Sports by the Numbers

Category: Major League Baseball

Did the Astros Spend Their Way to the Top?

Posted on by Peter Lemieux

The Houston Astros doubled their payroll in 2017 and won the World Series.  Was that the reason?

In 2013 the Houston Astros moved to the American League, dismantled the team, and won just in the process.  Last year Houston won the World Series. The Astros’ ascent from the bottom to the top of the league was powered by investing in both pitchers and positional players. The blue line measures wins while the bars indicate salaries allocated to positional players and pitchers.

In 2011 the Astros spent $72 million on player salaries, of which $42 million went to positional players.  Two years later as the team moved from the National to the American League, the Astros had the smallest payroll in baseball at just $11 million, fully $45 million behind the next-stingiest team, the Minnesota Twins.

After the move to the AL, owners began investing in the team once more, though still not profligately.  The Astros spent about as much on salaries in 2015 and 2016 as they did in 2011; they just got a much better return on their investment with 86- and 84-win seasons. Then, last year, ownership doubled the payroll, investing $16 million in the team’s first DH, Carlos Beltran, and signing contracts with 1st baseman Yulieski Gurriel, right fielder Josh Reddick, and catcher Brian McGann, who together earn $44 million.

A couple years back I posted an article here on the relationship between player salaries and team wins. Using data from 2011 through the first part of the 2015 season I showed there was a small, but statistically meaningful relationship between a team’s payroll and the number of games it wins.

I have now added data through the 2017 season and updated the figures for previous years.  In all cases I am relying on the Spotrac website for the data on salaries by position.

All told I have 210 team-seasons for the thirty teams across seven years.  Plotting the simple relationship between players’ salaries (defined as the sum of the salaries for positional players and pitchers) and the number of games a team won shows the same positive relationship we first saw back in 2015.

The 2017 Cleveland Indians may be the most efficient team in recent history winning 102 games while spending just $115 million, compared to an average per-team figure of $127 million.  They lost in the American League Championship Series to the eventual World Series winners, the Houston Astros.

That last burst of spending certainly contributed to raising Houston’s win total from 84 in 2016 to 101 a year later.  Yet as the first graph shows spending alone was not enough. Applying the slope coefficient of 0.12 from the first graph to a payroll increase of sixty million dollars should garner a team about seven wins on average (=60 x 0.12).  That leaves another ten victories that we might chalk up to good management, or maybe team chemistry, or both.

Does Spending Bring Victories in Major League Baseball?

Posted on by Peter Lemieux

Over the past five years the Boston Red Sox spent $587 million dollars on player salaries.1 In 2013 all that money help buy them a World Series, but in 2012 and 2014 the big-spending Red Sox ended the season in the cellar of the American League East.  They fell to the bottom of the division again this year on Memorial Day and only now, late in the season, do they have a chance to climb back out.  (Update: The Red Sox “surge” in September fizzled out leaving them once again in the cellar of the AL East.)

Over that same five-year period the Dodgers spent even more, $824 million, and the team’s investment has bought them a winning record but little else. The team advanced to the Championship round in 2013 with a victory over the Atlanta Braves, but lost to the St. Louis Cardinals.  Last year the Cards foiled the Dodgers chances by beating them in the first round, and this year they fell to the Mets in the five-game divisional series.

The New York Yankees have seen no better rewards than the Dodgers when it comes to their high-priced payroll.  The Yanks also spent about $800 million on player salaries between 2011 and 2015 and averaged one more win than the Dodgers.  Like the Dodgers, though, the Yankees’ playoff performance over these years has also been pretty dismal.  They lost to the Detroit Tigers in the divisional round in 2011, and though they got past the Baltimore Orioles in that round a year later, they fell to the Tigers once more when playing for the pennant.  This year they lost to the Houston Astros in the one-game wild-card playoff.

When fans see teams spend enormous amounts in player salaries and get such mediocre results, they rightly wonder whether highly-touted expensive players are really worth the investment.  These doubts only grow stronger when they see teams with considerably smaller payrolls like Kansas City, Oakland, Pittsburgh or St. Louis routinely make the playoffs and sometimes win the Series.

As it turns out, though, focusing on these particular high-spending teams leads us to the wrong conclusion.  We can see the general relationship between payrolls and victories by simply plotting each team’s total wins against its total spending on player salaries.  Here is the plot for all thirty MLB teams from 2011 to 2015:2

wins-vs-player-salaries

Teams that spend more on player salaries do win more games, but the price is pretty steep.  The “slope” of the line, 0.13, tells us that it takes about $8 million to improve an average team’s performance by one regular-season win, since 0.13 X 8 = 1.04.

We can also use this overall relationship between salaries and winning to see whether any teams do especially better or worse compared to what the model predicts for them.  For the 30 teams in Major League Baseball, I find just nine whose performance over the past five years deviated “significantly” from the model’s predictions:

team-performances

One striking result is that only the Cardinals do significantly better than we would predict based on player salaries alone, averaging another ten games per season.  No other team in baseball shows the savvy of the St. Louis front office in terms of staffing its clubhouse economically.  On the contrary, what stands out are the many more teams that significantly underperformed given their payrolls.

At the bottom of the list are the formerly hapless Houston Astros. In 2011, 2012, and 2013, the team spent about $80 million, $40 million, and just $11 million on player salaries.  According to the model those figures should have generated between 70 and 79 wins. The Astros managed just 56, 55, and 51 victories in those years. Last year Houston improved to 70 wins, and this year Houston beat the Yankees in the wild-card game before falling to the Kansas City Royals in the divisional series.

The other teams in the chart probably won’t come as a great surprise to anyone who follows baseball.  The most poorly-served fans are our friends from Chicago where both the Cubs and the White Sox should be winning another eighteen games or so between them given their salary budgets.  Notice that none of the big-spending teams I talked about at the beginning, the Dodgers, Yankees, or Red Sox make the list, though the Sox’ performance was only slightly better than Seattle’s.

Finally let’s look at some simple predictions from the model.  In this chart I have reproduced the relationship between spending and winning and added two vertical bars, at about $62 million and $150 million.

making-the-playoffs-costs-150-million-2

The first figure represents the amount an average team would have to spend to expect they can win half their games, or 81 from a 162-game season.  The second figure, $150 million, is the cost it takes to win 90 games.  Nearly every team that has made the playoffs since 2010 has won 90 games or more, so $150 million represents the “entry fee” for having a solid chance at the playoffs. Unless you are the St. Louis Cardinals, of course.

For more details see the Technical Appendix.

1I use “player salaries” rather than total payroll throughout. Player salaries include monies paid to positional players and pitchers. Total payroll can include other sums like “dead” money paid to departed players to whom the club still has a contractual obligation.

2For 2015, I have extrapolated teams won-loss record to the full 162-game season using their records through September 5th.

Technical Appendix: Using Player Salaries to Predict Wins

Posted on by Peter Lemieux

To get some perspective on the relationship between team performance and team payrolls, I have gathered data for each season from 2011 until 2015 on player salaries from the widely-cited database available at Spotrac.  These data are broken out by positional categories and include a figure for “dead” money, contractual obligations to players that are no longer with the team.

Regression Results

I start with a model that includes player salaries, the sum of payments to pitchers, catchers, infielders, outfielders, and designated hitters, in millions of dollars (“PlayersMM”) and a residual “other” category that is the difference between reported total payroll and player salaries again in millions of dollars (“OtherMM”).  As these results show clearly, the player salaries are what matter when it comes to winning

Pooled OLS, using 150 observations
 Included 30 cross-sectional units
 Time-series length = 5
 Dependent variable: Regular-Season Wins

             coefficient   std. error   t-ratio   p-value
 ---------------------------------------------------------
 const       69.2663       2.22782      31.09     1.62e-66 ***
 PlayersMM    0.130358     0.0227014     5.742    5.17e-08 ***
 OtherMM      0.00928354   0.0340035     0.2730   0.7852

Mean dependent var   81.02667   S.D. dependent var   11.10653
Sum squared resid    14929.62   S.E. of regression   10.07780
R-squared            0.187720   Adjusted R-squared   0.176668

The overall explanatory power of this model is pretty low.  Just under 19% of the variance in wins can be statistically accounted for using these salary data.  That’s just another way of stating what the graph in the main article shows, that there is a lot of “scatter” around the model’s predictions.  Teams with identical payrolls can win considerably more games than the model predicts, or considerably fewer.

Because the data contains multiple measurements on each of the thirty teams we can exploit that feature and allow for specific “team effects.”  These are the source of the second graph in the main article and comes from estimating a model with “dummy” variables included for each of the teams.  After whittling down the results to the teams with “significant” effects, we’re left with this model that forms the basis for the chart comparing teams in the main article:

Pooled OLS, using 150 observations
Included 30 cross-sectional units
Time-series length = 5
Dependent variable: Regular-Season wins

            coefficient   std. error   t-ratio   p-value
---------------------------------------------------------
const        75.3935      2.20255      34.23     2.64e-69 ***
PlayersMM     0.103430    0.0207827     4.977    1.89e-06 ***
OtherMM      −0.0360856   0.0302921    −1.191    0.2356
CHC         −10.1867      3.98745      −2.555    0.0117   **
COL         −13.5862      4.02725      −3.374    0.0010   ***
CWS          −8.46620     3.98705      −2.123    0.0355   **
HOU         −16.6031      4.11470      −4.035    9.00e-05 ***
MIA         −11.2013      4.08010      −2.745    0.0069   ***
MIN         −13.8250      4.01661      −3.442    0.0008   ***
PHI          −8.65976     4.05484      −2.136    0.0345   **
SEA          −7.50076     4.00319      −1.874    0.0631   *
STL          10.1054      3.98768       2.534    0.0124   **

Mean dependent var   81.02667   S.D. dependent var   11.10653
Sum squared resid    10435.62   S.E. of regression   8.695999
R-squared            0.432227   Adjusted R-squared   0.386969

After adjusting for the extreme cases, two changes happen to the effects of spending. One, the coefficient for player salaries falls from 0.13 in the simple model without adjustments to 0.10 here. That suggests that an average team needs to spend about $10 million to gain another victory, rather than the $8 million figure based on the simple model. However a more nuanced view of the spending effect includes the coefficient’s “standard error” of 0.02. That can be used to construct a “confidence interval” around the estimated effect; the actual effect of spending is 95% certain to fall somewhere in the range between 0.06 to 0.14, the result of subtracting or adding twice the standard error. That means it costs somewhere between $7 million (7 x 0.14) and $16 million (16 x 0.06) to gain another win.

Second, the portion of teams’ payrolls not devoted to players on the field now has the “proper” negative sign, though it still falls considerably short of conventional significance levels. It’s possible that teams are penalized for making bad decisions that lead to large pools of “dead” money, but the evidence is still pretty weak, and the effect quite small.

Finally we can ask whether spending on pitchers is more or less productive than spending on positional players. The answer is that it doesn’t matter. Including separate terms for both groups’ salaries adds no predictive power to the model. Spending another ten million dollars on pitching has the same effect as investing that money in the rest of the team.