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Wins versus Payroll in 2018: Fun with Numbers

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#1 caninatl04

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Posted 08 November 2018 - 05:44 PM


How much does it cost (in payroll) to win an extra baseball game? How much should a team expect to spend to win 85, 90, 100 games?

I did a few very simple things to attempt to answer that. First I collected payroll data and wins (both from 2018 regular season) from mlb.com

Then I calculated the correlation between the two and found it to be just under 39%, which means only around 16% of a team's success could be statistically explained by payroll. If you have studied statistics, the correlation is roughly 40%, so the R-squared is about 16%, or roughly 1/6th.

So, what explains the remaining 5/6ths? I don't know, but some obvious candidates would be the number (or percent) of a team's roster that is before or in arbitration.

I ran a regression and found the model is something like

Wins = 62 + .14 x Salary (in $millions). If a team had a zero payroll, they would be expected to win 62 games. (I've always been curious-- is this close to what a zero WAR / fWAR team would be expected to win?) More importantly, the .14 number suggests that increasing one's payroll by a million would result in only 1/7th of a win. So, increasing payroll by $35 million would result in about 5 more wins.

And in anticipation of many potential critiques, yes, what I did was quick and dirty. I was just trying to get an idea. It would be interesting to do this over many years. If anyone wants to volunteer to get me the data....

But since I had a model that predicted wins based on salary, I thought I would calculate team-by-team deviations from these forecasts, and they are here: Note that a positive number means a team won more games that would be predicted (again, based ONLY on payroll), while a negative number indicates a team that won fewer.

Oakland Athletics 24.1
Milwaukee Brewers 19.2
Tampa Bay Rays 18.7
Houston Astros 18.6
Boston Red Sox 14.7
New York Yankees 13.3
Atlanta Braves 10.2
Cleveland Indians 9.5
Colorado Rockies 9.3
Pittsburgh Pirates 7.7
Chicago Cubs 6.3
Seattle Mariners 4.9
Philadelphia Phillies 3.8
St. Louis Cardinals 3.5
Los Angeles Dodgers 2.6
Arizona Diamondbacks 0.6
Minnesota Twins 0.3
Washington Nationals -4.9
New York Mets -5.6
Los Angeles Angels -5.9
Cincinnati Reds -8.6
Chicago White Sox -9.7
Toronto Blue Jays -9.7
San Diego Padres -9.8
Miami Marlins -11.5
Texas Rangers -14.2
Detroit Tigers -15.9
San Francisco Giants -17.3
Kansas City Royals -21.8
Baltimore Orioles -32.4

Everything above in this post is based on data and statistics. Now I'll allow myself to opine. I don't think the top 3 are that much of a surprise-- many have identified them as "punching above their weight." I do find it a bit surprising that two of the richest teams--Yankees and BoSox still won many more than even their large payrolls.

At the other end, its really hard to understand how teams could lose 20 or even 30 more games than predicted.

The Twins won almost exactly the number of games as predicted.

I just thought this would be fun
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#2 Sconnie

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Posted 09 November 2018 - 08:20 AM

Great exercise! It would be interesting to see trends over time. If certain teams over or under perform more than others over periods. You could do so much over 3 or 5 year periods!

#3 dbminn

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Posted 09 November 2018 - 08:45 AM

 

I ran a regression and found the model is something like

Wins = 62 + .14 x Salary (in $millions). If a team had a zero payroll, they would be expected to win 62 games. (I've always been curious-- is this close to what a zero WAR / fWAR team would be expected to win?) More importantly, the .14 number suggests that increasing one's payroll by a million would result in only 1/7th of a win. So, increasing payroll by $35 million would result in about 5 more wins.

… 

At the other end, its really hard to understand how teams could lose 20 or even 30 more games than predicted.

The Twins won almost exactly the number of games as predicted.

I just thought this would be fun

 

Replacement level has been standardized, at least between Fangraphs and Baseball Reference. They have calculated the production of freely available AAAA players and found the number of wins they would produce. They do it by a simple calculation: actual runs per win. It comes out to roughly 48 wins per year, produced at a cost of league minimum per player.By setting "replacement level" as the baseline, it dampens the results of the calculation. 

 

RE: The Orioles - it isn't that your model overpredicted wins, it's that their FO overvalued their players :) and they are now all fired.

 

Smart work! I'm an engineer, so I'm on board with starting as clean and simple as possible.

 

 

 

Edited by dbminn, 09 November 2018 - 08:46 AM.

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#4 caninatl04

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Posted 09 November 2018 - 09:54 AM

Great exercise! It would be interesting to see trends over time. If certain teams over or under perform more than others over periods. You could do so much over 3 or 5 year periods!


If you get me the data, I'd be happy to do so. Instead of salary, I'd use (salary- median / mean salary) to adjust for inflation.

#5 caninatl04

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Posted 09 November 2018 - 10:24 AM

 

Great exercise! It would be interesting to see trends over time. If certain teams over or under perform more than others over periods. You could do so much over 3 or 5 year periods!

I have zero data / proof as to the other 5/6th of explanation.A complete guess is that salary would explain a lot more in prior years before teams figured out the way to win involved drafted players in their late 20's, still under some form of team control rather than 30+ FA's.

 

If anyone sends me data, I'm happy to run the numbers


#6 caninatl04

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Posted 12 November 2018 - 11:36 AM

 

Great exercise! It would be interesting to see trends over time. If certain teams over or under perform more than others over periods. You could do so much over 3 or 5 year periods!

If anyone could send me the data, I'd be happy to do it.


#7 Doomtints

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Posted 13 November 2018 - 10:21 AM

So for everyone who was upset that the Twins didn't win 95 games this year, here's the proof that the team performed exactly as expected.


#8 Loosey

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Posted 13 November 2018 - 12:14 PM

Very interesting.I'm not a statistician by any means and haven't ran a regression model for quite a while.

 

However, I wonder if payroll actually buys more wins than you model is initially telling you.Take for example time on the DL, pitchers, etc.

 

If you have your highest salaried player miss significant time they are not contributing to the wins and losses during their time off, in addition, the team has to add payroll (albeit very modest) when they bring up a minor leaguer or sign someone off the street.

 

I'd don't know how you would account for the DL piece but it may help answer why payroll is only correlating to 1/6.  

 

Also, a very high priced pitcher only plays 1 out of 5 games, but their salary is would be used in this formula for all 162. 

 

By somehow adjusting for starting pitcher salary and DL time I wonder how much better your correlation would be? 

 

Now, don't ask me how to do it because that sounds like a lot of hard work.




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