting average. Traits such as low amounts of strikeouts, especially relative to the number of walks, helping indicate a player’s pure ability to get on base. When evaluating college players, factors such as character build, work ethic and leadership abilities will be just as good as indicators for success for strong college ball players. Perhaps the linear weights measurements used in wOBA calculations are on to something. Accurate weights can obviously not be applied to college statistics without the proper data, but the comparisons using MLB weights for college players can still be useful. In addition, it is also well known that position players are traditionally safer higher-round picks than pitchers due to injury risk. I would argue that strong college hitters are often times the most productive top prospects, while younger pitchers who can develop in a team’s player-development system can be beneficial for a strong farm system and pipeline to the major leagues. Many high-upside arms can be found coming out of high school, rather than taking power college pitchers. In addition, arms from smaller schools often times are overlooked due to the competitive environment they player in. Nevertheless, hidden and undervalued talent exists that could result in high-upside rewards, both financially and productively for teams.

Let’s Find the Giants 88 Wins

We find ourselves in the midst of an exceptionally intriguing offseason. Rarely is there an opportunity to acquire a prior year’s MVP and remain in position to nab the number-two asset on the market: Shohei Ohtani. Given Ohtani’s decision to forego a contract that syncs up with his open-market value when he turns 25, he’ll hold a Black Friday-esque price-tag when posted. Virtually any team in baseball can make a play to acquire the former star from the Hokkaido Nippon-Ham Fighters, regardless of wallet size. That makes this particular campaign for a generational talent so intriguing.

Whether your team meets Ohtani’s duo of wants — independent of a passing grade on his questionnaire — is another story.

The San Francisco Giants are in a precarious position heading into 2018. Coming off a 64-win season, the lowest win total for their franchise since 1994, and the lowest of Bruce Bochy’s tenure by seven games, a rebound seems imminent. The current state of their roster, however, casts doubt on how relevant a rebound can make their team.

So, I sent out a tweet entertaining the possibility that one team lands the two biggest names of the offseason.

A little bit of mental math brought my over/under to 87.5 wins. Imprecise? Sure, but only three times since 2014 has one team improved on their prior year win total by more than 24 games: the Minnesota Twins (2016 to 2017, +26 wins), Arizona Diamondbacks (2016 to 2017, +24 wins), and Chicago Cubs (2014 to 2015, +25 wins). Whether a signal or mere noise, each of those improvements came without lavish acquisitions during winter (I used my subjective definition of “lavish”). Each was propelled to relevance by internal talent (Buxton/Sano, Ray/Godley, Arrieta/Bryant, etc.), superb management, and other favorable nods from the Baseball Gods. Each of the 29 responses to my poll came with three elements of consideration: Ohtani, Stanton, and everything else.


The pitching side of Ohtani’s value is interesting. ZiPS and Dan Szymborski were the first to throw their hat in the ring, giving Ohtani a 3.55 ERA over 139 innings of work, with 161 strikeouts, and a walk rate of 3.9 BB/9. It’s lukewarm, considering the hype around Ohtani and knowledge of his sub-1.1 WHIP over in the NPB. Do I agree with it? Not from a control standpoint, but we can work with it and my disagreement isn’t dismissal of a labor-intensive statistical model’s projection.

Taking the three essential components of FIP (walks, strikeouts, and homers), and our knowledge that pitcher fWAR is derived from FIP, we can backtrack from Ohtani’s ZiPS projection and in an anti-statistician kind of way. By comparing Ohtani’s per-nine peripherals to last year’s performers, we can infer his fWAR might be around 3.0 as a pitcher in 2018 (139 IP, 10.4 K/9, 3.9 BB/9, 1.0 HR/9). This ZiPS and fWAR magic says he’ll be slightly worse than 2017 Brad Peacock (that was a weird sentence to write).

Ohtani’s potential 3.0 fWAR is backed up when you look at his 2016 in the NPB. The righty posted 137 1/3 innings of work, with a 9.2 K/9, 2.9 BB/9, and a HR/9 just north of 1.0. This gives Ohtani something slightly better than Jose Berrios’ 2.8 fWAR 2017 campaign (an equally weird sentence to write).

Value for Ohtani with his bat on the Giants, a team obviously absent of a DH, is where confusion starts.

I want to keep this as simple as possible. It’s unlikely that he goes to the NL if contributing significantly on the mound and in the box are his main goals. The inherent risk for the lottery-winning club would be too high and uncertainty around whether Ohtani would prefer such a role plays an equally large factor. Travis Sawchik breaks Ohtani’s NL hitting value down better than I ever could, so I’ll only give you the product of his analysis.

Ohtani could have about 1.6 fWAR as a hitter. This is composed of 1.1 fWAR in his standard pitcher plate appearances, plus another .5 fWAR from regular pinch-hitting chances (emphasis on the word “regular”).

In total, we have a 4.6 fWAR player in Shohei Ohtani in the National League. Our 3.0 fWAR on the mound and an aggressive — but feasible — 1.6 fWAR in the box.

To find 88 wins for the Giants that my poll responders believe in, we need to start somewhere. It’s too easy to begin at a projection already circulating for the Giants’ 2018 win total, so I’ll make this hard for myself to execute, and likely, for you to rationalize. Let’s start with those 64 hard-fought wins Bochy’s squad scratched and clawed their way to. We’ll work backwards from there.

64 wins, plus roughly five we’re going attribute to Ohtani brings us to 69.


Now onto Stanton.

Eno Sarris, a familiar name to many, looked through the surplus value on a trade that would send Stanton to the Bay Area. The names included in that analysis revolve around the following:

To SF: Stanton, Dee Gordon

To MIA: Joe Panik, Tyler Beede, Chris Shaw

We don’t have confirmation this would be the package, but I remain adamant Miami wants contract relief more than anything. Centering an offer around the eight FanGraphs wins above replacement (fWAR) Panik has accumulated in his career feels like a proper balancing of sides, given how much money the Giants would take on in a scenario like this. Whether Stanton opts out or stays through the length of his contract muddies just how much money the Giants, or any team, will tie up through 2027. Although it seems like a risk teams are willing to take, how that opt-out risk factors into offerings is another confounding input.

However, Stanton’s value to teams from a performance standpoint is less cloudy than his monetary value. He’s good. Very good. Completing two 6-fWAR seasons before turning 28 is desirable trait for any player. One of the first projections kicking around — FanGraphs’ Steamer — holds Stanton somewhat steady with his torrid 2017.  5.3 fWAR, buoyed by another 45+ homer season, and a wRC+ that holds up to his career standard. I have little objection to this, even if worry consumes you that a healthy season for Stanton was an anomaly.

Ohtani brought us to 69 wins and now Stanton will take us north of the only number above 15 anybody is ever excited to see. We’re at 74 for the Giants by taking WAR and interpreting them as literal wins, something I probably shouldn’t do given the debate the industry just had, but I’ll test my luck.

Everything else

This subheading encompasses a lot of assumptions. In my tweet asking my loyal followers to quickly gauge whether the Giants could get above the 87.5 wins, this considered everything from a (hopefully) full season of good Madison Bumgarner and paying a priest to rid the bad juju from the Giants’ clubhouse, to a minor investment in separate baseballs juiced specifically for AT&T Park.

We could venture another 1,000 words on the improvements of San Fran, but there are far more qualified Giants fans on this website and others (shoutout to Grant Brisbee at McCovey Chronicles) that have surely detailed this difference with more care and a deeper knowledge of the Giants’ issues and internal fixes.

Cutting to the chase, let’s make a simple push to the 88-win mark. FanGraphs’ depth-chart projections currently has the Giants as a 78-win team. That’s 14 wins better than 2017. It is also exactly what we need to go from 74 wins to 88.

Sometimes, things work out better than anybody could have ever planned.

We found our 88 wins.

The only thing I’m left wondering is whether my tweet and over/under projection at 87.5 inspired hopes of 90-plus-win seasons in voters’ minds. If Bochy & Co. can accomplish that feat without even one of Ohtani or Stanton, I commit to paying the shipping fee for Bochy’s Manager of the Year Award.

A version of this post can be found on my site,, by following this link


Who Are the Top “Pound-for-Pound” Power Hitters?

We all know that Aaron Judge hit for more power this year than Jose Altuve. But, whose power was more impressive? Aaron Judge, who is 6’7 and 282 pounds, has a considerable size advantage over Jose Altuve, at 5’6 and 164 pounds. Perhaps Altuve is actually a better power hitter for his size than is Judge. Let’s expand this idea to the entire league: who is the pound-for-pound top power hitter?

Role of Height and Weight in Batter Power

Using simultaneous linear regression, I estimated the effects of two physical characteristics — height and weight — on batter power. Measures of batter height and weight were taken from For batter power, I used Isolated Power.

As shown in the figures below, weight and height have positive relationships with power.

Height and Weight

Weight has a stronger relationship with power than height, though it is difficult to see in the figures alone. (It’s also not intuitively clear exactly how height affects power.) In subsequent analyses, I consider both weight and height.

Who are the top pound-for-pound power hitters?

Using the model, one can predict a batter’s expected power (based on height and weight) and compare it to their actual power.

Who are the top pound-for-pound power hitters? See below for the results.

Top 10 hitters

Khris Davis, formerly the #9 top power hitter, emerges as the #1 pound-for-pound power hitter in baseball. In 2017, Davis, who is three inches and over 30 pounds below average for a Major League hitter, hit a remarkable 43 home runs in 2017, with an ISO of .281. Nolan Arenado and Josh Donaldson made similar jumps in the rankings, from #7 to #2, and #10 to #3, respectively.

Notable power hitters have fallen slightly on this list, though remain in the top 10. For example, Aaron Judge fell from the top spot to #8, while Giancarlo Stanton dropped three spots (#2 to #5). It is important to note here that these power hitters are still impressive – continuing to hold spots in the top 10, regardless of their size.

Biggest improvements in rankings

Which players showed the most improvement in the list? Below are results from the top 50 players on the list.

Top 3 improved rank players

Andrew Benintendi showed the largest increase in rankings (from 184 to 43). Jose Altuve nearly broke into the top 10, jumping from 132 to 12. Lastly, Eddie Rosario improved 68 spots (100 to 32). Altuve, in particular, has recently shown increases in power (from .146 to .194 to .202 in 2015-2017); as a result, his pound-for-pound status may continually increase in upcoming years.

Who was more impressive?

To reference the initial question in this article: was Jose Altuve’s or Aaron Judge’s power more impressive? Results from the above analyses were compiled from 2015 to 2017 seasons. To compare Altuve and Judge’s recent season, take a look below.

Altuve vs Judge

Aaron Judge tops Jose Altuve in the pound-for-pound hitter rankings – by a very thin margin – in 2017. Judge’s power performance exceeded expectations (as predicted by his height and weight) to a slightly higher degree than Altuve.

Full Rankings

If you want to see the full list of hitters for this dataset, including the worst pound-for-pound power hitters (poor Jason Heyward!), click here.


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