Best lefty off all time? My vote is Koufax!

[cardsagain74]

Originally Posted by Snowman

The underlying problem is that every statistic you read really should come with a confidence interval attached to it. But of course that's just too confusing for most people, and it would probably just annoy everyone. Plus, it's just impractical. But the reality for most of these statistics is that they are actually estimates of the athlete's underlying "true" abilities. Mike Trout's "true" batting average is some unknowable number, but we can estimate it using statistics. And that's precisely what we do. After the first game, he goes 3 for 4, we estimate it to be 0.750. Well, that's not going to fool anyone, because nobody hits 0.750, so we wait for more data. After a month, he's still hitting 0.414 though. Hell, by the all-star break, he's still hitting 0.392. That's after nearly 100 games and 400 at-bats! Surely, that's a large sample, right? Has he turned a corner? Rumors start spreading about him "putting in work in the off-season". They say he's "really focused now", etc. But none of this fool's the statistician, because we don't read his batting average as 0.392. We understand that 0.392 is just an estimate of his "true" batting average and that we can calculate a 95% confidence interval around this estimate by looking at the standard deviation and sample size associated with it. So, instead of reading it as being 0.392, we more appropriately read it as something like 0.392 +/- 0.130. In other words, his "true" batting average is 95% likely to be in the range of 0.262 to 0.522, which ultimately, just isn't all that helpful. Because we know this, we are hesitant to say things like "Trout is a better hitter this season than Harper since Trout is hitting 0.392 and Harper is only hitting 0.333 at the all-star break". The truth is, we just don't have enough data to make that determination. The sample sizes are simply too small, the standard devaition is too large, and thus the confidence intervals are too wide to be able to make claims "with confidence" about that statistic.

The same is true for something like ERA from season to season. It is a highly volatile statistic. When we say something like "it has too much variance", we mean that literally. Mathematically speaking, variance is the square of the standard deviation. Some statistics have extremely wide standard deviations, like ERA, batting averge, OBP, etc. Whereas other statistics have MUCH lower variance/standard deviations. Stats like FIP vary far less than ERA. This means we can compare two pitchers at the all-star break with much greater confidence by comparing their FIPs than we can by comparing their ERAs. It is a mathematical property of the inherent differences between those statistics. The same is true of K/9 and BB/9. They have lower variance than ERA, and thus have much narrower confidence intervals. A statistician might be able to read Koufax's K/9 rate at the all-star break with a fairly narrow confidence interval because of this. So they might read his K/9 of 10.1 as being something like 10.1 +/- 0.4, making comparisons against other pitchers much more possible. If two pitchers' statistics do not overlap when taking into consideration their confidence intervals, then you can say that you are 95% confident that Koufax is a better strikeout pitcher because his 10.1 +/- 0.4 K/9, or as an interval, read (9.7, 10.5) is greater than some other pitcher whose K/9 confidence interval is (8.8, 9.6). Note the bottom of Koufax's range (9.7) exceeds the top of the other pitcher's range (9.6), so we can state with confidence that he is indeed better. However, this is rarely possible to say with ERAs. The confidence intervals with those are just absolutely massive. Even after an entire season. One pitcher's ERA of 3.05 may look quite a bit better than someone else's 2.64, but we just can't state that with confidence because their intervals might be something like 3.05 +/ 0.65 and 2.60 +/- 0.75 resulting in ranges of (2.40, 3.70) and (1.85, 3.35). And since those intervals overlap, we cannot state with confidence that they are truly different or that one is clearly better than the other. This is why an asshole like myself says something along the lines of, "that doesn't mean shit", whereas someone more tolerant might say something like, "the standard deviations of that statistic are too wide and the sample sizes are too small for us to be able to make a determination about the differences between those two data points". One of the most fascinating aspects about baseball, which is probably a big part of why I love the game as much as I do, is that the game truly is subject to a MASSIVE amount of variance. Great hitters can hit 0.348 one season and 0.274 the next. People will come up with all sorts of explanations about what is causing the slump, whether his home life is affecting him too much, if he's injured or just experiencing a mental lapse, etc. However, the informed fan knows that this is simply within expectations, and looks to statistics like BABIP to help shed light on what the actual underlying cause is (the guy just got some lucky bounces last season and some favorable ones this season. Or perhaps he didn't. Perhaps his BABIPs are the same, and there actually really is something going on in his personal life or he really is injured. But variance/luck needs to be ruled out first, because if it's present, then you already have your answer). This is also precisely why I stated earlier that I see no reason to believe that Randy Johnson was tanking games in Seattle in 1998 before being traded to Houston that season. At first glance, his numbers appear to tell a significantly different story (ERA of 4.33 in Seattle and 1.28 in Houston). But when you dig in closer and look at the confidence intervals associated with those deltas, and look at his FIP, K/9, and BABIP values, and the confidence intervals around those, you'll see that they all overlap. We simply don't have enough data to say that those numbers are truly different, even though they certainly appear to be, and read that way to the non-statistician.

But these things do in fact matter. This isn't just some statistician's "opinion". We can actually calculate these things mathematically. We can also calculate the precise probability that pitcher A will have a lower ERA than pitcher B by the end of the season based on their differences at the all-star break. And if the formula says that pitcher A is 50% likely to have a higher ERA than pitcher B, based on their current ERAs and the confidence intervals associated with them, and if we run those comparisons for all pitchers in the league, we really will be "wrong" on 50% of them at the end of the season because these confidence intervals are real-world probabilities that will play out in the future. That's the beauty of the discipline of statistics. It's all based on sound theory that has been proven mathematically.

I am completely aware of the very elementary statistical principles that you just described. But none of that has anything to do with my point, which is sometimes coming to a biased or subjective conclusion from your data (and using just the "good contact pitcher" study as an example.

As a statistician, if McCracken didn't already have a tendency to lean toward certain preferred results, he never would've used those quotes by Maddux and Pedro to supposedly "prove" his point some (and actually would have likely mocked any mention of them doing so).

More often than not, I'm with you. Am the first guy to look for that progressive royal video poker machine that's gone to 100.75% in EV with perfect play and has a high enough hourly rate to be worth playing, etc etc. Anyone who doesn't trust the math in those completely quantifiable spots is ignoring undeniable reality.

But when it comes to spots where human elements are involved, my point here (and many others' point) is that there are too many intangibles that may or may not apply in some spots to come to such sound conclusions, even when some individual smaller pieces of that particular puzzle have been proven statistically.

It reminds me of how the EMH in the financial markets is seen by statisticians. When I actually read the "proof" that the market is supposedly 100% random, I was stunned by how elementary the research was. Especially given how some elite full-time traders have been highly successful over the course of many, many thousands of trades. Results that would be impossible by chance, no less.

You see someone like Bill Russell as highly overrated and extremely lucky. I see someone who likely didn't win 15 titles in the 16 years he was the core of his team from high school on by chance (and yes everyone, I know there were two years he didn't win a ring the pros...he got hurt early in their losing playoff series during one of those two seasons.) And see someone like Chris Archer as a guy who's just gotten extremely unlikely, rather than a pitcher who give up the big hit to decide a game much more often than the norm (over a period of many years and over 200 starts).

Sometimes there might be more to these things than just being that occasional outlier on the bell curve.

Dynamic events are just a totally different ballgame to datamine proof from than anything set in mathematical stone, imo. And I know you won't agree. Though I can't prove it

[Peter_Spaeth]

John, good post. As I recall saying to someone years ago who was stat oriented in discussing Kershaw and his post-season woes, we aren't just dealing with APBA cards where players inevitably regress to their mean, we're dealing with people.

[Snowman]

Originally Posted by Peter_Spaeth

John, good post. As I recall saying to someone years ago who was stat oriented in discussing Kershaw and his post-season woes, we aren't just dealing with APBA cards where players inevitably regress to their mean, we're dealing with people.

The point about Kershaw in the playoffs and sample sizes seems to be often misunderstood by both the people making the argument and those arguing against it.

It's not that we can say with confidence that his postseason performance being sub par is just bad luck and small sample sizes. The problem is that we can't say that it isn't. This is one of the most commonly misunderstood concepts in statistics. When I was in grad school, I tutored a lot of other students and this was something that many of them struggled with. The difference between "it's just luck" and "this is entirely explainable by luck" is important, and they're not the same thing. In the case of Kershaw, we simply don't have enough data to know either way (and will likely never have it). He very well could just be someone who folds under pressure, or he could just be getting unlucky. It could also be a bit of both. My guess is that he got unlucky at first, but then allowed that to get to his head because the narrative surrounding him was that he choked under pressure, and now he felt even more pressure to perform, but fell short mentally. But I don't know. That's just speculation. The statistical explanation should be that it is explainable by bad luck, but that we don't have enough data to know if that is indeed the case. I know, it's not helpful. But agnosticism in the absence of sufficient evidence should always be the default.

The problem I have is when people want to make claims like they know he chokes under pressure. Sure, it's possible, but then again, he also might not.

[Peter_Spaeth]

Originally Posted by Snowman

The point about Kershaw in the playoffs and sample sizes seems to be often misunderstood by both the people making the argument and those arguing against it.

It's not that we can say with confidence that his postseason performance being sub par is just bad luck and small sample sizes. The problem is that we can't say that it isn't. This is one of the most commonly misunderstood concepts in statistics. When I was in grad school, I tutored a lot of other students and this was something that many of them struggled with. The difference between "it's just luck" and "this is entirely explainable by luck" is important, and they're not the same thing. In the case of Kershaw, we simply don't have enough data to know either way (and will likely never have it). He very well could just be someone who folds under pressure, or he could just be getting unlucky. It could also be a bit of both. My guess is that he got unlucky at first, but then allowed that to get to his head because the narrative surrounding him was that he choked under pressure, and now he felt even more pressure to perform, but fell short mentally. But I don't know. That's just speculation. The statistical explanation should be that it is explainable by bad luck, but that we don't have enough data to know if that is indeed the case. I know, it's not helpful. But agnosticism in the absence of sufficient evidence should always be the default.

The problem I have is when people want to make claims like they know he chokes under pressure. Sure, it's possible, but then again, he also might not.

I understand what you're saying, but just looking at it statistically doesn't account for observations like body language, facial expression, very similar patterns of wilting (getting shelled all at once in a fateful inning), and so forth. In my view, sometimes anyhow, you don't need a weatherman to know which way the wind blows. Could I "prove" it objectively? No, probably not.

[Mark17]

Originally Posted by Peter_Spaeth

I understand what you're saying, but just looking at it statistically doesn't account for observations like body language, facial expression, very similar patterns of wilting (getting shelled all at once in a fateful inning), and so forth. In my view, sometimes anyhow, you don't need a weatherman to know which way the wind blows. Could I "prove" it objectively? No, probably not.

Still somewhat subjective, but I'll bet his catchers would have a worthwhile opinion as to his stuff and location in post-season vs. regular season.

[Peter_Spaeth]

Originally Posted by Mark17

Still somewhat subjective, but I'll bet his catchers would have a worthwhile opinion as to his stuff and location in post-season vs. regular season.

But here's the thing. In a number of the games I saw where I felt he wilted under pressure, he was cruising along looking very much like his Cy Young dominant self, then just had a massive meltdown. I recall that twice, I believe, in the 7th inning against the Cardinals. Other games as well. So it's not like he just pitched poorly, it's more that he reached a point where he couldn't handle it.

[Mark17]

Originally Posted by Peter_Spaeth

But here's the thing. In a number of the games I saw where I felt he wilted under pressure, he was cruising along looking very much like his Cy Young dominant self, then just had a massive meltdown. I recall that twice, I believe, in the 7th inning against the Cardinals. Other games as well. So it's not like he just pitched poorly, it's more that he reached a point where he couldn't handle it.

I was a pitcher/catcher in college and believe me, a catcher can tell when his pitcher starts to break down mentally, or when he begins to tire. Sometimes hitters hit quality pitches and to the average fan, it looks like the pitcher is losing it when he's actually still sharp. And vice versa.

[Bigdaddy]

Originally Posted by Peter_Spaeth

But here's the thing. In a number of the games I saw where I felt he wilted under pressure, he was cruising along looking very much like his Cy Young dominant self, then just had a massive meltdown. I recall that twice, I believe, in the 7th inning against the Cardinals. Other games as well. So it's not like he just pitched poorly, it's more that he reached a point where he couldn't handle it.

Or quite possibly, his manager managed him differently in the post season than in the regular season. We certainly see managers, especially today, manage their pitching staffs differently in the post season than in the regular season - because they are managing for five or seven games, not 162.
I can imagine that when you have a pitcher as dominant in the regular season as Kershaw, if he gets in a tight spot in the post-season, there may be a temptation to leave him in a bit longer and let him work through it. Not all pitchers, but one that got you this far. A manager/pitching coach looks down at the bullpen and asks himself - 'Who do I have that is better than Kershaw at this point?' Dance with who brung ya. If I'm a manager, I want my best pitchers throwing more innings in any postseason series.
I too had noticed the same thing with Clayton - great start to a game and then one bad inning. If it was the regular season, maybe he would have been pulled instead of staying out on the mound.

[BobC]

Originally Posted by cardsagain74

I am completely aware of the very elementary statistical principles that you just described. But none of that has anything to do with my point, which is sometimes coming to a biased or subjective conclusion from your data (and using just the "good contact pitcher" study as an example.

As a statistician, if McCracken didn't already have a tendency to lean toward certain preferred results, he never would've used those quotes by Maddux and Pedro to supposedly "prove" his point some (and actually would have likely mocked any mention of them doing so).

More often than not, I'm with you. Am the first guy to look for that progressive royal video poker machine that's gone to 100.75% in EV with perfect play and has a high enough hourly rate to be worth playing, etc etc. Anyone who doesn't trust the math in those completely quantifiable spots is ignoring undeniable reality.

But when it comes to spots where human elements are involved, my point here (and many others' point) is that there are too many intangibles that may or may not apply in some spots to come to such sound conclusions, even when some individual smaller pieces of that particular puzzle have been proven statistically.

It reminds me of how the EMH in the financial markets is seen by statisticians. When I actually read the "proof" that the market is supposedly 100% random, I was stunned by how elementary the research was. Especially given how some elite full-time traders have been highly successful over the course of many, many thousands of trades. Results that would be impossible by chance, no less.

You see someone like Bill Russell as highly overrated and extremely lucky. I see someone who likely didn't win 15 titles in the 16 years he was the core of his team from high school on by chance (and yes everyone, I know there were two years he didn't win a ring the pros...he got hurt early in their losing playoff series during one of those two seasons.) And see someone like Chris Archer as a guy who's just gotten extremely unlikely, rather than a pitcher who give up the big hit to decide a game much more often than the norm (over a period of many years and over 200 starts).

Sometimes there might be more to these things than just being that occasional outlier on the bell curve.

Dynamic events are just a totally different ballgame to datamine proof from than anything set in mathematical stone, imo. And I know you won't agree. Though I can't prove it

John,

Excellent post, great points, and I'm one of those people that keeps bringing up the variables, like you. Also like you, I understand the principles and such behind the math, and their use, especially in the example you gave with regard to the video poker machine. Great example.

What is funny is how statisticians seem to really despise the word "opinion" when used in reference to what it is they do. But you know right away in dealing with statistics, such as provided by baseball, that you're going to have recognized deviations and varying levels of confidence in the stats of a player as to what his "true" statistical measures (stats) should be. And since by a statistician's own understanding there is never going to be a 100% certainty as to a player's stats being their "true" stats then, the use of that player's stats for some comparison is never going to be 100% accurate, and therefore it is NOT an undeniable fact. And if a statistician uses something that is not an undeniable fact as even part of the basis for determing some answer, then that answer is their opinion, and can never be fact. They should look up the definition of the word "opinion". Putting it a simpler way, if someone says water is wet, that is a fact. But if a statistician says they are 95% confident water is wet, therefore I'm going to say it is wet, then that isn't a fact, that is their opinion. Simplistic, maybe, but I hope it drives my point home.

And using current stats to compare players all playing MLB at the same time is one thing, and obviously hard enough to do based on a lot of what has been discussed already. But to expand such comparisons to now include several players over a number of different years and dramatically different eras of the game, and to then think that statistics alone could ever provide a definitive answer to such comparisons, is sheer lunacy. And making and using a blanket statement that pitchers like Grove and Spahn played back in the day when players were weaker and nowhere near as good as today's ballplayers, and therefore Grove and Spahn are nowhere near as good as today's pitchers, as part of such a statistical analysis to compare pitchers, is not just wrong, it is downright insulting to Grove, Spahn, and everyone playing MLB back when those two were pitching. Just taking a pitcher today and throwing him back in Grove's day, completely ignores the context of the different times, different game, and on and on.

Often when people talk about financial matters from different periods or eras, they may at least try to reflect or account for those different eras by adjusting numbers for inflation so they can say something that cost $XXX in 1921, would cost or be worth $YYY in 2021, as "adjusted for inflation". It likely is not a perfect way to account for the different eras, but at least it lends for the information being more relevant and comparable to people today. What is needed to even begin to make blanket statements about how good (or bad) players from a certain era were, is some type of "adjusted for inflation" equation or formula to at least try to account for ALL the differences and variables faced by players from different times and eras. I doubt a formula/equation to perform such an "adjusted for inflation" calculation even exists. But I wouldn't be surprised if you asked 10 different statisticians to independently of each other work up such a formula/equation, assuming you could find 10 to even try, that they'd all (or at least a majority of them) come up with something at least slightly different. In other words, they'd each probably have their own, differing "opinion" as to what this "adjusted for inflation" calculation should.

And the very last line you typed highlights maybe the biggest problem of all. In the case of a subjective question like who's the greatesty lefty pitcher of all time, the statitisticians can't definitively prove they are right. But then unfortunately, we can't definitely prove them wrong either.