~~~ OFFICIAL YANKEES 2007 WORLD SERIES CHAMPIONS OR BUST THREAD ~~~

[shemp]

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I'm quite surprised as well and wouldn't mind someone checking to make sure I'm not an idiot reading the chart wrong even after quintuple checking.

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I'm floored by that stat. And not that it approaches 4% of a win (obviously), but there is (I'm guessing) a much greater than 4% chance that a save situation will arise tomorrow.

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The main thing you are missing is the difference between P(Rivera saves) and P(Proctor saves).

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To the extent that I'm missing it, it's because no one (me included) has produced it. Also, it's unlikely to be the main thing, in that we aren't talking about that situation...

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It is absolutely the main thing, because you claim that it is optimal to save Rivera for a "better" situation, which you maintain is bringing him in for a save situation either later in the game or tomorrow.

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I've made no such claim. My claim is that a sensible justification for Torre's action exists, and said actions are with-in the received wisdom of the game and are consistent with a division of labour that managers find useful. I would use my bullpen resources differently than Joe Torre. I'm convinced that that fact alone doesn't make him a moron-- and I find it more interesting to find a justification for what he's doing than declaring him an idiot.


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The probabilities we need to compare are

P(Rivera gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Proctor converts save)

and

P(Proctor gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Rivera converts save).



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I don't understand 1) why you think I need to compare these probabilities. 2) why the middle term of the multiplications disappears w/o comment (it changes magnitude) 3) why the final term is not the same for each (should be Mo saves in both?) 4) how the above values the specific thing that we are hesitant to do, namely, use our closer for 3 outs with no chance of a save, and for 6 outs when those six outs will often include no chance of a save.

The crux of it is the view that a d% increase in getting a win is more valuable than a d% decrease in avoiding a loss because of the finality of a closing a game versus the lack of finality of extending the game.

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According to the figures you made up, P(Rivera gets out of jam) = .33 and P(Proctor gets out of gam in 9th) = .25.

According to the Hardball Times article I linked to earlier, P(average MLB ace saves a 1-run, 1-inning lead) = .81. Proctor's a pretty good reliever, and there are some crappy "aces" out there, so let's say his ability to save a 1-run lead is close to this.

Rivera's career save percentage is .88, and while that includes some tough multi-inning saves, it also includes a lot of cushy 2- and 3-run, 1-inning saves. I'd estimate his ability to save a 1-run 1-inning game at around .85.

We have

P(Proctor gets out of jam) * P(Rivera converts 1-run 1-inning save) = .25 * .85 = .2125

whereas

P(Rivera gets out of jam) * P(Proctor converts 1-run 1-inning save) = .33 * .81 = .2673,

ergo, it is better to use Rivera to put out the fire in the 9th! The situation is even clearer than this, because the save situation that materializes down the road may be an even easier one in which the difference between Proctor's ability to save a lead and Rivera's ability to save the lead is even smaller.

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[GuyIncognito]

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I'm quite surprised as well and wouldn't mind someone checking to make sure I'm not an idiot reading the chart wrong even after quintuple checking.

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I'm floored by that stat. And not that it approaches 4% of a win (obviously), but there is (I'm guessing) a much greater than 4% chance that a save situation will arise tomorrow.

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The main thing you are missing is the difference between P(Rivera saves) and P(Proctor saves).

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To the extent that I'm missing it, it's because no one (me included) has produced it. Also, it's unlikely to be the main thing, in that we aren't talking about that situation...

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It is absolutely the main thing, because you claim that it is optimal to save Rivera for a "better" situation, which you maintain is bringing him in for a save situation either later in the game or tomorrow.

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I've made no such claim. My claim is that a sensible justification for Torre's action exists, and said actions are with-in the received wisdom of the game and are consistent with a division of labour that managers find useful. I would use my bullpen resources differently than Joe Torre. I'm convinced that that fact alone doesn't make him a moron-- and I find it more interesting to find a justification for what he's doing than declaring him an idiot.


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Saving the closer for a "save situation" is exactly how "conventional wisdom" dictates the "division of labor" in a bullpen. If that's not the "better situation" for which you're thinking of saving Rivera, what is???

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The probabilities we need to compare are

P(Rivera gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Proctor converts save)

and

P(Proctor gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Rivera converts save).



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I don't understand 1) why you think I need to compare these probabilities. 2) why the middle term of the multiplications disappears w/o comment (it changes magnitude) 3) why the final term is not the same for each (should be Mo saves in both?) 4) how the above values the specific thing that we are hesitant to do, namely, use our closer for 3 outs with no chance of a save, and for 6 outs when those six outs will often include no chance of a save.


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1) The point is to show that the strategy of using Rivera in a tie game dominates the strategy of saving him for a save situation; 2) the middle term is mostly a function of everyone else on the team and doesn't change much depending on who is used for the 9th; 3) replacing P(Proctor converts save) in the first situation with P(Bruney converts save) or P(tired Rivera converts save) also doesn't change much; 4) if you use simply P(Yankees score some runs in the 10th or later) for the middle term, it attempts to evaluate the chance of winning the game (up to some undetermined factors that are roughly equal in each scenario), which is what matters.

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The crux of it is the view that a d% increase in getting a win is more valuable than a d% decrease in avoiding a loss because of the finality of a closing a game versus the lack of finality of extending the game.


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You make two significant errors in the statement above:

1) In the first scenario you implicitly assume that the Yankees do get out of the 9th, score some runs and get into a position to win the game, whereas in the second you do not assume that.

2) Much more importantly, d is not the same in the two situations. Rivera has a bigger advantage over Proctor/Bruney/etc. in protecting a tie or getting out of a jam in the 9th than in closing out the 10th or later inning with a lead and no one on.

[Toro]

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I'm quite surprised as well and wouldn't mind someone checking to make sure I'm not an idiot reading the chart wrong even after quintuple checking.

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I'm floored by that stat. And not that it approaches 4% of a win (obviously), but there is (I'm guessing) a much greater than 4% chance that a save situation will arise tomorrow.

[/ QUOTE ]

The main thing you are missing is the difference between P(Rivera saves) and P(Proctor saves).

[/ QUOTE ]

To the extent that I'm missing it, it's because no one (me included) has produced it. Also, it's unlikely to be the main thing, in that we aren't talking about that situation...

[/ QUOTE ]

It is absolutely the main thing, because you claim that it is optimal to save Rivera for a "better" situation, which you maintain is bringing him in for a save situation either later in the game or tomorrow.

[/ QUOTE ]

I've made no such claim. My claim is that a sensible justification for Torre's action exists, and said actions are with-in the received wisdom of the game and are consistent with a division of labour that managers find useful. I would use my bullpen resources differently than Joe Torre. I'm convinced that that fact alone doesn't make him a moron-- and I find it more interesting to find a justification for what he's doing than declaring him an idiot.


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Saving the closer for a "save situation" is exactly how "conventional wisdom" dictates the "division of labor" in a bullpen. If that's not the "better situation" for which you're thinking of saving Rivera, what is???

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The probabilities we need to compare are

P(Rivera gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Proctor converts save)

and

P(Proctor gets out of jam in 9th) * P(save situation comes up later in the game or tomorrow) * P(Rivera converts save).



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I don't understand 1) why you think I need to compare these probabilities. 2) why the middle term of the multiplications disappears w/o comment (it changes magnitude) 3) why the final term is not the same for each (should be Mo saves in both?) 4) how the above values the specific thing that we are hesitant to do, namely, use our closer for 3 outs with no chance of a save, and for 6 outs when those six outs will often include no chance of a save.


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1) The point is to show that the strategy of using Rivera in a tie game dominates the strategy of saving him for a save situation; 2) the middle term is mostly a function of everyone else on the team and doesn't change much depending on who is used for the 9th; 3) replacing P(Proctor converts save) in the first situation with P(Bruney converts save) or P(tired Rivera converts save) also doesn't change much; 4) if you use simply P(Yankees score some runs in the 10th or later) for the middle term, it attempts to evaluate the chance of winning the game (up to some undetermined factors that are roughly equal in each scenario), which is what matters.

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The crux of it is the view that a d% increase in getting a win is more valuable than a d% decrease in avoiding a loss because of the finality of a closing a game versus the lack of finality of extending the game.


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You make two significant errors in the statement above:

1) In the first scenario you implicitly assume that the Yankees do get out of the 9th, score some runs and get into a position to win the game, whereas in the second you do not assume that.

2) Much more importantly, d is not the same in the two situations. Rivera has a bigger advantage over Proctor/Bruney/etc. in protecting a tie or getting out of a jam in the 9th than in closing out the 10th or later inning with a lead and no one on.

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Do you guys bring calculators to the ballpark when you go to a game?

[GuyIncognito]

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Do you guys bring calculators to the ballpark when you go to a game?

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Well, uh, my cell phone has a calculator in it.

But come on. Rob Neyer has been arguing this point for years.

[THAY3R]

It's not nerdy math it's just [censored] common sense.

If you let up a run, you lose the [censored] game, what's a more important situation than that?

[Triumph36]

shemp is trying to confound the issue with complex mathematics - as thayer says, it's straightforward

[shemp]

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The crux of it is the view that a d% increase in getting a win is more valuable than a d% decrease in avoiding a loss because of the finality of a closing a game versus the lack of finality of extending the game.


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You make two significant errors in the statement above:

1) In the first scenario you implicitly assume that the Yankees do get out of the 9th, score some runs and get into a position to win the game, whereas in the second you do not assume that.


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I just skimmed your post. This is another in a long line of non-sequitors that doesn't address what I've said and accuses me of some imaginary fundamental mistake.

My assertion that bringing in your closer with a lead to close the game does not contain a hidden assumption about bringing in your closer in a tie game.

You reasserting this and adding an "absolutely" will not make it so!

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2) Much more importantly, d is not the same in the two situations. Rivera has a bigger advantage over Proctor/Bruney/etc. in protecting a tie or getting out of a jam in the 9th than in closing out the 10th or later inning with a lead and no one on.

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This does address what I said and I find it interesting. Just to make sure I have you right.

Given two situations: 1) bottom of the ninth tie game, success is you need 3 outs to extend the game; 2) bottom of the ninth, you have a 1 run lead, success is 3 outs give you a win. I gather you are asserting that Rivera's success rate is higher in situation 1) than 2)? I would have guessed they were the same.

You have some rationale or data (assuming I've understood)?

[shemp]

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Saving the closer for a "save situation" is exactly how "conventional wisdom" dictates the "division of labor" in a bullpen. If that's not the "better situation" for which you're thinking of saving Rivera, what is???

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This seems to deserve an answer. I studied and worked in mathematical optimization for several years. I make no claims about which approach is optimal. I don't talk about optimization in these forums.

I do doubt the decision is of much consequence and close enough to rely on human factors-- and as I've said, I would handle it differently.

The approach that is looking for a better situation considers a close situation better, today or tomorrow-- also the exact same situation an inning deeper in the game without you having brought in your closer.

I may post in this thread tonight, after that I may or not come back to this for a couple days.

[GuyIncognito]

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The crux of it is the view that a d% increase in getting a win is more valuable than a d% decrease in avoiding a loss because of the finality of a closing a game versus the lack of finality of extending the game.


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You make two significant errors in the statement above:

1) In the first scenario you implicitly assume that the Yankees do get out of the 9th, score some runs and get into a position to win the game, whereas in the second you do not assume that.


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I just skimmed your post. This is another in a long line of non-sequitors that doesn't address what I've said and accuses me of some imaginary fundamental mistake.

My assertion that bringing in your closer with a lead to close the game does not contain a hidden assumption about bringing in your closer in a tie game.


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Buh? If I employed a non-sequitur, it's not in the part of my post that you just quoted. My point, and everyone else's, was that the "d% increase in getting a win" never materializes if Proctor loses the game in the 9th. Sure, you get the upside of keeping Rivera fresh, but that's not really much of an upside given that Rivera is 6th among his bullpen mates in innings pitched this season.

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2) Much more importantly, d is not the same in the two situations. Rivera has a bigger advantage over Proctor/Bruney/etc. in protecting a tie or getting out of a jam in the 9th than in closing out the 10th or later inning with a lead and no one on.

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This does address what I said and I find it interesting. Just to make sure I have you right.

Given two situations: 1) bottom of the ninth tie game, success is you need 3 outs to extend the game; 2) bottom of the ninth, you have a 1 run lead, success is 3 outs give you a win. I gather you are asserting that Rivera's success rate is higher in situation 1) than 2)? I would have guessed they were the same.

You have some rationale or data (assuming I've understood)?

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Assuming the offensive lineups are the same, then yes, situations 1) and 2) are identical. But that's not the whole story here -- we must also consider in 1) situations where men are on base, and in 2) situations where the Yankees have more than a 1-run lead in the 10th (or later). In each modification, you prefer to have Rivera pitch the 9th and a lesser reliever pitch the 10th. In yesterday's game, not only did the Orioles load the bases in the 9th with 1 out , they had their big bats coming up. Once that happens, Rivera's gotta come in.

The data I supplied was that Rivera has maybe a 85:81 advantage in saving a 1-run lead for 3 outs with nobody on. This ratio goes down significantly if the lead is 2 runs or more. In the bases-loaded-and-1-out-in-a-tie-game scenario, the figure we made up was 33:25, which is quite a bit bigger.

[Triumph36]

good thing rivera was all rested for his appearence in the 8th tonight - we needed those outs