Wednesday, March 12, 2014
Wednesday, March 5, 2014
Year-to-year Correlation In Team Winning Percentage, 1901-60
For the whole period, it is .663. There were 16 observations for 1901-02, 16 for 1902-3, and so on. A total of 944 observations.
I also broke it down by decades
1901-10) .668
1911-20) .521
1921-30) .725
1931-40) .711
1941-50) .642
1951-60) .727
Not sure what happened in the teens. One year Connie Mack sold his best players after losing the World Series (1914). So they did very poorly in 1915. It does not seem likely that one team in one year would make that much difference. The 1940s might be a bit low due to the war. With players coming and going, teams could be much different in consecutive years.
Here are the five highest years
1936-1937) 0.877
1922-1923) 0.879
1930-1931) 0.885
1910-1911) 0.890
1941-1942) 0.896
Here are the five lowest years
1914-1915) 0.127
1917-1918) 0.221
1913-1914) 0.224
1901-1902) 0.298
1944-1945) 0.370
This graph shows the yearly correlations.
I also broke it down by decades
1901-10) .668
1911-20) .521
1921-30) .725
1931-40) .711
1941-50) .642
1951-60) .727
Not sure what happened in the teens. One year Connie Mack sold his best players after losing the World Series (1914). So they did very poorly in 1915. It does not seem likely that one team in one year would make that much difference. The 1940s might be a bit low due to the war. With players coming and going, teams could be much different in consecutive years.
Here are the five highest years
1936-1937) 0.877
1922-1923) 0.879
1930-1931) 0.885
1910-1911) 0.890
1941-1942) 0.896
Here are the five lowest years
1914-1915) 0.127
1917-1918) 0.221
1913-1914) 0.224
1901-1902) 0.298
1944-1945) 0.370
This graph shows the yearly correlations.
Thursday, February 20, 2014
"Variation in payroll in baseball explains less than 20 percent of the variation in winning percentage"
That quote is from Dave Berri, professor of economics at Southern Utah University. He researches the economics of sports. See Why Masahiro Tanaka’s Yankees Contract Is Good for Baseball at Freakonomics, 2-4-2014.
Berri goes on to say:
I did a post in 2008 called Another look at salaries and wins. I got payroll explaining close to 50% by using average wins per year over a long periods and each team's average percentage above or below the league average in salary. By using the averages, I think the randomness from year-to-year is eliminated. Here is that post:
Alot of people have looked at this. But I started thinking about it again after I came across some data at JC Bradbury's site. You can view that data here. The data shows how many games, on average, that teams won each year from 1986-2005. It also shows how much above or below the league average in total salary each team paid in percentage terms. Again, it shows yearly averages. Suppose a team was 10% above average one year and 30% above average another year, they would get 20 (if were just over two years).
What I did was to run a regression with average wins per year as the dependent variable and the average salary (SAL, the % above or below the league average) as the independent variable.
Here is the regression equation
Wins = 0.157*SAL + 80.22
The r-squared was .489 and the standard error was 3.89 wins. The T-value for SAL was 5.17. The .157 means that if you spent 10% more on salaries than the average team, you win 1.57 more games than the average team. A zero for SAL would mean that a team spent the average amount on salaries. A negative number means the team spent below the average salary level. The table below summarizes each team.
Tampa Bay, for example, on average, had a payroll that was 38.87% below the league average. They were predicted to win 74.12 but only 64.33 wins per game. If a team were to spend 100% more than average, it should win about 96-97 games a year. The Yankees had the highest payroll above average. They spent about 70% more than the average team. They were predicted to win 91.26 games a year but actually only won 90.24.
I think the results are fairly strong. 16 of the 30 teams were predicted to within 3 or fewer wins. Only 3 were off by 6 or more wins. I think what I did differently than JC Bradbury was to use the average annual values for each team, instead of each team's data for each year. By using the averages, I think the randomness from year-to-year is eliminated. A team can sign a big free agent and maybe one year he does not do well. Or you get lucky and some non-arbitration eligible young players do very well. So by averaging, some of the good and bad luck gets flushed out.
The graph below also summarizes the results. You can see that the relationship is strong.
Berri goes on to say:
"One reason why spending doesn’t match outcomes is that forecasting the future in baseball is difficult. We can look at the stats and know who was “good” or “bad” in the past, but the future – especially for pitchers – is hard to predict. Consequently, it is hard for the richest teams to simply spend money and win."He doesn't give any more details, like what years he looked at, if he combined many years together in a regression analysis, etc.
I did a post in 2008 called Another look at salaries and wins. I got payroll explaining close to 50% by using average wins per year over a long periods and each team's average percentage above or below the league average in salary. By using the averages, I think the randomness from year-to-year is eliminated. Here is that post:
Alot of people have looked at this. But I started thinking about it again after I came across some data at JC Bradbury's site. You can view that data here. The data shows how many games, on average, that teams won each year from 1986-2005. It also shows how much above or below the league average in total salary each team paid in percentage terms. Again, it shows yearly averages. Suppose a team was 10% above average one year and 30% above average another year, they would get 20 (if were just over two years).
What I did was to run a regression with average wins per year as the dependent variable and the average salary (SAL, the % above or below the league average) as the independent variable.
Here is the regression equation
Wins = 0.157*SAL + 80.22
The r-squared was .489 and the standard error was 3.89 wins. The T-value for SAL was 5.17. The .157 means that if you spent 10% more on salaries than the average team, you win 1.57 more games than the average team. A zero for SAL would mean that a team spent the average amount on salaries. A negative number means the team spent below the average salary level. The table below summarizes each team.
Tampa Bay, for example, on average, had a payroll that was 38.87% below the league average. They were predicted to win 74.12 but only 64.33 wins per game. If a team were to spend 100% more than average, it should win about 96-97 games a year. The Yankees had the highest payroll above average. They spent about 70% more than the average team. They were predicted to win 91.26 games a year but actually only won 90.24.
I think the results are fairly strong. 16 of the 30 teams were predicted to within 3 or fewer wins. Only 3 were off by 6 or more wins. I think what I did differently than JC Bradbury was to use the average annual values for each team, instead of each team's data for each year. By using the averages, I think the randomness from year-to-year is eliminated. A team can sign a big free agent and maybe one year he does not do well. Or you get lucky and some non-arbitration eligible young players do very well. So by averaging, some of the good and bad luck gets flushed out.
The graph below also summarizes the results. You can see that the relationship is strong.
Wednesday, January 15, 2014
Using A Player's WAR To Predict First Year Hall Of Fame Vote Percentage (and possibly estimate "underratedness")
I took all the Hall of Fame votes from 1966-2014 from Baseball Reference. On those pages, BR shows the vote% each player got but also their career WAR (it also shows the combined WAR of their seven best seasons as well as the Jay Jaffe stats "Jaws" which combines career and 7 best).
Five players were tossed out of the analysis: Barry Bonds, Rafael Palmeiro, Mark McGwire, Sammy Sosa and Pete Rose. The voters have severely penalized the first four for possible PED use, not because they underrated them. Something similar with Rose. There was a cloud of scandal over him when he first came up because of betting on baseball.
One thing I wanted to do was find a trend line for the vote. I could not find one that made sense using career WAR or Jaws. Any trend line had too many ups and downs. Vote% should not go down as WAR goes up. But once you look at the trend line I used for WAR7, you will see how non-linear the data is.
So when I had Excel put in trend lines, the only one that made reasonable sense was a sixth degree polynomial with WAR7 as the independent variable and vote% as the dependent variable. It does have some ups and downs where I really don't want them, but they are not too severe.
Click here to see the graph.
So I hope you can see that trying to fit a trend line to the data has problems. This seems like the best I could do.
Using the regression equation, I then calculated each player's predict 1st year vote% (the equation you seen in the graph probably does not show enough decimal places for the coefficient values-x in the graph is WAR7). Then that was subtracted from their actual 1st year vote% and a difference was found. I then ranked them all from the biggest negative difference to the biggest positive difference.
The player with the biggest negative differential, whom we might say was the most underrated, was Ron Santo. He got only 3.9% of the vote in his 1st year but if he was right on the trend line, it would have been 75.4%.
The most overrated player was Lou Brock. He got 79.7% of the vote while the model predicts he would get 6.7%. It helps to reach a milestone like 3000 hits, retire as the all-time SB leader and perform very well in three 7-game world series. Click here to see my research that supports this. As for Santo, click here to see my post that explains he got about the vote% we would expect, given the general preferences of the voters.
Click here to see the complete rankings
Five players were tossed out of the analysis: Barry Bonds, Rafael Palmeiro, Mark McGwire, Sammy Sosa and Pete Rose. The voters have severely penalized the first four for possible PED use, not because they underrated them. Something similar with Rose. There was a cloud of scandal over him when he first came up because of betting on baseball.
One thing I wanted to do was find a trend line for the vote. I could not find one that made sense using career WAR or Jaws. Any trend line had too many ups and downs. Vote% should not go down as WAR goes up. But once you look at the trend line I used for WAR7, you will see how non-linear the data is.
So when I had Excel put in trend lines, the only one that made reasonable sense was a sixth degree polynomial with WAR7 as the independent variable and vote% as the dependent variable. It does have some ups and downs where I really don't want them, but they are not too severe.
Click here to see the graph.
So I hope you can see that trying to fit a trend line to the data has problems. This seems like the best I could do.
Using the regression equation, I then calculated each player's predict 1st year vote% (the equation you seen in the graph probably does not show enough decimal places for the coefficient values-x in the graph is WAR7). Then that was subtracted from their actual 1st year vote% and a difference was found. I then ranked them all from the biggest negative difference to the biggest positive difference.
The player with the biggest negative differential, whom we might say was the most underrated, was Ron Santo. He got only 3.9% of the vote in his 1st year but if he was right on the trend line, it would have been 75.4%.
The most overrated player was Lou Brock. He got 79.7% of the vote while the model predicts he would get 6.7%. It helps to reach a milestone like 3000 hits, retire as the all-time SB leader and perform very well in three 7-game world series. Click here to see my research that supports this. As for Santo, click here to see my post that explains he got about the vote% we would expect, given the general preferences of the voters.
Click here to see the complete rankings
Sunday, January 12, 2014
Eddie Robinson's Great Homerun-To-Strikeout Ratio
Update Jan. 13: He is actually not in the top 25, but he is pretty close. One thing I forgot to take into account when using the Lee Sinins Complete Baseball Encyclopedia is what the league average is based on. I just looked at his page and what he and the league average had. But it needed to be consistent with my earlier research. Click here to see the new, complete list.
I used all guys from 1920-2012 who had 4500+ PAs (the first study excluded Robinson because he had 4891). I set the Sinins database to compare players to non-pitchers and used each guy's rate of HRs & SOs on a per plate appearance basis (you could choose to go with all players including pitchers and use ABs instead of PAs, for example). Robinson is 40th out of 884 players, so that puts him in the top 5%. When you look the list, you will see him ahead of some great hitters.
**********************************************************
Eddie Robinson played for several teams in the 1940s and 50s, including the Indians, White Sox and Yankees. He was the regular first baseman on the 1948 world champion Indians. Click here to go to his Baseball Reference page. He batted .348 in 23 World Series at-bats.
Here is a link to his SABR biography written by C. Paul Rogers III. One thing it says is
"He was the seventh player and first White Sox to hit a ball over the roof at old Comiskey Park (in 1951); the first six were Hall of Famers Babe Ruth, Lou Gehrig, Jimmy Foxx, Hank Greenberg, Ted Williams and Mickey Mantle."
He is also author (along with C. Paul Rogers III) of the 2011 book titled Lucky Me: My Sixty-five Years in Baseball.
Robinson struck out less than the league average (356 vs. 489). But his HR rate relative to his strikeout rate was outstanding. He it 172 HRs while the league average player would 85. So his relative HR rate was 202.35. His relative strikeout rate was 73.868 (356/489 times 100). Then 202.35/73.868 = 2.739. That would put him in the top 25 all-time. But when I did this analysis I only included guys with 5000+ PAs. He just missed with 4891. See my post Which Players Had The Best HR-To-Strikeout Ratios?
I used all guys from 1920-2012 who had 4500+ PAs (the first study excluded Robinson because he had 4891). I set the Sinins database to compare players to non-pitchers and used each guy's rate of HRs & SOs on a per plate appearance basis (you could choose to go with all players including pitchers and use ABs instead of PAs, for example). Robinson is 40th out of 884 players, so that puts him in the top 5%. When you look the list, you will see him ahead of some great hitters.
**********************************************************
Eddie Robinson played for several teams in the 1940s and 50s, including the Indians, White Sox and Yankees. He was the regular first baseman on the 1948 world champion Indians. Click here to go to his Baseball Reference page. He batted .348 in 23 World Series at-bats.
Here is a link to his SABR biography written by C. Paul Rogers III. One thing it says is
"He was the seventh player and first White Sox to hit a ball over the roof at old Comiskey Park (in 1951); the first six were Hall of Famers Babe Ruth, Lou Gehrig, Jimmy Foxx, Hank Greenberg, Ted Williams and Mickey Mantle."
He is also author (along with C. Paul Rogers III) of the 2011 book titled Lucky Me: My Sixty-five Years in Baseball.
Robinson struck out less than the league average (356 vs. 489). But his HR rate relative to his strikeout rate was outstanding. He it 172 HRs while the league average player would 85. So his relative HR rate was 202.35. His relative strikeout rate was 73.868 (356/489 times 100). Then 202.35/73.868 = 2.739. That would put him in the top 25 all-time. But when I did this analysis I only included guys with 5000+ PAs. He just missed with 4891. See my post Which Players Had The Best HR-To-Strikeout Ratios?
Wednesday, January 8, 2014
What Made Maddux So Unique?
It was a highly unusual combination of being able to prevent HRs without walking many batters and without striking many out. I created an index to measure this and he is far ahead of anyone else. See Who Was More "Magical" Than Greg Maddux? (Or Pitcher's HR/BB/SO Rating) from December 2, 2009.
Tuesday, January 7, 2014
Has Albert Pujols Been Getting More MVP Votes Than Expected Based On WAR?
This is based on a couple posts you can probably see below. So read them for explanations and technical details. Those posts have been discussed over at Baseball Think Factory.
I did the analysis for each year of Albert Pujols' career. In each year I tried to find a polynomial trend line that best fit the voting that year. Who was included in the analysis each year? Anyone who had at least as many ABs as the lowest AB total for anyone who got votes. Sometimes players don't get any votes but have a pretty good WAR and I don't think they should be left out of the analysis. So there had to be some way to decide who got included. So it is a different number of players each year.
I usually went with the highest r-squared among 2nd, 3rd degree, etc. polynomials. But they had to make sense. Sometimes the line goes up and down alot and I preferred lines like the ones in the graphs I used already. Logs and exponential functions would not work be cause of zero values for WAR and MVP shares. Sometimes even negative WAR values came up.
So I got a predicted value for each year of his career (including 2013 when he got no votes and had only 391 ABs, so I included everyone in the AL who had 391+ ABs).
In 11 of his 13 seasons his share was higher than predicted. Adding up all of the differences between his predicted share and actual share I got 1.73. So, although his rank in the MVP vote is about right based on his rank in WAR, his vote total is still higher than expected based on the overall pattern of the vote by the writers.
Now this 1.73 is lower than the 3.78 I currently have for him. But to know where that ranks I will have to go through every season since 1931 for each league one by one and get a total for all players. That will take some time.
I did the analysis for each year of Albert Pujols' career. In each year I tried to find a polynomial trend line that best fit the voting that year. Who was included in the analysis each year? Anyone who had at least as many ABs as the lowest AB total for anyone who got votes. Sometimes players don't get any votes but have a pretty good WAR and I don't think they should be left out of the analysis. So there had to be some way to decide who got included. So it is a different number of players each year.
I usually went with the highest r-squared among 2nd, 3rd degree, etc. polynomials. But they had to make sense. Sometimes the line goes up and down alot and I preferred lines like the ones in the graphs I used already. Logs and exponential functions would not work be cause of zero values for WAR and MVP shares. Sometimes even negative WAR values came up.
So I got a predicted value for each year of his career (including 2013 when he got no votes and had only 391 ABs, so I included everyone in the AL who had 391+ ABs).
In 11 of his 13 seasons his share was higher than predicted. Adding up all of the differences between his predicted share and actual share I got 1.73. So, although his rank in the MVP vote is about right based on his rank in WAR, his vote total is still higher than expected based on the overall pattern of the vote by the writers.
Now this 1.73 is lower than the 3.78 I currently have for him. But to know where that ranks I will have to go through every season since 1931 for each league one by one and get a total for all players. That will take some time.
Monday, January 6, 2014
Was Willie Mays The Most Underrated Player In History? Or Was It Wade Boggs? Is Albert Pujols The Most Overrated? (Revised)
Click here to see the original post from a few days ago. The idea was to see the relationship between MVP shares and WAR.
If you read that, you will see that the regression line estimate was a 2nd degree polynomial. But to calculate the predicted MVP shares, I used the equation that appears when I ask Excel to graph it. That equation only goes to a few decimal places. In this case, it matters because the values of the WAR variable can be very large.
So I had Excel do the line estimate and I had the coefficient values go out several more decimal places. The new equation is
MVPShares = 0.000256845*WARSquared + 0.010979681*WAR - 0.11979
Squaring Willie Mays' WAR gives us about 24,000. Now .003*24,304.81 = 7.291. But if I have
0.000256845*24,304.81 = 6.24
That alone lowers May's predicted MVP shares about 1 (again, using the regression estimate). Mays actually slips from the most underrated player to the second most underrated player. Lou Whitaker, who did very poorly in the Hall of Fame vote (unjustly so), is now number 1.
Click here to see the revised list. It does not look like players moved very much. Pujols was still the most overrated by this measure.
The new equation for the case where I used only each player's seven best seasons of WAR is
MVPShares = 0.001807713*WAR7Squared - 0.041037828*WAR7 + 0.268264829
The original post had a + in front of the 2nd coefficient. It should have been minus and has been corrected. Wade Boggs was still the most underrated here and Pujols was still the most overrated.
Click here to see the revised results.
If you read that, you will see that the regression line estimate was a 2nd degree polynomial. But to calculate the predicted MVP shares, I used the equation that appears when I ask Excel to graph it. That equation only goes to a few decimal places. In this case, it matters because the values of the WAR variable can be very large.
So I had Excel do the line estimate and I had the coefficient values go out several more decimal places. The new equation is
MVPShares = 0.000256845*WARSquared + 0.010979681*WAR - 0.11979
Squaring Willie Mays' WAR gives us about 24,000. Now .003*24,304.81 = 7.291. But if I have
0.000256845*24,304.81 = 6.24
That alone lowers May's predicted MVP shares about 1 (again, using the regression estimate). Mays actually slips from the most underrated player to the second most underrated player. Lou Whitaker, who did very poorly in the Hall of Fame vote (unjustly so), is now number 1.
Click here to see the revised list. It does not look like players moved very much. Pujols was still the most overrated by this measure.
The new equation for the case where I used only each player's seven best seasons of WAR is
MVPShares = 0.001807713*WAR7Squared - 0.041037828*WAR7 + 0.268264829
The original post had a + in front of the 2nd coefficient. It should have been minus and has been corrected. Wade Boggs was still the most underrated here and Pujols was still the most overrated.
Click here to see the revised results.
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