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

[craig]

From my understanding, you are essentially right that it is 50% Taking the two teams playing into consideration I cannot imagine that one team is ever more than 53% chance.

craig

[shemp]

I would have to reacquaint myself with Poussin distributions to accept this presumably elementary fact... It's late and I'm old and lazy.

Heh. Now I've convinced myself it is trivial (assuming the top half is independent of the bottom half). I'm still surprised.

Aye. There's the rub. It shouldn't be independent.

Okay. I give.

[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).

According to this article, P(average MLB ace saves a 1-run game with 0 out) is .81. Think about it.

[THAY3R]

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Let's go pitcher by pitcher :

Wang : Taken out in the 7th after 86 [censored] pitches. OH NO A LEFTY IS UP LETS TAKE OUT ONE OF THE BEST STARTERS IN THE LEAGUE SO WE CAN PITCH THIS REALLY OLD GUY FOR ONE AT BAT BRILLIANT!!

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i thought clemens was better than him? ONE OF THE BEST STARTERS

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Clemens is better than Wang....what's your point?

[disjunction]

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Let's say that you have a 50% chance to win if you come up in the top of the 10th. I thought it would be lower but just looked it up in The Book and it said .500. If you pitch Proctor you win (2/3)(1/2) or a 33.3% of the time. With Rivera you win (3/4)(1/2) or 37.5% of the time. So putting Rivera in is worth over 4% of a win. While I can't recall the numbers from stuff I've read on the closer, it's hard to imagine that in expectation he will be worth more than that tomorrow.

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The 50% isn't constant for both cases. In one case, you have a fresh Mariano Rivera coming in to pick up the save. In the other case, you have a fresh Scott Proctor. Now of course, as Triumph has said, you may score 5 runs in the top of the 10th, in which case it doesn't matter who comes in, it only matters who got you past the 9th. In return, you get to keep Rivera for tomorrow but it's not enough compensation by itself.

But the argument for the other side is that Proctor somehow becomes less effective when protecting a 1-run lead, and the whole game is on him. If this is true at all, it is THE determining factor. I don't know what the research says about what happens to setup men in closer situations. I'm sure we can guess what Torre would say.

I'm late to this discussion, sorry if I missed something.

[shemp]

Another part of both teams winning 50% of tied 9th inning games/extra inning games (that go at least one more inning) is that they don't necessarily win them in the next inning. So assuming that less than 1/2 are ended in precisely the next inning, the result for the calculation Jared is using (using made up numbers) is somewhere around 2% (as opposed to 4%, above).

[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...

[Triumph36]

disjunction -

there is no reason to assume that proctor is any worse at holding one run leads than he is at preserving a no-run lead. even though proctor has several blown saves in his career (and only one save, IIRC), we'd need a much bigger sample size.

how about having rivera warming up for a higher leverage situation in the ninth? baltimore's best hitters were coming up if patterson got on. after chris gomez, mariano rivera should've been brought in.

i mean, it's pretty intuitively obvious that rivera should be brought in - why was chris ray brought in for the top of the ninth? oh because 'there won't be a lead he has to protect'.

[disjunction]

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disjunction -

there is no reason to assume that proctor is any worse at holding one run leads than he is at preserving a no-run lead. even though proctor has several blown saves in his career (and only one save, IIRC), we'd need a much bigger sample size.

how about having rivera warming up for a higher leverage situation in the ninth? baltimore's best hitters were coming up if patterson got on. after chris gomez, mariano rivera should've been brought in.

i mean, it's pretty intuitively obvious that rivera should be brought in - why was chris ray brought in for the top of the ninth? oh because 'there won't be a lead he has to protect'.

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Well since there is an absence of information you'd have to assume Proctor's change of effectiveness in one-run situations is "average" for a middle reliever. Problem is I don't know what "average change" means. Torre might think he'd fall apart and be devasted at turning a win into a loss and lose his effectiveness for the next 2 months. A google search of clutch pitching sabermetric turned up nothing.

Since the situation he was in seemed like a lot of pressure anyway, I guess I buy your argument.

[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.

[/ QUOTE ]

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).

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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.

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).

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.