# Economically Speaking, Should the Pittsburgh Pirates Try for Manny Machado?

Manny Machado is not going to sign with the Pittsburgh Pirates.

There. It???s been said. Don???t go reading this article thinking that there is any hope that the Pirates are going to overspend on one of the best shortstops in the game, for a 1 year $35-40+ mil contract.

Now that that???s been said, it does make for an interesting thought experiment. Is it possible for a small market team to make an unwieldy contract like that profitable?

It???d be difficult. That team would have to be in a very particular situation where they have a deep need at shortstop, have a relatively low payroll where they could afford such a player and are, in spite of their low payroll, on the verge of competitiveness and just need to gain 5-6 more wins. Even then it???s not entirely clear.

Huh. The Pirates are a team with a pressing need for an everyday short stop, have a low payroll, even by their standards, and are projected as roughly a .500 team, meaning 5-6 additional wins would put them in contention. Let???s break these three down a bit more.

__Shortstop Need__

__Shortstop Need__

The Pirates??? need at shortstop is glaring. No matter how many comments Neal Huntington gives about the team feeling comfortable going into the season with Kevin Newman and Erik Gonzalez as their starting shortstops, the need is obviously there. Taking a look at Steamer???s projections for the 2019 Pirates: Kevin Newman projects as a 1.1 WAR player and Gonzalez projects as just a 0.3 WAR guy. Neither are truly impactful players. That puts Newman as the equivalent of Jordy Mercer, who never had more than a 2.0 fWAR season. While there are large error bars around any projection, the reality is that the Pirates are looking to improve on a 82-79 season, not maintain status quo.

On the flip side, Machado lists as the 3^{rd} highest projected WAR among all shortstops at 5.2 in Steamer???s projection. Over the past 3 seasons, only Cleveland???s Francisco Lindor has posted more WAR than Machado. There???s no such thing as a sure thing, but conditional on him being healthy, Machado would be a multi-win upgrade for the Pirates.

__Low Payroll__

__Low Payroll__

The team that signs Machado is obviously going to have to pay a ton of money for his services. For a small market like Pittsburgh, that means having some free space in the payroll. Fortunately for them, it seems like they do.

As it currently stands the Pirates have an Opening Day payroll somewhere in the $70mil range. If we look at that relative to what the team has spent in the past, there is obviously at least a bit of that runway left on the books.

Their raw payroll by year went as high as $117 mil in 2017. However, baseball has persistently seen its players, on the whole, get paid more and more every year, at least over the past eight years of data presented here.

How much more? The average payroll inflation over these 8 years was 9.01% per year. For perspective, the average annual inflation rate of the American economy according to the St. Louis Federal Reserve, over that same time period was just 1.69%, markedly less. It???s worth making that adjustment into 2018 ???baseball dollars??? to get a better sense of what the Pirates might be able to spend on the team in 2019.

Ahh so in 2015, the Pirates spent the 2018 equivalent of $122.6 mil on the team. It???s worth considering that 2019 will almost certainly see additional inflation, but rather than forecasting it, we???ll stick to 2018 dollars.

This means that the Pirates have somewhere in the neighborhood of ($120mil-$70mil=) $50mil that they could spend to get back to their previous high; that kind of money could land them Machado and then some. That being said, it???s also not known if that $120mil mark is actually feasible without actually seeing their books, perhaps the team over extended a bit in their bid for competitiveness. If we knock an extra $10mil off of our ???runway???, we still see serious cash to land Machado, at least for 2019. Additionally, the Pirates spent that $122 mil adjusted dollars on a 98 win club. Adding Machado would likely take them to a upper 80???s win club, so that roof ought to be lowered a bit. We???ll settle on $110mil in 2019.

__In Need of 5-6 More Wins__

__In Need of 5-6 More Wins__

The Pirates currently project as roughly a .500 club. That???s good enough to make any given game entertaining, but certainly not good enough to make the team competitive for the division or likely even the Wild Card in 2019. Interestingly, this puts the Pirates in the highest leverage position to add wins.

Just because this is the data I had on hand, I ran a logistic regression of a team???s likelihood of making the playoffs based on their record using 1996-2017 seasons and applying the 2012 Wild Card rule change to all seasons prior to 2012. Here???s what I got.

The graph is pretty clear — at 80 wins you have almost no chance of making the playoffs and at 90+ wins you???re essentially a lock for the playoffs.

Assuming the Pirates to be an 83 win team, or just a half game better than they were last season, their estimated probability of making the Playoffs is just 5.6%. If Machado is worth 6 wins that puts the Pirates as 89 win team, with an estimated 81.1% chance of making the Playoffs. That 75.4% chance difference is the second largest playoff probability improvement possible for a team gaining 6 wins. In other words, the Pirates are in one of the highest leverage positions of just about any team in the league to get Machado???s services.

This introduces another key point. Not all wins are valued equally. Teams that are on the precipice of contention should be willing to spend more money on players who will add the wins that push them into the playoffs, rather than teams that are either already good enough to make the playoffs, or are nowhere near being contenders.

__The Win Curve__

__The Win Curve__

The Win Curve is an idea that I first ran into reading *Baseball Between the Numbers* where Nate Silver hypothesized that teams don???t face linear increases in their revenue as they gain additional wins, but rather they see flat revenues as a losing team, then a sharp increase in revenue as they get into contention for the playoffs, then revenues fall back to flat once again when they???re locked up in the playoffs. If we???re graphing revenue as a function of wins, this generates an ???S??? shaped curve where revenues are flat and low for losing teams, then shoot up between 80-95 wins, then flatten back out after 95+ wins. If you???re interested, Max Gruber did some great work expanding out on the Win Curve here.

What does that mean for the Pirates? Well if the win curve hypothesis is true, that means that they *should* be paying more for the wins that get them into contention, as those wins generate them more revenue to pay those players. In essence, Machado is more valuable to the Pirates and should cost more since they???re on the verge of being a contender.

Now, it???s worth considering whether the win curve is true or not. Do teams actually see their revenues rise as they achieve postseason contention and how can we estimate it?

We can start off by looking at team revenue by wins. I took Forbes estimates for MLB team revenues from 2013 through 2017 and compared them to each team???s win total that season.

First off, this isn???t super informative as revenues in baseball have been increasing year over year for a number of years so there is a non-stationarity that we???re not accounting for in the data.

That being said; look closely at the loess regression line between roughly 70 wins and 95 wins, the area where the error bars are the smallest. What do we see? Between roughly 70 and 80 wins, the line is more or less flat; meaning a team going from 70 to 76 wins or 74 to 80 wins would see no appreciable difference in their revenues. However, starting just before 80 wins, we see a jump in the average amount of revenue from about $250mil at 80 wins to just shy of $290mil at around 90 wins, meaning those wins actually start generating the team additional revenue. While we can???t speak to the accuracy of these specific numbers in the Pirates situation, it???s encouraging to see that there is an increase in team revenues along with high leverage wins that that the Win Curve predicts. Let???s dig deeper.

As before, we should make an adjustment for annual inflation, this time on the revenues earned by the teams over the 5 years of data we???re using. This adjustment to 2017 dollars will control for the non-stationarity of revenues during this time period, as well as increasing the size of our effective sample as a result.

Again we see the ???S??? shape of the Win Curve between roughly 70 and 95 wins. There is still a problem of outliers well above the rest of the group in this graph though, meaning there is something causing these large revenues outside of just wins that we???re not controlling for. The first and perhaps most obvious place to look for this unknown factor is in market size.

I copied the market size numbers from this Business Insider article as a proxy variable for the team???s current market size and found a linear weight of $9.24 in revenue per person in a team???s market when controlling for wins.

I chose a linear weight because it makes the most sense, to me at least, that teams in bigger markets should, ostensibly make more revenue directly proportional to their market size. There are some other factors that I could have controlled for, like whether a team splits a big market with another baseball team etc. but for our purposes of estimating, the simple linear weight works well enough.

I then adjusted all the already inflation adjusted revenues down by their market size times $9.24 per person to get a Market Size and Inflation Adjusted Revenue (MSIA Revenue). In theory, we???re now just looking at the revenues actually impacted by the product put on the field.

As you can see the data is a bit more evenly distributed, and we???ll assume that it???s evenly distributed enough to carry out the remainder of this analysis. Finally, we can estimate the value of how much additional revenue the wins Manny Machado would bring to the Pirates are worth.

Briefly, we can see that the Win Curve hypothesis holds up, teams at the lower end of wins have relatively flat marginal revenues, while teams that get into contention have higher marginal revenues while moving into contention.

So, on average, what would Machado be worth to the Pirates in 2019? At 83 wins, the Pirates??? projected MSIA Revenue is $248.4mil. At 89 wins with Machado, the Pirates MSIA Revenue is $264.0mil, a difference of $15.6mil. Ultimately, Machado???s on the field value doesn???t amount to enough to warrant his $35+ million dollar contract for the Pirates.

There are off-the-field considerations that likely raise his value beyond just his $15.6mil estimate; people might come out to the park simply to watch a generational talent like Machado, fans would buy his jersey, Pittsburghers would tune in to watch him play, etc. That being said, it???s unlikely that this additional revenue would cover the total of the $19.4 million hole left over. At the very best I???d guess it covers between a quarter and half that; the bigger the market, the more that this off-the-field source of revenue might cover. Pittsburgh is, however, not a big market. Fortunately, the Pirates have the money to cover that if their financial roof is really our estimated $110 mil. Unfortunately, they???d be silly to do something so inefficient.

While in a vacuum the Pirates signing Machado feels really good, it simply isn???t the case in reality that Machado would be worth it for the Pirates. Perhaps a more efficient, far less sexy move for the Pirates to make is to take that $15.6 mil ???Win Curve??? revenue and some of the $40 mil unused cap, and find some 3 WAR players to improve the team by a Machado margin. Machado to the Bucs is a pipedream, a fun one to talk about during the off season, but a pipedream nonetheless.

Really enjoyed this roller coaster ride! I think you did an excellent job of putting it in terms that the team may look at it. They have to see that a playoff race benefits them financially.

This offseason has hurt, and I don’t know why.. what did I expect? I don’t like seeing guys like Dozier or Lowrie go for pennies. Perhaps there are a few targets left that they can use w/ that $15M of added revenue from a playoff race. Not sure they make that bet though.

Nonetheless, I love these articles. You guys crush it. Keep ’em comin’.

Thank you very much, Joe. I’m glad that Nate will be contributing here periodically.