Should the Indians Re-Sign Scott Kazmir

December 21st, 2012: the day the world was going to end. Since you are in front of your digital device of choice reading this, you know that it did not. Rather, on that date a former Major League burnout and then current independent Atlantic League star decided to pick up the pen and sign his name on a Cleveland Indians contract to give his career another shot. 

That evening, after taking a collective deep breath realizing the Mayans were indeed wrong, Indians fans read that the team had reached a minor league deal with LHP Scott Kazmir. With that announcement, no fanfare was raised and nothing more was said on Cleveland media. Both the fans and media were still excited about the possibility of Nick Swisher calling Ohio home again.

Fast forward nearly ten months later and fans are eagerly awaiting the date when the Indians and Kazmir decide their future together.

Statistically, Kazmir was the best Indians free-agent pitcher signing of  the 2012 off season. While they signed a slew of fringe major leaguers to minor league deals, Kazmir was the most beneficial. Despite making "only" $1 million this past season, he earned a 2.5 WAR and a 4.04 ERA.  Among the five Indians starters with 130+ IP in 2013, Kazmir ranked second in K/9 (9.23), BB/9 (2.68), K/BB (3.45), and K% (24). In fact, his K/BB rate was the best of his career indicating he arguably had the best command of his career. Not bad for a guy who was forced to pitch in an independent league the season before.
Kazmir's improved four seam fastball velocity was the most impressive feature of his 2013 season. Not only did he see an improvement from his career average, he got better as the season progressed. The first table shows his season to season average four seam fastball speed as calculated in MPH:

Year Four Seam
2007 93.45
2008 92.76
2009 92.12
2010 91.4
2011 88.21
2013 93.56

(Table(s) courtesy of Brooks Baseball Pitch f/x data)

As you can see, his 2013 was the best of his career while course correcting his downward spiral. Up to this point, Kazmir's velocity dropped quicker than anything Snoop Dog deemed "hot" as declining velocity had became a major problem during his career. The 2008 season appears to be the start of Kazmir’s decline. Not only did Kazmir start the season on the disabled list, but that is when the velocity began its decline as well. Unfortunately for Kazmir, those trends would stick with him for four more seasons. From 2007 to 2011, his fastball velocity dropped each season from 93.5 mph to 88.2 mph; a pretty big fall for a guy who relied on his four seam fastball to retire batters. According to Brooks Baseball's Pitch f/x data, Kazmir’s four seamer rated as his best pitch, according to pitch-type values  used as percentages. But as his go-to pitch started to fade, Kazmir stopped being a viable major league starter.
The following table shows his velocity this past season on a month by month basis:

Month Fourseam
March 91.94
April 92.15
May 92.75
June 93.41
July 94.02
August 94.2
September/October 94.23
He threw harder as the season wore on. A remarkable turn around from a southpaw who had trouble hitting 90 mph on the radar gun two years ago. With his aforementioned WAR total this season, there is statistical proof that the Indians would not have won one of the two wild card spots without him. He was a bargain find and both he and the team capitalized.
This brings us to this question: Would it be beneficial for the Indians to sign Kazmir to an extension? Before we answer this question, it would be useful to briefly explain the two primary economic methods that the Indians front office will utilize to decide whether or not Kazmir will be worth the extension: Market-based and marginal revenue approach. 
With the market-based approach, the assigned members of the baseball operations staff would calculate the going rate for a certain level of expected performance by comparing players' salary levels and their performances. They would then forecast what dollar amount Kazmir would likely be offered on the open market. This would be accomplished using classical micro-economic principles. There are two qualities that drive the price of any good: supply and demand. Kazmir will be priced at the point where the supply curve and demand curve intersect. The fact that Kazmir did not sign an extension during the season means it is more than likely he will accept offers from other clubs. Since more clubs will perceive themselves as contenders because of the additional wild-card, more clubs will scour the open-market for starting pitching that will aid in their pursuit of reaching the postseason. A brief look at the starting pitching free agent list this off-season shows a relatively thin one particularly among the south-paws. We can assume that, because of the aforementioned scarcity, that clubs will place added value on Kazmir's new-found fastball. Since demand is high and supply is low, the price-tag for Kazmir will be high based on market assumptions.
The marginal revenue approach requires considerably more detailed analysis built on a set of fragile assumptions. The main tenant of this approach is dissecting the Indians revenue components and estimating how they fluctuate with the team's on field performance. By converting Kazmir's on-field performance into his impact on his team's wins and then translating those wins into attendance and revenue, we can quantify his dollar value to the team. Essentially this answers the question: "How much more revenue are the Indians expected to earn because Scott Kazmir is one member of the team's starting five in the rotation?" The first portion of the player valuation equation-measuring Kazmir's performance in terms of this impact on team wins-has been one of the most debated topics in the sabermetric world. In our case, we will use Kazmir's 2013 WAR total of 2.5 because indexing performance to replacement level simplifies the valuation process, as it provides a benchmark against which to measure Kazmir's marginal value. 
The next portion of Kazmir's valuation equation focuses on converting the Indians wins into a dollar revenue. Technically, it converts marginal winsattributable to Kazmir into expected marginal revenue for the Indians. This is what baseball economist and writer Vince Gennaro calls the "win-curve." According to Gennaro in his landmark book Diamond Dollars: The Economics Of Winning In Baseball, the win curve "is a team-specific estimate of the relationship between a team's win total and the revenue is can expect to generate, based on market size, the loyalty of the team's fans, and ticket prices, while adjusting for other revenue drivers …"
To spare the gory details of how regression analysis is used to to figure the definitive and measurable relationship between winning ball games and a team's revenue, we will use Gennaro's findings based on 30 years of data. Yes, many factors have changed in 30 years of attendance figures ( the opening of Jacobs Field, the higher capacity of Cleveland Municipal Stadium) so one must bear in mind that this statistic is an average. Based on Gennaro's regression analysis, he figured the dollar value of five wins where the win-curve is most non-linear: 86 to 91 wins. As we found out in 2013, 86 wins will keep a team in contention for most of the season but fade before the final week. However 91 wins will almost assure a team will not be mathematically eliminated from contention until the final weekend, or game.  From which we can expect revenue to increase as the team inches closer to playing in the playoffs. The following table shows the projected revenue increase from the aforementioned described change in wins:
Team    78-83         86-91
CLE    $5 million    $12.5 million
With Kazmir, the Indians won 92 games. Without him it could be argued that they would have won 89. Even though the win-curve is non-linear, we will divide $12.5 million by five (the difference of 91 and 86) for simplicity. That leaves us with $2.5 million per additional win in that range. That tells us that Kazmir brought in an additional $7.5 million this season  — a $6.5 million dollar net profit for the club. If the front office valued him close to this figure, his expected pay would be less when taking into account the club's desired profit margin per player.
Converging the two main valuing methods, we set the break-even bar at $6.5 million. If the market gets any higher than this figure it would be wise that the Indians part ways with the resurrected lefty. This, however, is not taking into account sophisticated projection models used by the club for 2014 and beyond. The break-even point of $6.5 million assumes that Kazmir will be a 2.5 win player next season also.
The good news for the front office is that local gate receipts (ticket sales) are no longer one of the main generators of income for Major League Baseball teams. With a bigger windfall from revenue sharing and the $40 million per year paid to the club from Fox Sports Ohio in rights fees, we can expect the Indians to increase the budget once again. This will allow the club to use other variables other than the fixed relationship between wins and revenue.
With the information provided, I would estimate Scott Kazmir to be worth around $4 million dollars next season to the Indians. This figure depends entirely on how close Chris Antonetti and the gang want to get to that $6.5 million break-even point.  However, Kazmir will almost assuredly be looking for a multi-year deal taking into account his previous struggles and potential injury risk. It's up to the front office to decide if taking the multi-year risk is worth it. 
Or maybe they can find another "diamond in the rough" for close to league minimum.
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