How to measure Pythagorean expectation

[wavygravy2k]

How do you measure Pythagorean theorem when you compare it to your actual record? What does it mean when Pythagorean is higher than your actual score? Would this mean that you aren't managing your team as well as its potential or does it mean you have won many blowouts?

If Pythagorean is lower than your record does that mean that you've gotten some lucky breaks?

[MARCPELLETIER]

[quote:6074128bcb]Would this mean that you aren't managing your team as well as its potential or does it mean you have won many blowouts?
[/quote:6074128bcb]

Could be either...or both!!!

Blowouts generally happen both ways, unless you consistently have teams with exceptional offensive power. Another possibility: you are extremely strong vs lhp, but somewhat weaker vs rhp. You win your games by blowouts vs lhp, but lose tight games vs rhp.

But generally, being under your expected record means you don't manage well games decided by one or two runs.

This could be the result of numerous factors: not having a closer or having a too thin bullpen or not having your best reliever when you need it, or yet nothing to be blame for: your relievers are just screwing up too many games. Any way, bullpen is generally the culprit. You should go at the strategy section, I explained there an experiment I did with simulations done on the CD.

Other factors that could make you lose tight games: not having proper pinch-run/pinch-hitter, or relying too heavily on the 3-run homerun strategy.

[MARCPELLETIER]

This said, being constantly OVER your expected record may also be a sign that your team is probably underperforming!!!

If you spend too much money of bullpen, or too much on your bench, or if you keep your best reliever strictly to a closer role, you will overperform your expected record, but chances are your team will struggle to be over .500 ...

Think of it this way: your record shows how good you are as a GM, and your record vs expected record shows how good you are as a coach.

[J-Pav]

[quote:fdc5a81ac9="wavygravy2k"]How do you measure Pythagorean theorem when you compare it to your actual record? [/quote:fdc5a81ac9]

From Wikipedia, the free encyclopedia:

Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky that team was (by examining the variation between the two winning percentages). The term is derived from the formula's resemblance to the Pythagorean theorem.

The basic formula is: Win% =

[u:fdc5a81ac9].............Runs Scored^2................[/u:fdc5a81ac9]
Runs Scored^2 + Runs Allowed^2

where Win% is the winning percentage generated by the formula. The expected number of wins would be the expected winning percentage multiplied by the number of games played.

[quote:fdc5a81ac9="wavygravy2k"]What does it mean when Pythagorean is higher than your actual score? [/quote:fdc5a81ac9]

It means your net runs scored indicate you should have a higher record than what your team currently shows. More net runs equates to more wins.

[quote:fdc5a81ac9="wavygravy2k"]Would this mean that you aren't managing your team as well as its potential or does it mean you have won many blowouts? [/quote:fdc5a81ac9]

This is apparent only in hindsight. I would challenge anyone to show me evidence that you can manage a team to over or under produce. If that were the case, everyone would choose to overproduce, no?

[quote:fdc5a81ac9="wavygravy2k"]If Pythagorean is lower than your record does that mean that you've gotten some lucky breaks? [/quote:fdc5a81ac9]

Yes. Like [b:fdc5a81ac9]Marcus[/b:fdc5a81ac9] points out, this usually means winning more one run games (ie, winning more coin tosses). Bill James reports that after extensive analysis, the art of winning one run games comes down to luck (although you can squint at the stats long enough to make it look like bullpen, small ball, speedy runners, or some other quantifiable measure).

[maligned]

Changing the "2" to 1.82 in each of its three locations in the formula makes the formula slightly more accurate in most run scoring environments.

[Mean Dean]

Even more accurate is to use this exponent: (Runs Scored Per Game + Runs Allowed Per Game) ^ .287, a.k.a. [url=http://en.wikipedia.org/wiki/Pythagenpat]Pythagenpat[/url].

I think it's an overstatement to claim that performance in close games is all luck and the bullpen has nothing to do with it; I am with [b:d8bcdc713e]lucky[/b:d8bcdc713e] rather than [b:d8bcdc713e]J-Pav[/b:d8bcdc713e] on this. I think that if you looked at teams that over/underachieved by Pythag, you would find a very strong correlation between that tendency and bullpen quality, far more than could be dismissed as coincidence.

That being said, it is hard to say what specific managerial or GM decisions you can make based on Pythag, other than "if you're underachieving, try working on your bullpen." The temptation is to think that the runs scored/runs allowed is your team's "true talent", and thus your W-L is bound to come into line with it eventually. But I think there's far too much noise in the data to make that assumption. There's at least a substantial chance that your W-L better reflects your true talent.

[coyote303]

marcus wilby said:

[quote:2e53f15042]But generally, being under your expected record means you don't manage well games decided by one or two runs.[/quote:2e53f15042]

In general I like posts by Marcus, but I couldn't disagree with this more. How you do in close games is primarily driven by luck.

If you shift $ away from your hitters or starting pitchers to your bullpen, it simply means you will score less total runs or allow more runs early in exchange for allowing less runs late.

I'm not saying having a bad bullpen won't make you lose games (and certainly many of them will be close games). I am saying having a bad one won't mean you will lose more games than are "expected" by the formula and having a good pen won't mean you should win more than expected.

Every manager will have teams that underperform and others that overperform. In the long run, run differential will determine how many games they win and luck will determine whether they do better or worse than expected based on that run differential.

Let's look at an example. I have an outstanding manager in my 70s keeper league (total 70s winning pct. = .561). His team is 55-44 but his expected W/L is 59-40, and he has a losing record in 1-run games. Somehow, I think he manages his 1- and 2-run games just fine! One season proves nothing, but on average this manager's teams will have a positive run differential, they will win most of their games, but whether his teams do better or worse than "expected" in any given season is random chance.

[J-Pav]

[quote:ce0bb8ce2b="DeanTSC"]That being said, it is hard to say what specific managerial or GM decisions you can make based on Pythag, other than "if you're underachieving, try working on your bullpen." [/quote:ce0bb8ce2b]

This is exactly what I'm saying. Bullpen "quality" is only determined with hindsight, especially if we're equating quality with price.

I've used $3 set-up guys and $1 closers with both success and not so much success. I've used high dollar guys, low dollar guys and every combination in between. Sometimes it works out, sometimes it doesn't.

Bill James' study on one run games (if I remember correctly) revealed the teams with the best one run records had horrible overall records for the most part. In SOM Online, I think because of the pricing structure, one run games are maybe just an indicator of the overall strength of the team. Good teams win more, not so good teams win not so much. So it might be an overstatement to say "one run games are all luck" because there is a context about the overall quality of the team.

You might be right by saying "if you're underachieving, try working on your bullpen." But by working on your bullpen, you might be pulling salary better utilized on offense or even SP. Winning a few more close games might be coming at the expense of your overall productivity, as [b:ce0bb8ce2b]coyote[/b:ce0bb8ce2b] wrote.

So then the question becomes "what is the optimal amount of salary to spend on bullpen?" From everything I've seen and written about on these boards, the basic "quality" bullpen structure looks like this:

$4-$3-$2-$1-$1.

From there you have to differentiate between all the $4 guys, etc. down the line. Then this comes within the context of the FA pool. Then there's the SP context (three stud starters on slow hook usually affords you the opportunity to spend less on bullpen).

Then, when all this is said and done and you have an optimal team drafted and analyzed, you can still go 19-33 in one run games (I managed to achieve this once). So, was it the bullpen or just bad dice that made it look like it was the bullpen (in hindsight)?

[MARCPELLETIER]

[quote:ccd1bbf356](Runs Scored Per Game + Runs Allowed Per Game) ^ .287[/quote:ccd1bbf356]

Hey Dean, you might check that formula, because it didn't make sense to me

BTW, I totally agree with you. I wouldn't base any judgment on a single season. Too noisy. But some coaches have a trend to always underperform their pythagorian record, well, I would think there is something you need to change.


This said, the point of J-PAV and coyote is well taken: you must be careful to not hurt the rest of the line-up while doing so.

[MARCPELLETIER]

[quote:7beda27b60]the basic "quality" bullpen structure looks like this:

$4-$3-$2-$1-$1.[/quote:7beda27b60]

I must disagree here. The structure of a quality bullpen entirely depends on the number of leverage innings left out by starting pitchers.

If you go with 4 stellar SPs who can eat up eight innings (S8*), then your need of bullpen is minimal, maybe 2-1-0.5-0.5-0.5. In fact, the best TSN-STRAT team according to the record book had relievers all priced at 0.5M, precisely for the reason that all his starters were stellar S8*. Had this team went with a basic 4-3-2, needless to say it wouldn't be in the record book.

On the contrary, if you with 5 cheap S5, then you need to go with at least 2 stellar relievers (in 80M, at least).