ESPN: Blue Jays with best offense of 21st century

[Sherlock]

http://espn.go.com/mlb/insider/story/_/id/13500816/case-made-toronto-blue-jays-having-best-al-offense-century-mlb

After their most recent blowout of the Angels, the Jays have scored 670 runs in 124 games (5.40 per game), with a .332 team on-base percentage and .445 slugging percentage. All those figures currently lead the AL, as does their context-adjusted 114 OPS+. Since 2000, 12 clubs (including this year's Jays) -- less than one club per season -- have posted a seasonal 114 OPS+ mark. Of those 12, nine (again including the '15 Jays) also led the league in runs scored. Below, we rank those nine clubs by the number of standard deviations they are above that year's AL average in runs scored.
Best American League offenses since 2000

Code: Select all

Year   Team         Runs above standard deviation
2015   Toronto Blue Jays   2.64
2007   New York Yankees   2.28
2003   Boston Red Sox      1.88
2009   New York Yankees   1.77
2008   Texas Rangers      1.76
2001   Seattle Mariners   1.66
2013   Boston Red Sox      1.59
2011   Boston Red Sox      1.59
2002   New York Yankees   1.31


As you can see, in terms of the average variance from the norm in runs scored, the Jays have the premier AL offense since 2000. In fact, being more than two and a half standard deviations above the norm in anything is a really big deal. Two-thirds of the values in any range are within one standard deviation of the average; only the top and bottom one-sixth lie outside it. By this measure, the Jays are the elite of the elite since the turn of the century.

Pretty impressive stuff. Though the last paragraph I quoted is somewhat confusing. The title suggests that the Jays offense is 2.64 runs above the mean. Whereas the text suggests that the offense is 2.64 standard deviations above the mean. The latter would suggest that this Jays offense is better than 99.6% of all offenses that have ever existed in the MLB.

I don't have Insider so can't see what the rest of the article has to say, but either way this is pretty amazing.

[Indiana Jones]

http://espn.go.com/mlb/insider/story/_/id/13500816/case-made-toronto-blue-jays-having-best-al-offense-century-mlb

After their most recent blowout of the Angels, the Jays have scored 670 runs in 124 games (5.40 per game), with a .332 team on-base percentage and .445 slugging percentage. All those figures currently lead the AL, as does their context-adjusted 114 OPS+. Since 2000, 12 clubs (including this year's Jays) -- less than one club per season -- have posted a seasonal 114 OPS+ mark. Of those 12, nine (again including the '15 Jays) also led the league in runs scored. Below, we rank those nine clubs by the number of standard deviations they are above that year's AL average in runs scored.
Best American League offenses since 2000

Code: Select all

Year   Team         Runs above standard deviation
2015   Toronto Blue Jays   2.64
2007   New York Yankees   2.28
2003   Boston Red Sox      1.88
2009   New York Yankees   1.77
2008   Texas Rangers      1.76
2001   Seattle Mariners   1.66
2013   Boston Red Sox      1.59
2011   Boston Red Sox      1.59
2002   New York Yankees   1.31


As you can see, in terms of the average variance from the norm in runs scored, the Jays have the premier AL offense since 2000. In fact, being more than two and a half standard deviations above the norm in anything is a really big deal. Two-thirds of the values in any range are within one standard deviation of the average; only the top and bottom one-sixth lie outside it. By this measure, the Jays are the elite of the elite since the turn of the century.

Pretty impressive stuff. Though the last paragraph I quoted is somewhat confusing. The title suggests that the Jays offense is 2.64 runs above the mean. Whereas the text suggests that the offense is 2.64 standard deviations above the mean. The latter would suggest that this Jays offense is better than 99.6% of all offenses that have ever existed in the MLB.

I don't have Insider so can't see what the rest of the article has to say, but either way this is pretty amazing.

99.6% of all offenses (in the AL??) since 2000, not of all time.

[Dennis 37]

While watching the last game in Anaheim my friend and I agreed, this team is better than 1992/93. We didn't google the stats, or anything, we just relied on our aging memories, and it seemed to us that there are many more patient hitters on this Blue Jay team right down to the utility guys.

[Skin Blues]

This is a very bad way to use Z-Scores. This team (so far) is nowhere close to the best offense of the past 15 years, despite being almost a full standard deviation from the mean "better" than the 2003 Red Sox. The author either doesn't understand how to use statistics, or is being purposefully deceitful. I'm going to assume it's the first one.

[dante9988]

if travis was playing the gap would be even greater lol

[tempests_dawn]

This is a very bad way to use Z-Scores. This team (so far) is nowhere close to the best offense of the past 15 years, despite being almost a full standard deviation from the mean "better" than the 2003 Red Sox. The author either doesn't understand how to use statistics, or is being purposefully deceitful. I'm going to assume it's the first one.

Genuinely interested into why this is a bad way to use z-scores...can you elaborate?

[Kurtz]

I'm a bit confused by these stats.

Jays score 5.4 runs per game. League average is 4.2 runs per game. Jays thus score 1.2 runs above mean. Standard deviation is 0.36. Thus the Jays score more that 3.3 standard deviations higher than the mean, no?

Also, the author seems to use variance and standard deviations interchangeably, which is kinda odd seeing as standard deviation is the square root of variance...

[Skin Blues]

Where Z-Scores are useful is in comparing two things that aren't easily compared directly against one another. For instance, if we want to compare how good Billy Hamilton is at stealing bases to how good Josh Donaldson is at hitting home runs. We could find the Z-Score for each one. Hamilton might be 3 SD's better then the mean at SB's, and Donaldson might be 2 SD's better than the mean at HR. It doesn't tell the whole story, because maybe there's much less incentive to steal bases than there is to hit HRs, but at least we have a way to compare them. Other than using raw totals.

We know the run environment doesn't change all that much year to year in baseball, and we know ways to accurately measure it when it does change. Whether or not there is a big spread in talent in any given year is almost entirely due to variance. Standard deviation of "runs per game" changes independently of the actual run scoring environment. So if you score a lot of runs in a year that has a low standard deviation (more parity) then you will have an abnormally high Z-Score, whereas if you score the same amount of runs, in the same run scoring environment, in a year with a very large standard deviation (like, for instance, if there were a few really brutal teams and a few really good teams) your Z-Score would be significantly lower.

[Jays4WS]

Soooooo.. we have the better beer league team then?

[Skin Blues]

Here's some data:

Code: Select all

Year   SD      R/G
2000   0.49   5.1
2001   0.48   4.8
2002   0.48   4.6
2003   0.55   4.7
2004   0.51   4.8
2005   0.41   4.6
2006   0.35   4.9
2007   0.43   4.8
2008   0.42   4.7
2009   0.46   4.6
2010   0.47   4.4
2011   0.51   4.3
2012   0.36   4.3
2013   0.45   4.2
2014   0.35   4.1
2015   0.36   4.2


Notice the smooth, gradual changes in R/G. And then look at the random variance from year to year in SD.

Lets look at a specific example. In 2011, the Cardinals scored 4.7 runs/game in an MLB run scoring environment that allowed 4.3 runs per game. The next year, in 2012, those same Cardinals scored 4.7 runs/game in an MLB run scoring environment that allowed 4.3 runs per game. Pretty consistent, right? Yet their "standard deviations above the mean" was 0.83 in 2011 and 1.11 in 2012. In terms of Z-Score, that is a huge difference. Moral of the story: don't blindly believe what people are trying to tell you with statistics unless they're willing to show you the work and what it means, even if they're touted by a smart guy like Tony Blengino.

[Kurtz]

Here's some data:

Code: Select all

Year   SD      R/G
2000   0.49   5.1
2001   0.48   4.8
2002   0.48   4.6
2003   0.55   4.7
2004   0.51   4.8
2005   0.41   4.6
2006   0.35   4.9
2007   0.43   4.8
2008   0.42   4.7
2009   0.46   4.6
2010   0.47   4.4
2011   0.51   4.3
2012   0.36   4.3
2013   0.45   4.2
2014   0.35   4.1
2015   0.36   4.2


Notice the smooth, gradual changes in R/G. And then look at the random variance from year to year in SD.

Lets look at a specific example. In 2011, the Cardinals scored 4.7 runs/game in an MLB run scoring environment that allowed 4.3 runs per game. The next year, in 2012, those same Cardinals scored 4.7 runs/game in an MLB run scoring environment that allowed 4.3 runs per game. Pretty consistent, right? Yet their "standard deviations above the mean" was 0.83 in 2011 and 1.11 in 2012. In terms of Z-Score, that is a huge difference. Moral of the story: don't blindly believe what people are trying to tell you with statistics, even if they're touted by a smart guy like Tony Blengino.

I'm not sure I see the issue here. Variance would be derived via squaring the difference between mean and each of the 30 team's productions, and diving it by N (30). Then take the square root of that value and you have your standard deviation value. So even if the mean remained the same in consecutive years, the standard deviation could change considerably, I think.

In simplest terms, if one year 3 teams in a sample score 2,4,6 runs respectively, and in the next year they score 4,4,4, the mean is 4 in both years, but the standard deviation changes drastically, from 2 to 0.

I'm not an expert on this though, so maybe I'd missed your argument. As per my earlier post in this thread, I agree that the math in this article seems off, but for a slightly different reason.

[Skin Blues]

Right. It's easy to calculate it, but the result is just not very valuable. I don't know about the actual numbers they used, I didn't calculate them to verify. And I have actual work to do now unfortunately, so can't stop and check... but I'll look into it a bit more later, since it's interesting.

[Kurtz]

Right. It's easy to calculate it, but the result is just not very valuable. I don't know about the actual numbers they used, I didn't calculate them to verify. And I have actual work to do now unfortunately, so can't stop and check... but I'll look into it a bit more later, since it's interesting.

I calculated the 2015 SD and Mean in my first post and my numbers match up to theirs, so it looks to be accurate (at least for 2015). What I don't get is the original post suggesting 2.64 standard deviations, when by my count, we're 3.3+deviations off...which would make us a total outlier, which is pretty cool.

[satyr9]

The only argument I'd make is that a low standard deviation means the runs above may be more valuable than other times as it's strong against more teams. High deviation would indicate more top heavy and bottom heavy teams, creating larger variances. There must be thresholds where your strength stops helping. If I score 3 runs instead of 2 runs a game more than the bottom offenses, that won't help me win too many extra games, but if I'm 0.50 runs ahead of the second best team instead of just 0.10, that's hugely impactful, especially in the playoffs when the top teams are the only ones left.

So, while it's true on the whole, the low standard deviation probably oversells how dominant we are in comparison to the entire league in relation to a juggernaut like the '07 Yankees, it might mean if you compare that Yanks team vs. its top competitors and this year's Jays to its opponents, then the advantage remains the way the article lays out. And I think even if you use higher deviations, they'd likely still be right there with any team other than those damn Yankees, which is still pretty damn strong company IMO.

BTW, let me know if this is kosher or not:

https://www.reddit.com/r/Torontobluejays/comments/3i80es/case_can_be_made_for_blue_jays_having_best_al/

Top comment has the article. Reddit surely can't be a secret, but take it down if a link like this is out of bounds.

[Sherlock]

Right. It's easy to calculate it, but the result is just not very valuable. I don't know about the actual numbers they used, I didn't calculate them to verify. And I have actual work to do now unfortunately, so can't stop and check... but I'll look into it a bit more later, since it's interesting.

I calculated the 2015 SD and Mean in my first post and my numbers match up to theirs, so it looks to be accurate (at least for 2015). What I don't get is the original post suggesting 2.64 standard deviations, when by my count, we're 3.3+deviations off...which would make us a total outlier, which is pretty cool.

I think (based only on the excerpt) that he's calculating mean and SD not just for 2015, but for all years from 2000 onwards (so a 16-season sample). That could explain the discrepancy between his numbers and yours?

[Skin Blues]

OK, he's using AL only. That drops the sample size in half and adds 50% more variance.

Code: Select all

Year   SD      R/G
2000   0.46   5.3
2001   0.52   4.9
2002   0.56   4.8
2003   0.57   4.9
2004   0.47   5.0
2005   0.43   4.8
2006   0.37   5.0
2007   0.47   4.9
2008   0.44   4.8
2009   0.47   4.8
2010   0.58   4.5
2011   0.44   4.3
2012   0.32   4.4
2013   0.47   4.3
2014   0.32   4.2
2015   0.43   4.3


Here's the top 12:

Code: Select all

                R/G      SD   AVG      Z
2015 BlueJays   5.40   0.43   4.29   2.62
2007 Yankees    5.98   0.47   4.90   2.28
2006 Yankees    5.74   0.37   4.97   2.08
2013 Red Sox    5.27   0.47   4.33   2.01
2005 Red Sox    5.62   0.43   4.76   1.98
2003 Red Sox    5.93   0.57   4.86   1.89
2014 Angels     4.77   0.32   4.18   1.85
2004 Red Sox    5.86   0.47   5.01   1.81
2008 Rangers    5.56   0.44   4.78   1.79
2009 Yankees    5.65   0.47   4.82   1.78
2012 Rangers    4.99   0.32   4.45   1.71
2001 Mariners   5.72   0.52   4.86   1.65


Blengino omitted the three teams that didn't have at least a 114 OPS+ for some reason, which includes the team that ranks third, the 2006 Yankees.

Anyway... this is a pretty poor article, and no, the Blue Jays have not been close to the best offense in baseball of the past 15 years, not even for the past 3 years for that matter. And I haven't even touched on the fact that this doesn't include park adjustments, so he's directly comparing the runs scored in SKyDome to the runs scored in Petco, etc. Anyway... this was a fun little bit of research. Heh.

[tempests_dawn]

Thanks for explaining.

So with that written explanation, maybe I'm missing something here. In scenario 1 with lots of parity, and your team is the outlier, your SD should be higher. That makes sense. All the other teams have proven that they score about the same amount of runs compared to each other, but you score THAT MUCH more. Your SD should be higher

In scenario 2, you have middle-ground teams, but you also have some really low scoring teams, and some really high scoring teams. Your SD shouldn't be that high compared to scenario 1 because that environment also produced teams that scored a lot, more than the middle-ground teams. Other top teams were able to produce what you did, so your offensive accomplishments aren't as great vs scenario 1.

Pardon my lack of stats background, but does the [edited]runs above[/edited] SD in the OP capture what I just described?

[Skin Blues]

If the only information we had were the runs/game of all teams from 2003, and all teams from 2015, we would assume that the best Z-Score was the best team. A good example is students taking tests. Imagine there are 2 different schools in a district that each have their own distinct history tests, and their own students. The test at School A might be a lot harder than the test at the other school, so we can't simply look at it and say the student with the highest overall grade was the best at taking the test. And what if the test at School A has 50 easy questions, and 50 very hard questions? So, most students get the easy 50 right, but very few get more than a few of the hard questions. So the scores might all be bunched tightly around the average of 65. School B might have no easy or very hard questions and 100 medium difficulty questions. The average is also 65, but there are a lot of kids who can hardly answer any medium questions, and lots of kids who can answer all of them. Getting a grade of 80 at School A would be very impressive since you'd have to correctly answer 30 of the difficult questions. While a grade of 80 at School B might be easy because you don't need to answer any difficult questions. So both schools have the same average score, but very different standard deviations. So, a kid with a grade of 80 at School A might be 2.5 standard deviations above the mean of 65, while a kid with a grade of 85 at School B is only 2.0 standard deviations above the mean.

Now... that example works well for schools, because we presumably don't know anything about the tests other than the scores. But for an analogy to MLB, imagine we know that both schools have the exact same test, only one school removed one of the questions because it offended their catholic beliefs. We can easily compare the scores of the kids in School A vs School B by simply looking only at the answers to other 99 similar questions. With MLB, we have tons of data on how hard it is to score runs. We know almost exactly how much harder it is to score runs in 2015 vs 2013, 2006, etc. We know pretty well how much harder it was for the Mariners to score runs in Safeco than it is for the Blue Jays to score in the SkyDome. We know in general, league wide, how hard it is to score runs on a per-half-inning basis because we have a sample size of ~45,000 half-innings per year (times 16 years = 720,000 half innings). There's no reason to use Z-Scores. They're meant to compare apples to oranges, not apples to apples.

[Kurtz]

OK, he's using AL only.

Ok, good find. That explains it.

I think he does have a bit of an argument for his case, although what hurts him is that the standard deviation in any single year is pretty random, especially when the population is ...15.

[Kurtz]

Thanks for explaining.

So with that written explanation, maybe I'm missing something here. In scenario 1 with lots of parity, and your team is the outlier, your SD should be higher. That makes sense. All the other teams have proven that they score about the same amount of runs compared to each other, but you score THAT MUCH more. Your SD should be higher

In scenario 2, you have middle-ground teams, but you also have some really low scoring teams, and some really high scoring teams. Your SD shouldn't be that high compared to scenario 1 because that environment also produced teams that scored a lot, more than the middle-ground teams. Other top teams were able to produce what you did, so your offensive accomplishments aren't as great vs scenario 1.

Pardon my lack of stats background, but does the [edited]runs above[/edited] SD in the OP capture what I just described?

You're basically right. If year 1 every team scores 4 runs, and you score 6, then the standard deviation for that year will be something like 0.1. So the difference in mean (between what ur team produces vs league average) will be 2, which will be 20 standard deviations above the mean.

But year 2 you may have normal binomial distribution of runs, which means that the unit of standard deviation may be 0.5 or more. So even if you again produce 2 runs above the mean, now you're only 4 standard deviations above the mean.

That's the trouble with using such a small sample size (15 AL teams in that year), and why Skin points out that this is a pretty weak argument.