## This is Part 2 of our analysis on how the Pittsburgh Pirates can improve their World Series chances for the 2018 season.

Here, we will be referring to the conclusions from Part One of our look at how the Pittsburgh Pirates get to — and even win — the World Series, and so I recommend at least skimming it here before reading this piece, for clarity’s sake.

As promised, this piece will serve as an economic analysis of some of the traditional wisdom about building a World Series contender. Using things like cost benefit analyses and real payroll information, we will be scrutinizing some of these commonly accepted ideas for their truthfulness.

One of the first ideas that some baseball fans give as the surest way of building a World Series contender is to spend more money on the team. The hypothesis goes like this: more talented players cost more money. The more talented a team is, the more likely the team is to win games.

Therefore, teams have to spend more money to win more games.

In order to analyze this theory, I’ve pulled Payroll data on every major league team from 2012-2016 according to Baseball Prospectus. I then put each of these terms in terms of 2016 dollar values by according to the league average payrolls in each of those years. For those more familiar with economic terms, I just calculated baseball’s inflation rate between years, then adjusted everything in terms of 2016 baseball dollars (I say “baseball dollars” because baseball’s inflation rate is much greater than the inflation rate of the rest of the U.S. economy).

The top spending team in terms of inflation adjusted dollars, was the 2015 Dodgers at $293 million, and the top 10 highest spending teams in the 5 year span between 2012-2016 have four appearances by the Dodgers, five by the Yankees, and one by the Red Sox.

None of those teams won a World Series in their top spending years.

The Pittsburgh Pirates’ top spending team was the 2016 version of the club, spending $99.9 million, followed by the 2015 team which spent $93.8 mil.

Herein lies the first bit of evidence that spending more money doesn’t necessarily imply more wins. The 2015 Pirates spent $6.1 mil less in inflation adjusted dollars, than their 2016 counterpart, yet the 2015 team registered 20 more wins than the 2016 team did.

This is a trend that plays out pretty similarly in the data. Here’s a graph of each team’s inflation adjusted payrolls versus their respective wins;

The black line is the trend line for payroll and wins, and we can learn two important things from it.

### Lesson time

The first is that the trend is slightly positive, meaning that increasing payroll does have *some* positive impact on wins.

The second is that the trend line is not very “descriptive”; meaning that if we look at the distance between the blue dots and the black trend line, we see that there is quite a large variation at times. If you look at, for instance, the 92 win, $293 mil Dodgers, represented by the dot closest to the top of the graph, then look at the black trend line, which estimates of the payroll of a 92 win team, there is a $148 mil difference, which is pretty significant.

Mathematically speaking, this trendline correlates at about 28 percent. In plain English, **this means judging a team’s ability to win based on the amount of money spent on them is a pretty useless measure**, having little ability to project the success of a team.

The reason for this has to do with a false assumption we made in the beginning; more talented players don’t always cost more money, and players that cost more money aren’t always more talented.

Take for instance the Pittsburgh Pirates pitching staff. Ivan Nova has been worth 2.2 bWAR this year and is being paid $7.7 mil. Gerrit Cole on the other hand has been worth 2.4 bWAR and is only being paid $3.75 mil.

If it were true that players were paid strictly based on their ability to contribute to their team, we would expect that Ivan Nova would produce roughly twice as many wins as Gerrit Cole, while in reality Cole has produced 0.2 more wins than Nova at about half the pay.

This introduces the idea of cost effectiveness, or a team’s payroll per win. A cost per win measure assesses the ability of a team to convert dollars spent into actual wins. A team could theoretically overpay for mediocre talent that only produced a few wins, thus having a really high cost per win ratio. On the other hand, a team could have a bunch of Gerrit Cole-type situations, where the team is underpaying good talent that is giving the team more wins, thus having a low cost per win ratio.

Here’s the graph of team’s inflation adjusted cost per win ratios vs their actual wins;

Again, we can draw two key conclusions from this trend line. The first is that the smaller a team’s cost per win ratio is, the more wins we expect a team to have. So teams that spend money effectively tend to win more games than teams that spend money ineffectively.

The second is similar to the earlier “wins vs payroll graph”; there is very little correlation between the trendline and the data points.

In fact, this trendline correlates even worse than payroll and wins, at only about 6%. In other words, only using cost effectiveness to estimate a team’s ability to win is not a particularly useful measure either.

However if we combine both the total payroll, and the cost effectiveness of that payroll into a model we get a much better correlation. Here is a linear regression of wins on inflation adjusted payroll and cost per win.

(The term “iapayroll_mil” means “Inflation Adjusted Payroll in millions of dollars”, and “iacw_mil” means “Inflation Adjusted Cost per Win in millions of dollars”.)

### Here’s the formula written out: Wins = 81.936 + .565 * Payroll – 46.189 * Cost per Win

From this analysis we get that each additional million in payroll we expect .565 more wins. More clearly stated, this means an additional win costs about $1.77mil holding steady a team’s cost per win.

We also find that the lowering of a team’s cost per win of $1million should result in about 46 additional wins. More simply, that means a team has to decrease their cost per win by $20,000 to get 1 additional win in a season, holding their payroll constant.

This model has the additional benefit of correlating at about 94% (sqrt(.8790)=.9375), much better than either of the two previous models of just payroll or just cost effectiveness.

The conclusion we draw from this is that teams that spend a lot of money, and do so effectively, tend to win the most games, which is rather intuitive, but is now at least backed up by data.

This analysis becomes really important in conjunction with my analysis from Part 1. If we take the Pirates’ average cost per win between the ‘12 and ’16 seasons, which was $0.98mil/win and assume we would like them to have at least a 90% chance of making the playoffs, which from last week equates to 90 wins. We can then plug these numbers, 90 wins and $0.98mil/win, into our formula and solve for what we would expect their payroll to be.

### 90 Wins = 81.936 +.565 * Payroll -46.189 * $0.98mil per Win (Payroll=$94.39mil)

This $94.39mil is in 2016 dollars, so adjusting for inflation to the 2017 season gives us a 2017 payroll of $96.78mil to have a 90% chance of making the playoffs. The Pirates are pretty close to this mark in 2017, with Baseball Prospectus putting them at $95.8mil in payroll for the year, which is less than $1mil of difference.

Since the team is not currently projecting to hit a 90 win season, it is safe to assume that the team has lost something in terms of cost effectiveness. Where exactly this loss in efficiency came is not something I can necessarily show in the numbers.

Perhaps it came due to the loss of one of the most effective bullpens in baseball between 2013-2015, perhaps the rest of the league is catching up to the inefficiencies the Pirates exploited over the past several years, perhaps it is due to losing your top producing player of 2016, Marte, for the first half of 2017, and losing the second highest producing player, Kang, for the entirety of the 2017 season.

We can, however, find out how much efficiency they lost by assuming the Pirates will win between 77 to 80 games this season (for simplicity’s sake we’ll call it 78.5 wins). Since we also know their current payroll, we can plug those two numbers into our formula and get the resulting cost effectiveness. For consistency’s sake, the Pirates current payroll of $95.8mil in 2017 dollars is $93.4mil in 2016 dollars giving us the equation;

### 78.5 Wins = 81.936+.565 * $93.4mil-46.189 * Cost per Win (Cost per Win = $1.21mil/Win)

This tells us that the Pirates are paying $230,000 more per win than their average cost over the past 5 years. Since it’s about $20,000 per win, that means that the 2017 Pirates lost 11.5 more games due to loss in cost effectiveness. However, they also won about 2.5 more games in the 2017 season due to increases in payroll.

In any case, the Pirates don’t actually need to be spending any more money on the team to make them a winner (and if you read my last article, a serious World Series contender). What the Pirates need to do is find ways to spend their money more efficiently, like they did so well between 2012 and 2015.

Unfortunately this is no easy task.

In the past the PIttsburgh Pirates have made use of undervalued skills in baseball to improve their cost effectiveness. Things like a catcher’s ability to frame pitches, a pitcher’s ability to induce ground balls, talents of hitters from the Korean Baseball League, the ability to work a count at the plate and get on base, etc. were all undervalued parts of baseball that the Pirates were able to exploit in years gone by.

Nowadays, however, most major league teams recognize the value of these skills and players, so the Pirates have to find other inefficiencies and under-valuations.

One place I think the Pittsburgh Pirates are exploiting this type of inefficiency is in the trade market.

While many fans and reporters like it when teams make a “big splash” at the trade deadline, this is really a pretty bad strategy, for teams looking to boost their cost effectiveness, and thus their wins.

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