Are Perfect Team Results realistic?

[uschi_baerchen]

I remembermany posts who complain about the statistical reliability of the engine ofOOTP. I recently checked the WAR which Robinson Cano provided for 500 PA andfound a minimum of 0,5 and a maximum of 3,5 WAR. A difference of 3 WAR betweenmaximum and minimum is about the difference between Mookie Betts - for whom youhave to pay 40.000 PP - and the average player on the market, whom you will getfor 2000, I guess. It seems to be insane, doesn`t it (both, the 40.000 and thedifference)?
How can wefind out, if the aberration is insane or normal? A guy from Germany called CarlFriedrich Gauss found the answer for questions like these. Now, I will not use thewhole Gauss apparatus, maybe someone who makes such calculations professionally,has time and has access to the statistical package for the social sciences too coulddo this. What I will do is some calculations, which are mathematically nottotally correct but will lead us into the correct direction, I hope.
I willassume, that the probability distribution for hitters is of the same type asfor election forecasts. For election forecasts and parties, which will getbetween 40% and 60% of the votes, you have to question about 1700 typicalvoters to get the correct values within 1 % of the mean of the answers about95% of the time. TRANSLATION: if 901 of 1700 voters (= 53%) would say “I will vote for Mr.Trump”, then in 19 of 20 cases (=95%) Mr. Trump would get between 52,5% and 53,5%of the votes. In 1 of 20 cases he would get a lower of higher percentage. Incase of less he could even go down to 901 voters at all, because all voters ofMr. Trump might have been included in the poll already, although that would bevery improbable.
Now we dothe same calculation for a very good hitter and his batting average. The verygood hitter is supposed to hit 300. Now, for a sample of 1700 at bats we canassume, that in 19 of 20 1700-at-bat-tries he will bat between 295 and 305. Wehave to consider, that 1700 at bats is about is 3 – 4 seasons of work of a verygood batter. If we are considering one season only with say 400 at bats, thegaps will be much larger, I guess 280 to 320 is realistic. For this reasoning itis absurd to assume, that Mookie Betts will not - once in a while - bat southof the Mendoza line for 25 games or Mr. Cano north of the Ted Williams line.
One otherthing you also have to consider is, that your players averages go up and down withthe league you are in.

[Threnodas]

The variability is actually even greater than the previous comment suggests. For a proportion P such as a batting average, the standard deviation after N observations (at-bats) is sqrt(P * (1-P) / N), and a 95% confidence interval is P +/- 2 * SD. So, for a .300 hitter, P = 0.3, 1-P = 0.7, and after 525 at-bats, the standard deviation is sqrt(0.3 * 0.7 / 525) = sqrt(21 / 100 / 525) = sqrt(1/2500) = 1/50 = 0.020. Thus, after 525 at-bats, you can only be 95% confident that a truly .300 hitter will have a season batting average anywhere between .260 and .340. The standard deviation only scales with the square root of N, too, so even after 4 seasons and 2100 at-bats, the .300 hitter's 95% confidence interval for their career batting average is still .280 to .320. The point is, baseball stats being displayed to 3 significant figures makes them seem much more authoritative than they really are, but outcomes are random, so relax.

[zrog2000]

The biggest factor in results is the quality of competition. PT is never going to be realistic with ratings used for players who played in the talent level of the season they played in, when they're playing against far, far better competition.

However, I do question the variability of results at times. For example, I don't see how it's possible for this to happen to Anthony Rizzo in a silver league with over 600 PAs:

I mean a .215 slugging percentage? A .056 ISO?

[Ty Cobb]

Haaaaaaaaaaaaaaa-hahahahahaha

[<Pion>]

Originally Posted by zrog2000

The biggest factor in results is the quality of competition. PT is never going to be realistic with ratings used for players who played in the talent level of the season they played in, when they're playing against far, far better competition.

However, I do question the variability of results at times. For example, I don't see how it's possible for this to happen to Anthony Rizzo in a silver league with over 600 PAs:

I mean a .215 slugging percentage? A .056 ISO?

600 PAs? Isn't that the same numbers from the other thread you posted in where he only had around 120 PAs to generate the .215 SP? He has 600 PAs if you add both years together, but not 600 PAs in either season.

[zrog2000]

Originally Posted by <Pion>

600 PAs? Isn't that the same numbers from the other thread you posted in where he only had around 120 PAs to generate the .215 SP? He has 600 PAs if you add both years together, but not 600 PAs in either season.

600 PAs together with an OPS+ of around 50, which is still absurdly low. It does not make sense that someone with Rizzo's ratings would be able to be that bad in a silver league. The variability of some of these cards is way higher than it should be. Someone like Rizzo doesn't just have a bad year with a 50 OPS+ in 600 PAs in the majors unless he's hurt or on a steep and permanent decline, which isn't possible in PT. So either the game is way too random or the ratings are nowhere close to accurate, take your pick.

I don't think you can look at his real life stats and tell me his card and/or the game is realistic in any way. This is beyond bad luck in small sample sizes.

[<Pion>]

Originally Posted by zrog2000

So either the game is way too random or the ratings are nowhere close to accurate, take your pick.

False dilemma definition
A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option. A false dilemma can arise intentionally, when a fallacy is used in an attempt to force a choice or outcome.


I'll choose a third option... small sample size and/or stiffer competition.

[zrog2000]

Originally Posted by <Pion>

False dilemma definition
A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option. A false dilemma can arise intentionally, when a fallacy is used in an attempt to force a choice or outcome.


I'll choose a third option... small sample size and/or stiffer competition.

I disagree that 600 PAs is a small sample size, unless you've ever seen someone like Rizzo with a ~50 OPS+ in a full season when he wasn't hurt or in rapid decline. And I also disagree that a silver league is that competitive. Even if the competition WAS that difficult in a silver league, it's still not a realistic outcome! If it was a diamond or perfect league, then I wouldn't be posting this.

I fully understand sample sizes and competition levels as I've argued against people complaining about this all the time. But a ~50 OPS+ is outside of a reasonable outcome for a full season for someone like Rizzo at that level. I mean you may as well use any card at all and expect a better outcome than that. Something does not jive here.

[Orcin]

Prior to the 2018 season, Chris Davis had a 118 OPS+ in 4700 plate appearances. In 2018, Chris Davis had a 50 OPS+ in 532 plate appearances.

Is the MLB engine broken too?

[zrog2000]

Originally Posted by Orcin

Prior to the 2018 season, Chris Davis had a 118 OPS+ in 4700 plate appearances. In 2018, Chris Davis had a 50 OPS+ in 532 plate appearances.

Is the MLB engine broken too?

And compare his 2017 Live card to his 2018 Live card (if they existed). The results in OOTP are based on his present live card, not the previous season's live card.

2018 Live cards should be based on 2018 results, not predict a steep decline in 2019. There is no decline and no injuries in OOTP PT. Chris Davis is in a steep decline. He wasn't just unlucky last season.

[<Pion>]

Originally Posted by zrog2000

I disagree that 600 PAs is a small sample size, unless you've ever seen someone like Rizzo with a ~50 OPS+ in a full season when he wasn't hurt or in rapid decline. And I also disagree that a silver league is that competitive. Even if the competition WAS that difficult in a silver league, it's still not a realistic outcome! If it was a diamond or perfect league, then I wouldn't be posting this.

I fully understand sample sizes and competition levels as I've argued against people complaining about this all the time. But a ~50 OPS+ is outside of a reasonable outcome for a full season for someone like Rizzo at that level. I mean you may as well use any card at all and expect a better outcome than that. Something does not jive here.

Feel free to disagree, but the larger sample sizes have shown that the problem is not with the Rizzo card but with the smaller sample.

[mclellan36]

Originally Posted by Threnodas

The variability is actually even greater than the previous comment suggests. For a proportion P such as a batting average, the standard deviation after N observations (at-bats) is sqrt(P * (1-P) / N), and a 95% confidence interval is P +/- 2 * SD. So, for a .300 hitter, P = 0.3, 1-P = 0.7, and after 525 at-bats, the standard deviation is sqrt(0.3 * 0.7 / 525) = sqrt(21 / 100 / 525) = sqrt(1/2500) = 1/50 = 0.020. Thus, after 525 at-bats, you can only be 95% confident that a truly .300 hitter will have a season batting average anywhere between .260 and .340. The standard deviation only scales with the square root of N, too, so even after 4 seasons and 2100 at-bats, the .300 hitter's 95% confidence interval for their career batting average is still .280 to .320. The point is, baseball stats being displayed to 3 significant figures makes them seem much more authoritative than they really are, but outcomes are random, so relax.

Holy cow...I started reading this and I sprained my brain. I need to dust off my statistical analysis for dummies book!!

[zrog2000]

Originally Posted by <Pion>

Feel free to disagree, but the larger sample sizes have shown that the problem is not with the Rizzo card but with the smaller sample.

No f'ing Rizzo should have a 50 OPS+ in a full season sample size! That is exactly the problem. Normal expectations for All-Star level players (gold cards) are not ever going to be completely unplayable for an entire season even at a 0.1% expected outcome.

[<Pion>]

Ok

[BMW]

Having a league with J.T. Realmuto and Cap Anson is unrealistic.

How you would set expectations in a league where a team can have a starting rotation of four Cy Young award winners and Cy Young himself to boot?

Everything is theoretical in this environment. If every batter hit according to their stats, then every pitcher in the league would have a 6.00 or 7.00 ERA.

[zrog2000]

Originally Posted by BMW

Having a league with J.T. Realmuto and Cap Anson is unrealistic.

How you would set expectations in a league where a team can have a starting rotation of four Cy Young award winners and Cy Young himself to boot?

Everything is theoretical in this environment. If every batter hit according to their stats, then every pitcher in the league would have a 6.00 or 7.00 ERA.

We were discussing a silver league where there were likely 0 diamond pitchers.

[BMW]

You don't need to get anywhere close to Diamond card pitchers to throw out a starting rotation of five Cy Young caliber pitchers.

I could build a rotation of these Cy Young level players for about the PP I got from one guy striking out 4 guys in an inning, or getting two guys voted to the all-star game in PT.

These are Silver starting pitchers:
Mark Fidrych '76 - All Star, ROY, 2nd in CY voting, got MVP votes
Jerry Koosman '68 - All Star, 2nd in ROY voting, got MVP votes
Tom Seaver '67 - All Star, ROY, got MVP votes
Jim Turner '37 - no CY or ROY yet, got MVP votes
Juan Marichal '66 - All Star, got MVP votes
Andy Pettite '96 - All Star, 2nd in CY voting, got MVP votes
Randy Jones '75 - All Star, 2nd in CY voting, got MVP votes
Johnny Antonelli '54 - All Star, got MVP votes
Catfish Hunter ' 75 - All Star, 2nd in CY voting, got MVP votes
David Cone '94 - All Star, Cy Young, got MVP votes
David Wells '98 - All Star, 3rd in CY voting, got MVP votes
Dock Ellis '71 - All Star, 4th in CY voting
Sam Jones '56
Wilbur Wood '72 - All Star, 2nd in CY voting, got MVP votes
Vic Raschi '51 - got MVP votes
Sad Sam Jones '21
Mark Langston '89
Mike Witt '84
Bob Ojeda '86 - 4th in CY voting, got MVP votes
Jim Abbott '91 - 3rd in CY voting
Rick Ankiel '00 - 2nd in ROY voting
Justin Thompson '97 - All Star
Herman Pillette '22
Todd Ritchie '99
John Maine '07

[uschi_baerchen]

Originally Posted by mclellan36

Holy cow...I started reading this and I sprained my brain. I need to dust off my statistical analysis for dummies book!!

Actually, you must not since Threonodasmade it quite easy, I try to explain it a bit more elaborate:

• We assume, that the batting average follows the normal distribution(otherwise the following would be a bit more complex, but the assumption with the the normal distribution isfair)
• Now, in this case, we assume, that a certain event has a probability ofP, this means in our example: the event that the ball is hit has a probabilityof 30% (i.e. we consider a batter with a batting average of 300).
• If P = 0,3 then (1-P) = 0,7 this is simple arithmetic
• Now, the so called “standard deviation after N events” is defined as sqrt(=square root of … )( (P * (1-P) / N). That this “standard deviation after Nevents” is meaningfull has to be believed for the time being, otherwise you haveto get your “ … for dummys” – book to find out, why this is the case.
• In our case P = 0,3, 1-P = 0,7, N = 525 and if you put these values intoexcel, you get – voila - : 0,02.
• What does this “standard deviation after N events” mean in practicalmatters? It means, that about 68% of the observations will be within the interval(mean-value minus deviation to mean – value plus deviation). In our case themean value is 0,300, the deviation is 0,02, so 68% of the occurences will bebetween 0,280 and 0,320.
• It also means, that 32% of the occurences will be outside the above intervall.If we enlarge the interval to (mean-value minus twice the deviation to mean –value plus twice deviation) now 5% only will be outside the interval, this translatesto 5% of the occurences will be outside 0,260 and 0,340.
• Now an exercise. We are looking at a 0,250 batter, we observe him six seasons(555 AB per season), which means 3330 at bats. Which will be his performance intervalin 95% of the observations?
• P = 0,25 , 1-P = 0,75 è deviation is (using excel or a calculator) sqrt(P*(1-P)/3330) = 0,0075;for this reason twice the deviation is 0,015.
• So we conclude: in six seasons our 0,250 hitter will hit between 0,235and 0,265 in 19 of 20 times. (In other words: if I observe 20 250-hitters for 6years, 19 of them will hit between 235 and 265 and only one will hit more ORless.

[Izz]

Originally Posted by zrog2000

We were discussing a silver league where there were likely 0 diamond pitchers.

For the record, there are plenty of diamond pitchers in my silver league. 14, to be precise. And 19 more rated 89.

[zrog2000]

Originally Posted by Izz

For the record, there are plenty of diamond pitchers in my silver league. 14, to be precise. And 19 more rated 89.

Then I guess every batter should shave about 300-400 points off their OPS compared to major league competition? Doubt it.