Regress toward the mean

[cubbieinexile]

.

 

If the Cubs can eek out at around .500 until Wood and Prior and D Lee/(Any help) then they have a nice chance of getting that bounce in wins.

 

The bounce would be small. This wasn't a team expected to win 100 games. If 50 games are played before these players comeback and they go .500 in tham then if you think the Cubs are a 90 win team originally that means the Cubs would be expected to win about 87 games if you still think they have the talent for a 90 win team.

 

There is no real thing as a bounce back, regression doesn't work like that. If you are a .600 level team and you play at a .700 level for a stretch that doesn't mean you will play at a .500 level for another stretch to even it out. It means one can expect them to play at a .600 level in the future.

 

On top of that you have to throw in other teams and their impact on your team. The Reds might be a true .525 team but because of who they play and their talent level they are a .585 team. If thats the case then one shouldn't expect the Reds to regress back to .525 but instead maintain a .585 winning %. Unless of course something changes in the dynamic to alter that view.

[Cubzfan64]

Scott, I appreciate that you're trying to give a sense of hope for the Cubs for the year 2006, but your idea of regressing to a mean just doesn't work here - there's just way too many variables to do a kind of statistical analysis on something like baseball the way one would control chart the diameter of a widget manufactured at ACME widgets.

 

Let me take a stab at what I think you're implying...

 

The winning percentages of each team in baseball can be plotted daily, and although I haven't done it, you should be correct that it would look like a gaussian (or bell shaped) curve with the mean being 0.500 (afterall, for each win, someone has to lose).

 

I think what you're saying is that it's still early in the season, and that gaussian curve may be quite wide because of such a small set of win/loss data. As the season progresses, the curve should start narrowing with the tails of the distribution coming closer and closer to the mean value. That's about all you can say statistically about baseball and win/loss percentages.

 

The problem with your theory is that no matter what the width of that bell shaped curve is, there has to ALWAYS be teams at the edges, and those teams of course end up being the worst teams in the league on one end, and the best on the other.

 

To have the best statistical chance of winning it all year in and year out, your team needs to always end up on the high tail of the curve - it doesn't mean you'll always win a WS of course, but it gives you the best chance.

 

It would take all day to list all the factors and variables that go into the "process" of baseball, and once you're done listing them you would easily see why the idea of "regressing to a mean" isn't really something to tie too much hope on.

 

I've always thought it was ironic that a sport that is SO full of statistics, where everything is documented, measured, compared, etc... that the game of baseball is impossible to statistically predict to any decent degree of accuracy.

[Scott G. F.]

Scott, I appreciate that you're trying to give a sense of hope for the Cubs for the year 2006, but your idea of regressing to a mean just doesn't work here - there's just way too many variables to do a kind of statistical analysis on something like baseball the way one would control chart the diameter of a widget manufactured at ACME widgets.

 

I disagree

 

The winning percentages of each team in baseball can be plotted daily, and although I haven't done it, you should be correct that it would look like a gaussian (or bell shaped) curve with the mean being 0.500 (afterall, for each win, someone has to lose).

 

That logic would create a line, one win one loss vs each game played?

Plot the Cubs division by winning percent. I top will regress not based on a hope and a prayer.

 

I think what you're saying is that it's still early in the season, and that gaussian curve may be quite wide because of such a small set of win/loss data. As the season progresses, the curve should start narrowing with the tails of the distribution coming closer and closer to the mean value. That's about all you can say statistically about baseball and win/loss percentages. ).

 

If that's all that can be said statistically about baseballs win/loss % then why claim a team underachieved/overachieved?

 

 

The problem with your theory is that no matter what the width of that bell shaped curve is, there has to ALWAYS be teams at the edges, and those teams of course end up being the worst teams in the league on one end, and the best on the other.

 

I don't see that as the problem at all. I see it as the hope for the Cubs. The bell shape is shaped top to bottom (or side to side) with a majority in the middle. The Cubs must stay in the middle at least until August when they need to push out toward the upper edge. A big trade at the dead line does increase this chance and a bounce in winns is created (looks at Cubbiesinexile). The Cubs have 3 big bounces due this year in the forms of Wood Prior and D. Lee. Now add in a suprise trade or flashes of a career year (looks at Am Ram) and the Cubs will have a nice shot at the end of this season.

 

It would take all day to list all the factors and variables that go into the "process" of baseball, and once you're done listing them you would easily see why the idea of "regressing to a mean" isn't really something to tie too much hope on.

 

All those variables do add up like adding percentages. It means that each team will regress toward the mean sometime during the year. The Cubs have time to fix the problems they have.

 

I've always thought it was ironic that a sport that is SO full of statistics, where everything is documented, measured, compared, etc... that the game of baseball is impossible to statistically predict to any decent degree of accuracy.

 

I disagree, I bet between you and I we can pick the playoff teams for 2006 right now based on the upper Gauissan bell curves of the past 3-4 years.

 

Throwing all voodoo "their due" crap out the window. The Cubs will have better people getting back on the team for the Cubs to push toward the top of the bell curve by the end of the season. The other clubs ahead of the Cubs as of today will regress. Unless the bottom falls completly out of the Cubs season all they have to do is hang around until they can realize the bounce. If the timing is right the CUbs will surge when the regression happens making the season for us Cub fans very exciting.

[CubinNY]

Scott, all I'm going to say is that you are trying to fit a square peg (regression analysis) into a round hole (team winning %). The metric is entirely off base, even if the theme is not.

[Scott G. F.]

Scott, all I'm going to say is that you are trying to fit a square peg (regression analysis) into a round hole (team winning %). The metric is entirely off base, even if the theme is not.

 

We all have our opinions and I respect yours.

 

I just plotted all of 2005 results and comparied them to 2006 thus far and feel even more confident now.

 

The Cubs as of right now today are "dead nuts" in the middle of the pack. 8th out of 16 teams in the NL. Last year they finished 7th out of 16.

[Cubzfan64]

Scott: I can see where you're coming from with your comments but I guess we'll just have to disagree on how much stock can be put into the statistics. You just put significantly more into it than I do.

 

I've always thought it was ironic that a sport that is SO full of statistics, where everything is documented, measured, compared, etc... that the game of baseball is impossible to statistically predict to any decent degree of accuracy.

 

I disagree, I bet between you and I we can pick the playoff teams for 2006 right now based on the upper Gauissan bell curves of the past 3-4 years.

 

If you sit back and look at what you just said here, it really contradicts your whole premise that the Cubs have a chance in 2006 doesn't it? I mean if based on previous years performances we can accurately predict the division winners, then why play the games?

 

I honestly think you're using logic to try to make sense of something and make accurate predictions in regards to something (baseball) that in many ways defies logic.

 

There's only so much you can do with statistics and I think you're trying to do too much. Hard to argue too much with a Cub fan who's optimistic though - I tip my hat to you there :-)

[CubinNY]

Scott, all I'm going to say is that you are trying to fit a square peg (regression analysis) into a round hole (team winning %). The metric is entirely off base, even if the theme is not.

 

We all have our opinions and I respect yours.

 

I just plotted all of 2005 results and comparied them to 2006 thus far and feel even more confident now.

 

The Cubs as of right now today are "dead nuts" in the middle of the pack. 8th out of 16 teams in the NL. Last year they finished 7th out of 16.

 

It's not an opinion.

 

here is an informative website.

 

http://www.socialresearchmethods.net/kb/regrmean.htm

[Scott G. F.]

Scott, all I'm going to say is that you are trying to fit a square peg (regression analysis) into a round hole (team winning %). The metric is entirely off base, even if the theme is not.

 

We all have our opinions and I respect yours.

 

I just plotted all of 2005 results and comparied them to 2006 thus far and feel even more confident now.

 

The Cubs as of right now today are "dead nuts" in the middle of the pack. 8th out of 16 teams in the NL. Last year they finished 7th out of 16.

 

It's not an opinion.

 

here is an informative website.

 

http://www.socialresearchmethods.net/kb/regrmean.htm

 

 

Thanks for the link.

 

Plotting teams trends that made the playoffs for 2005 an overwhelming majority of the teams maintained a presence in the popultion or bulk of the bell curve. Just as I have suggested the Cubs try and do. An overwelming majority of the teams that were at the top of the bell curve dropped back into the population aka regressed.

 

There in lies the hope that math brings. Cross reference these trend with addition of a trade and the results are even more pronouned. That bounce (as I've been calling it ) has the same effect with either a trade or a return of a healthy player.

 

The Cubs will have 3 this year without doing anything.

 

If the Cubs can maintain a presense on the bulk of the bell curve thoughtout the season until they can receive the bounces they need. they should be on good shape for the strech run.

[Yestheydo]

It was a nice post and I agree for the most part, but the statistical analysis analogy isn't even in the ball park.

 

The mean isn't .500. There is no mean in this case.

 

True, but players will regress towards their established levels of performance.

 

Brandon Phillips and Bronson Arroyo wont help keep the Reds on top all year long to the degree that they're doing now.

 

Yeah, just like Eric Milton and Danny Graves couldn't possibly stay as bad as they were at the beginning of last year. I hate to say this, but I live near Cincinnati and the new owner is doing and saying everything I wish Cubs ownership would do -- instilling an attitude of excellence that permeates the entire organization. It's depressing. Plus their hitting coach drew more than 30 freaking walks in his best year as a player. Don't count the Reds out; not this time. Mark my words.

[Scott G. F.]

It was a nice post and I agree for the most part, but the statistical analysis analogy isn't even in the ball park.

 

The mean isn't .500. There is no mean in this case.

 

True, but players will regress towards their established levels of performance.

 

Brandon Phillips and Bronson Arroyo wont help keep the Reds on top all year long to the degree that they're doing now.

 

Yeah, just like Eric Milton and Danny Graves couldn't possibly stay as bad as they were at the beginning of last year. I hate to say this, but I live near Cincinnati and the new owner is doing and saying everything I wish Cubs ownership would do -- instilling an attitude of excellence that permeates the entire organization. It's depressing. Plus their hitting coach drew more than 30 freaking walks in his best year as a player. Don't count the Reds out; not this time. Mark my words.

 

Consider you words "marked". I just don't see the Reds having depth to maintain. The ownership can "rah rah" all it wants. It'll be interesting to see.

[TruffleShuffle]

Regressing to the mean is what Greg Maddux's last start was.

 

Truest statement in this thread

[Rob]

True, but players will regress towards their established levels of performance.

 

Brandon Phillips and Bronson Arroyo wont help keep the Reds on top all year long to the degree that they're doing now.

 

to play devil's advocate...didn't we all say that about chris carpenter in '04 and '05?

 

Carp didn't exactly have an established level of performance... at least not while healthy. 05 is the first year I can think of where he spent the entire year healthy and pain-free.

 

I can understand making allowances for injury in regression, but there are plenty of cases where the higher level of performance has nothing to do with lack of an injury, and it's natural to be more skeptical about those performances.

[JC]

When in Toronto, Carptenter was a HIGHLY touted talent by baseball people and the media alike. Injuries derailed Carpenter's Blue Jay career when they felt like they were nearing a point when their young pitching was about to take off.

 

While I've never delved into his minor league stats, I recall Phillips being a well thought of prospect in the Expos system. In addition, I've always thought Arroyo had better stuff than his consistency showed off. If those two have "found their stride" rather than played above their heads, I wouldn't be shocked.

[Rob]

When in Toronto, Carptenter was a HIGHLY touted talent by baseball people and the media alike. Injuries derailed Carpenter's Blue Jay career when they felt like they were nearing a point when their young pitching was about to take off.

 

While I've never delved into his minor league stats, I recall Phillips being a well thought of prospect in the Expos system. In addition, I've always thought Arroyo had better stuff than his consistency showed off. If those two have "found their stride" rather than played above their heads, I wouldn't be shocked.

 

I don't know if this is specifically directed at me, but I'm egocentric so I'm going to respond as if it is.

 

Yeah, I know Carp was a higly touted pitcher. That's why I was referencing the fact he didn't really have an injury-free level of performance established. His one year prior to '05 where he pitched over 200 innings, he amassed a WARP1 of 5.6. That's exactly why I said I'd make allowances for people with injury problems being healthy for once.

 

I suppose in Carp's case, regression to the mean would be mostly PT based.

 

Arroyo was never really a great prospect. Looking at my old copies of BP, he's referred to as "a poor man's Jimmy Anderson: great record, good ERA, lousy peripherals and mediocre stuff" and "basically a right-hander with a marginal left-hander’s repertoire" The best thing about his pitches is that he manages to throw most of them for strikes, but he's got nothing really special. I don't think he's just "found his stride." His absolute ceiling is an innings-eater type of #3 starter, not the top of the league ace that he's impersonating now.

 

Looking at Phillips' record, perhaps I jumped the gun on him a bit. He could post a .800 OPS if a few balls fall in for him... but I don't think he'll keep up the .996 OPS with runners in scoring position.