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February 11, 2008 at 8:50 AM

The uncertain nature of probability

Came across yet another interesting read on Lookout Landing over the weekend. What makes it interesting is that it strikes at the heart of the disconnect between those fans who lean heavily on newer, statistics-based research versus those who insist the uncertain nature of baseball makes it unlikely that any season can be predicted reliably.
Here is the main thrust of the argument the author makes:
“Two friends are arguing over the likely outcome of a set of ten coin tosses.
One declares — quite sensibly, since these coins are known to be fair — that he expects said coins to be distributed evenly.
The other, more radical in thought, feels that they’ll come up all heads but one.
The coins are flipped. Nine heads, one tails.
‘Ah’, says the second friend, quite happy, ‘You were wrong. That’s why we flip the coins!’

Very clever post. A response, one would think, to our “That’s why they play the games” point from last week. Hey, I welcomed folks to start using and thinking about that line, so I’m glad to see some are taking me up on it. First off, let me clear up some perceptions: all of you are fans of baseball, if not the Mariners, or I doubt you’d spend much time on this site. So, please, when you’re talking to one another, do it with respect. Adam is as much a part of this blog as Merrill, or Mr. X, or Oregongal.
Secondly, when we talk about “That’s why they play the games” we’re not suggesting the Kansas City Royals have as good a shot as, say, the Boston Red Sox do of winning the World Series this coming season. In regards to the Mariners, we are simply basing that statement off of our own list of analytical points, which, quite clearly, run contrary to opinions — because that’s what they are — espoused by some other, equally devoted, fans or bloggers. We are conceeding that we are not always going to be right and that those who disagree with us do have a shot at seeing some of their predictions come true.
Of course, some predictions are “more probable” than others. A lot of legwork goes into some and they can be more valid than those that involve gut hunches.
But can this be likened to a coin flip? As much as I loved the author’s anecdotal style, no. Because the absolute certainty of coin flips — in which there are two absolute outcomes of ‘heads’ or ‘tails’ with no degree of variance from that 50-50 proposition — does not exist in a sport where perhaps a 75-sided coin might better explain the challenges any prediction faces.

My first hunch that the coin-flip analogy would be misused by some was confirmed when I saw a reader in the LL thread write in about last Sunday’s Super Bowl.
“You’d think this would be common sense,” he writes of the coin-flip analogy. “But it’s not. Football Outsiders correctly argued this last Super Bowl was one of the largest mismatches ever, but when the Giants won, countless people took that as proof that their system doesn’t work. Or, worse, is fabricated. I hate to be intolerant or elitist, but some people seem, if not incapable, at least retarded from thinking in anything but absolutes. I fear you cannot simply explain away that weakness.”
Forget the condescending tone for a moment and examine the argument. It states that anyone who argued beforehand that last weekend’s Super Bowl was one of the largest mismatches ever were totally correct. Really? By what measurement? Las Vegas oddsmakers? What were they basing their arguments on? How about the arguments by Football Outsiders (I suspect this term means stats-minded fans who never really played the game…but I don’t know for sure). So, they were ‘correct’ in calling it a mismatch? Really? OK, so what were they going off of?
I dispute the contention that the Super Bowl was one of the greatest mismatches ever. Here is what I wrote on this blog the night before that game was played.
“By the way, for what it’s worth, I think the Giants have a good shot at upending New England tomorrow. Better than just about any NFC team would have. Aw heck, I think they’re going to win, and not just because of the defensive line. That alone won’t do it. For me, having a 265-pound running back helps. If the Giants control the ball, it should be very interesting. That means Plaxico Burress needs to play the game of his life and make the first down catches like he did in Green Bay. If you can beat up on Al Harris, you can take any corner in the league. The biggest deal in this game? If I was a betting man, I’d say the lack of a fear factor plays into New York’s hands more than anything else. They won’t waste the first quarter being in awe of the Patriots, since they just played them a month ago. That’s a huge deal in football. Bigger than some folks realize.”
Apparently so, since the Giants did indeed win. Sure, not every word of what I wrote is what actually transpired. But as far as predicitons go, it was a pretty darned good one. The Giants did indeed control the ball and threw Tom Brady and his offense off their rhythm. Without the full 265-pound girth of running back Brandon Jacobs, the Giants probably would have been stopped on a 4th-and-1 play at midfield on the game’s decisive drive. And while Burress did make the winning TD catch, he was double-and-triple-teamed throughout the contest — though that did free-up other receivers to make those crucial third-down conversions (hello David Tyree). The defensive line, as expected, was a dominating force. As for the fear factor, or lack of one? At game’s end, the Giants, to a man, cited this as the reason for their victory. They talked of the confidence gained from nearly beating New England at season’s end and how they were not intimidated by the Patriots, their 18-0 record or their historical stats.
So, I reject the contention that “Football Outsiders” who labeled this one of the biggest mismatches of all-time were “correct” in that thinking. I’ll argue that folks who understand the game of football and were willing to look past the hype and put their reputations on the line would have logically concluded this was going to be a very close game. In fact, I’d argue that — because of the non fear-factor — these two teams could have played a best-of-seven series and it would have gone down to the wire. I feel the Pats were fortunate to have the lead in the final minute. They were badly outplayed. If Eli Manning makes a simple dump-off pass to Burress early in the final quarter, it’s an 80-yard New York TD and probably a 10-point win by the Giants.
Yes, I know that former star receiver and current NFL analyst Chris Collinsworth knows more than I ever will about football and picked the Pats. But he has a rep to protect and “called” the Pats as the game’s greatest team ever back in Week 5. Do you really think he was going to go out on a limb and pick the Giants?
So, was the analysis used by Collinsworth and the other fans who picked the Patriots in a Super Bowl mismatch, based on record and stats, any more valid than my own? Or were the factors I looked at (and which transpired, for the most part) the more valid factors to be studied? This is crucial to understanding the whole “coin flip” premise and why it’s inapplicable to the coming Mariners season.
I feel that my factors were the most prevalent in this case. Any coach will tell you the basics of football begin at the line of scrimmage. Control that and you control the game, its tempo and usually its outcome. That’s how I begin my analysis. So, when I see folks beginning theirs with a look at the quarterbacks and wideouts, I usually look at the opposing defense and whether it can neutralize a threat. Think the Pittsburgh Steelers and their defense and blitz schemes upending the “unbeatable” Colts back in January 2006, then holding Shaun Alexander to under 100 yards in that year’s Super Bowl. I look at whether a team’s offense can control the ball and keep the other side’s dominant QB and wideouts off the field.
Let’s move over to baseball now and some of the pro-versus-con arguments for the Mariners acquiring starting pitcher Erik Bedard.
There have been some compelling, well-researched arguments on both sides. But research alone will not make one argument more valid than the other.
One of the more compelling cases against acquiring Bedard is that Seattle’s outfield defense and offensive productivity will take too big a hit for the pitching upgrade to matter. Many of those favoring the coin-flip analogy see the defense-offense argument with as much certainty as they do a two-sided coin.
I do not.
For one, I have yet to see any defensive arguments that convince me. We all know defensive metrics are still in their infancy. Most of them look at a player’s ability to get to balls within a certain, pre-determined range, or make plays that an “average” fielder could get to. The balls “missed” by sub-par fielders are then looked at in a totality and assigned a run value over time.
It’s all a nice, neat package. But does it work? I didn’t see it work with Raul Ibanez last season. I was told his defense was costing the team a truckload of runs, though I went back and looked at every game and was hard-pressed to find many where he actually cost his team the decision. I saw far more where his bat helped decide the outcome.
I know, I know, the team defense thing works off averages and assumes that too many poor plays will ultimately lead to runs allowed. But what about the other variables? If Ibanez allows a single to drop in front of him, but Miguel Batista erases it with a double-play grounder on the next pitch, is Batista’s start really impacted by poor defense in left field?
If Ibanez allows one double to fall into the gap in left center for a run, but later hits a grand slam and Seattle goes on to win 8-1 in a three-hitter, how badly was the team and pitcher impacted?
Will Ibanez, or Brad Wilkerson, or Richie Sexson be harming Bedard if he strikes out every other batter he faces? If a ground-ball pitching staff can induce double-plays, is the poor defense mitigated?
In theory, I’ll agree that a team that makes too many mistakes in the field will allow more runs and lose more games.
But how much weight should this team be giving to that theory? More weight than the fact that teams with two potential “ace” pitchers (who can escape jams via strikeouts independent of fielders) tend to make the post-season more frequently than clubs with only one ace?
I tend to believe the defensive shortcomings in Seattle’s case are being overstated. I saw this team win 88 games last season with an outfield defense that was about as bad as this year’s is likely to be. I’d be a lot more worried if this team had five flyball pitchers in the starting rotation.
Some anti-trade advocates like to view the right field situation as a subtraction from Adam Jones to Brad Wilkerson. I don’t. I view it as going from Jose Guillen to Brad Wilkerson, since that’s what last year’s 88-win model was based off of. The defensive situation doesn’t seem as dire from year-to-year when you do it that way, does it?
In looking at the starting five, some people like to view a pitcher’s total contributions as a series of individual achievements. They’ll look at each pitcher’s projected performance and assign a “win value” to each and boost the team’s overall wins accordingly.
I don’t like to make my analysis so simple and neat. For instance, how much of a positive (or negative) impact will Felix Hernandez experience now that he’s no longer under pressure as the No. 1 guy in the rotation? Based on how young players can be negatively impacted by undue pressure as they try to find their way, I’d say it gives him one less thing to worry about. One more possibility of having that breakout season.
If the M’s lose four in a row, how will the increased likelihood of having at least a league-average starter (as opposed to Jeff Weaver or Horacio Ramirez) going in Game No. 5, reduce the possibility of a longer losing streak? I’d say it reduces the chance plenty. The thing with losing streaks is, the longer they get, the more pressure is put on a team and the more they tend to lose games that they’d otherwise win if entering the contest in a better frame of mind. Players and managers think so anyway. I know there are no statistics for this, but does that make the argument less important?
The whole point of this is that the “coin flip” and probability argument is only valid if you believe the starting point for a particular argument is correct.
I don’t believe that discussion on the 2008 Mariners begins with the outfield defense. I don’t believe that it begins with the offense needing to improve. I actually feel this offense can regress ever so slightly and still be part of a contender if the pitching upgrade is what I think it will be. My contention is actually validated by the team ERA+ and OPS+ stats of past playoff clubs. You don’t have to be outstanding in both scoring runs and not allowing them. You do usually have to excel in one area and be about league average or better in the other to have a chance at post-season play.
I believe the M’s can be a league average offensive team (they were four percent better than average last season) and post a well above-average ERA+ with roughly the same positional defense as they had last year.
We hear talk of Seattle’s Pythagorean record of 78 wins last season and are told they should come back down to Earth. What about the stats that show that teams outperforming their Pythag one year are likely to do so again the following season? (CORRECTION: I phrased this poorly; it should say that such teams are more likely to improve the following season than teams that underperformed their Pythag. There is a difference). Why do I rarely hear those numbers brought up? And what about the impact that a team’s bullpen can have on helping it outperform the Pythag. I know the stats we have on that are limited, but does that make the argument less compelling? I’d like to know whether adding two starters who threw as many or more seven-inning games as Hernandez last season will take pressure off the bullpen and prevent it from burning out down the stretch. Some will say those pitchers won’t go seven innings as often because of poor M’s outfield defense. Others say those pitchers can notch the strikeouts and infield double plays that will negate fielding mistakes.
So, who is right? Which sides of the coin are we looking at? Whose “probabilties” are we to believe and how many of the non-numbers factors can we choose to ignore?
For me, this is the most attractive part of the debate about the coming Mariners season. And for all I know, the people arguing that a defensive and offensive decline will kill this team may be right. But they could also, for the reasons I’ve explained, be very wrong.
And make no mistake. There will be some rights and wrongs at the end of this one. Using the coin flip analogy actually takes the heat off both sides in that whichever one is wrong can always say that they may have been right if the season were played out another nine times. The model was right even if the outcome was wrong, so to speak.
If only real life were that easy.
If only a GM could make that argument to his boss when all of his best-laid plans go up in smoke one or two particular times.
We all know that folks working in professional sports don’t always have that luxury.
Believe me, Bill Bavasi right now is basing his “coin flip” approach on the premise that having two potential aces in his rotation the two coming seasons is going to trump the need for an outstanding right fielder over the next six years. If it works out, it works out. That he may be excorciated as “wrong” from the outset and will always be “wrong” because the probabilities are against him seems a tad unfair.
Once again, whose probabilities? Those who feel positional defense needs to improved? Is their opinion the be-all, end-all of this debate?
I don’t think so. But then again, I could be wrong. Perhaps my starting point is the flawed one. We’ll have a better idea once the season gets underway. I’m very curious about the answer and whether I need to place greater weight on some other opinions I’ve heard about where my starting point for M’s analysis should be. As I’ve said, that’s why they play the games.



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