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Stupid Math Tricks: ERA

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#1 caninatl04

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Posted 19 March 2018 - 01:08 PM

I did some math.
Assuming
i) the Pythagorean theory of winning percentage, and
ii) the Twins score the same number of runs in '18 as they did in '17 (788),

then a .05 (not .5) decline in ERA results in additional win.

Last year, the Twins' ERA was 4.59. So, if you want to forecast this years team ERA with all the additions, then one can forecast win totals.

Examples- if all the additions result in a decline from 4.59 to 4.54, the model predicts one more win.

If predicted ERA drops to 4.39, four more wins.

ERA of 4.19, eight more wins or roughly 92 wins.

By the way, the above are approximations. If your a math nerd, I'd be happy to provide math details.
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#2 spycake

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Posted 19 March 2018 - 01:17 PM

Note that the Twins over-performed Pythag by 2 wins next year, so you wouldn't necessarily add these wins to 85, you should add them to 83.

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#3 spycake

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Posted 19 March 2018 - 01:43 PM

You also have one more unstated assumption here -- that our number of unearned runs stays the same too.

 

I notice Toronto is projected very close to the numbers you reference -- 5.01 runs per game, and a 4.24 ERA -- but they are only projected for 86 wins. The unearned run difference works out to 3-4 wins from your Twins model.

 

https://www.fangraph...ition=Standings

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#4 jkcarew

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Posted 19 March 2018 - 01:44 PM

You also are implicitly assuming that defense is constant year over year (i.e., the same number of un-earned runs as last year.)

 

Cool.Thanks for sharing.

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#5 spycake

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Posted 19 March 2018 - 01:46 PM

 

You also are implicitly assuming that defense is constant year over year (i.e., the same number of un-earned runs as last year.)

Great minds think alike! :)

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#6 jkcarew

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Posted 19 March 2018 - 02:01 PM

 

Great minds think alike! :)

Yeah...but I notice that some think faster.Oh, Well!

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#7 Brock Beauchamp

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Posted 20 March 2018 - 06:19 AM

Also, I doubt that increases/decreases in ERA are linear with wins. At some point, you're going to see diminishing returns.


#8 diehardtwinsfan

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Posted 20 March 2018 - 06:41 AM

To be fair, this is a pretty decent start. The other side is the runs scored side of it too, increasing them should also add wins. I think the offense should be better as well, namely b/c I don't think Buxton will be an abomination at the plate to start the year, and many of the kids should take steps forward (even if they all make incremental improvements, that's going to add wins). You may see a guy like Dozier taking a step back (hope not), but there's not a lot of regression candidates in the offense. The team is young, there's really not much in terms of regression candidates at all. Santana is probably the biggest. I'm hoping the extra month off actually does him a bit of good in this front. 


#9 Brock Beauchamp

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Posted 20 March 2018 - 06:57 AM

 

To be fair, this is a pretty decent start. The other side is the runs scored side of it too, increasing them should also add wins. I think the offense should be better as well, namely b/c I don't think Buxton will be an abomination at the plate to start the year, and many of the kids should take steps forward (even if they all make incremental improvements, that's going to add wins). You may see a guy like Dozier taking a step back (hope not), but there's not a lot of regression candidates in the offense. The team is young, there's really not much in terms of regression candidates at all. Santana is probably the biggest. I'm hoping the extra month off actually does him a bit of good in this front. 

I think the offense holds steady somewhere between the first and second half of last season. They'll be very good but not elite, I think. Losing Polanco hurts for sure.

 

There are some regression candidates but none appear particularly note-worthy IMO. Dozier might fade a bit but he has pretty firmly established a baseline. I think Mauer is for real and will continue being a productive player. Escobar might get exposed as a full-time player but hopefully, he won't be out there every day for long. Rosario *might* regress but I don't think he will, at least not much.

 

On the other hand, Buxton has room to grow. As does Sano. Kepler has tons of headroom.

 

In the end, I think it all balances out.

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#10 caninatl04

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Posted 21 March 2018 - 01:17 PM

Note that the Twins over-performed Pythag by 2 wins next year, so you wouldn't necessarily add these wins to 85, you should add them to 83.


Actually, that’s exactly what I did

#11 caninatl04

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Posted 21 March 2018 - 01:19 PM

Also, I doubt that increases/decreases in ERA are linear with wins. At some point, you're going to see diminishing returns.


IF you believe the pythag model, it actually works the other way since there are a bunch of “squared” terms.
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#12 spycake

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Posted 21 March 2018 - 01:38 PM

 

Actually, that’s exactly what I did

Yup. Sorry, that was more directed to readers who might try this experiment at home. :)


#13 Brock Beauchamp

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Posted 21 March 2018 - 02:37 PM

 

IF you believe the pythag model, it actually works the other way since there are a bunch of “squared” terms.

Right, I said that backwards.


#14 Loosey

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Posted 21 March 2018 - 03:26 PM

 

Also, I doubt that increases/decreases in ERA are linear with wins. At some point, you're going to see diminishing returns.

What if the ERA is 0.00? :)


#15 ashburyjohn

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Posted 21 March 2018 - 03:58 PM

Right, I said that backwards.

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#16 Darius

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Posted 21 March 2018 - 06:58 PM

Also, I doubt that increases/decreases in ERA are linear with wins. At some point, you're going to see diminishing returns.

This is exactly right, and I don't think Pythag could possibly compensate for that completely.

The number of wins each unit of ERA is worth would look like a bell curve (more likely a triangle with a sharp peak). If you're up at a 5.5 ERA, and you drop to a 5.0, or conversely are at a 2.5 ERA and drop to 2.0, you aren't going get a large number of wins added in return. You're likely going to find the large fluctuations in wins (without doing any math) between 3.5 and 4.5.

A drop from 4.5 to 4.0 would likely be worth a significant amount more than those mentioned in the previous paragraph. I think that is clear, and don't think anybody would doubt that. Pythag has some correction in sure, but it wouldn't eliminate this.

This isn't even considering the unlimited variables that can be introduced (weather, injuries to position players, inevitable statistical fluctuation of position players offensive and defensively, the strength of schedule, how well the pitching staff is managed, the stadium you're playing in, the proportions of LH/RH pitcher and hitter combos). It's endless, and basically futile to attempt a calculation of such magnitude short of having access to a supercomputer.....Unless your comfortable with a margin for error that could possibly put you in the neighborhood of unrealistic ERAs.

You could just stop at the assumption that all thing are constant except for ERA. The statistical chance of that happening is microscopic, destroying the integrity of any output. Could possibly be a useful guide...but you'd need a lot of testing to show its reliable.

Edited by Darius, 21 March 2018 - 07:08 PM.


#17 Sconnie

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Posted 21 March 2018 - 09:39 PM

This is exactly right, and I don't think Pythag could possibly compensate for that completely.

The number of wins each unit of ERA is worth would look like a bell curve (more likely a triangle with a sharp peak). If you're up at a 5.5 ERA, and you drop to a 5.0, or conversely are at a 2.5 ERA and drop to 2.0, you aren't going get a large number of wins added in return. You're likely going to find the large fluctuations in wins (without doing any math) between 3.5 and 4.5.

A drop from 4.5 to 4.0 would likely be worth a significant amount more than those mentioned in the previous paragraph. I think that is clear, and don't think anybody would doubt that. Pythag has some correction in sure, but it wouldn't eliminate this.

This isn't even considering the unlimited variables that can be introduced (weather, injuries to position players, inevitable statistical fluctuation of position players offensive and defensively, the strength of schedule, how well the pitching staff is managed, the stadium you're playing in, the proportions of LH/RH pitcher and hitter combos). It's endless, and basically futile to attempt a calculation of such magnitude short of having access to a supercomputer.....Unless your comfortable with a margin for error that could possibly put you in the neighborhood of unrealistic ERAs.

You could just stop at the assumption that all thing are constant except for ERA. The statistical chance of that happening is microscopic, destroying the integrity of any output. Could possibly be a useful guide...but you'd need a lot of testing to show its reliable.

uhh, Baseball Prospectus, Fangraphs, they have great big models to run those kinds of things. They are great, but take way more resources than I have.

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#18 Platoon

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Posted 22 March 2018 - 05:59 AM

So correct me if I am wrong here........ You are saying that if we score the same amount of runs as last year, and give up less runs, we will win more games? That seems a reasonable assumption to me. We will be a better team, than last year. Count me in! Then again, what if some other teams increase their scoring, and their ERA stays the same? Who gains the upper hand in that scenario? Or is it a wash. :) :)
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#19 caninatl04

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Posted 22 March 2018 - 10:52 AM

What if the ERA is 0.00? :)


Roughly speaking, runs for squared divided by (runs for squared plus zero squared) = 100%.

#20 caninatl04

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Posted 22 March 2018 - 10:59 AM

I thank everyone for their incredibly thoughtful comments. The basic point was that, roughly, decreasing ERA would increase wins at a ratio of -0.05 to +1. Yes there are many, MANY assumptions.

I guess is was hoping readers would guess what all the FA additions would do to team ERA. And then use the approximation to again guess the value of these additions to wins.

My guess is a reduction by .25, so maybe 5 wins?



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