Baseball probability ??? Plz help

In baseball, if the score is tied at 4 midway through the ninth inning, and the home team wins, what is the approximate likelihood of the total being higher than 9.5?

Also how would I aquire this calculation



Thanks

Is there another place that I should post this?I apologize if it's in the incorrect place.Also is there a way to specifically ask the wizard? This is a test question for a job opportunity.Almost seems to be a trick question the way it's worded.

Thanx

Quote: Newtostats

In baseball, if the score is tied at 4 midway through the ninth inning, and the home team wins, what is the approximate likelihood of the total being higher than 9.5?

Also how would I aquire this calculation



Thanks

I would have posted this in the sports betting section. The way I would analyze this is to through by brute force, going through as many games as possible in which you have inning by inning scores.

Quote: Newtostats

In baseball, if the score is tied at 4 midway through the ninth inning, and the home team wins, what is the approximate likelihood of the total being higher than 9.5?

One of either things has to happen:
(a) The home team scores 2 runs (or more) in the bottom of the ninth;
(b) Either team scores 2 runs (or more) in the tenth or later inning;
(c) Both teams score 1 run in the tenth or later inning.

I am assuming that this sort is question is answered by seeing how often it has happened up to this point. There are any number of baseball statistics sites; the question is, how many have this kind of information? For example, does anybody maintain a list of the games that were tied after 8 1/2 innings?

Quote: ThatDonGuy

One of either things has to happen:
(a) The home team scores 2 runs (or more) in the bottom of the ninth;
(b) Either team scores 2 runs (or more) in the tenth or later inning;
(c) Both teams score 1 run in the tenth or later inning.

I am assuming that this sort is question is answered by seeing how often it has happened up to this point. There are any number of baseball statistics sites; the question is, how many have this kind of information? For example, does anybody maintain a list of the games that were tied after 8 1/2 innings?

Aren't B & C the same thing? If both teams score one run in the tenth, or later, inning AND the game cannot end in a tie, one team must score two, or more, runs in the tenth inning or later.

Quote: Mission146

Aren't B & C the same thing? If both teams score one run in the tenth, or later, inning AND the game cannot end in a tie, one team must score two, or more, runs in the tenth inning or later.

The question stats the HOME TEAM WINS just does not say in the 9th inning

Quote: Mission146

Aren't B & C the same thing? If both teams score one run in the tenth, or later, inning AND the game cannot end in a tie, one team must score two, or more, runs in the tenth inning or later.

But also note that he said the HOME team has to win, as well. So if the Away team scores at all in extras, the Over hits because he only wants to look at games that Home team wins, and the Home team is going to have to score again (at least twice actually) to win.

So it's
Home team scores one in the Bottom 9th UNDER
Home team scores two in the Bottom 9th or 10th or later (HR or Ground Rule Double or other, rarer oddity) OVER
Away team scores 1 run in 10th or later and Home team comes back to win. OVER
(The subset of just the Away Team scoring a Run in the 10th or later doesn't count because the Home team has to win.)
Home team scores 1 run in 10th or later UNDER

I think you can reduce the number of scenarios further -
Visiting team scores next - over
Home team scores next - under if one run, over if two or more.

Simplistically, if you believe each of those has an equal chance of occurring, then the answer is 2 out of 3.

Otherwise, you might have to do a statistical analysis to determine how frequently each of those things happened and add them up.

Quote: coilman

The question stats the HOME TEAM WINS just does not say in the 9th inning

I missed that part. Either the home team scores 2 runs in an inning, or both teams score 1 each in the same inning (and then the home team scores more than the visiting team in a later inning).

Quote: cclub79

But also note that he said the HOME team has to win, as well. So if the Away team scores at all in extras, the Over hits because he only wants to look at games that Home team wins, and the Home team is going to have to score again (at least twice actually) to win.

So it's
Home team scores one in the Bottom 9th UNDER
Home team scores two in the Bottom 9th or 10th or later (HR or Ground Rule Double or other, rarer oddity) OVER
Away team scores 1 run in 10th or later and Home team comes back to win. OVER
(The subset of just the Away Team scoring a Run in the 10th or later doesn't count because the Home team has to win.)
Home team scores 1 run in 10th or later UNDER

A bases loaded ground rule double in the bottom of the 9th of a 4-4 game, results in a 5-4 final score. This was a long debated topic on several forums for years, as it leads to conflicting rules coming into play
1. The game is over as soon as the runner from 3rd crosses home plate
2. On a ground rule double all runners advance 2 bases.

Quote: Dalex64

I think you can reduce the number of scenarios further -
Visiting team scores next - over
Home team scores next - under if one run, over if two or more.

Simplistically, if you believe each of those has an equal chance of occurring, then the answer is 2 out of 3.

Otherwise, you might have to do a statistical analysis to determine how frequently each of those rhings happened and add them up.

This is an elegant idea. However, the 1/3 is going to way too simplistic, even comparing home team scores first vs visiting team scores first is not straightforward, since home team is up next.

Quote: michael99000

A bases loaded ground rule double in the bottom of the 9th of a 4-4 game, results in a 5-4 final score. This was a long debated topic on several forums for years, as it leads to conflicting rules coming into play
1. The game is over as soon as the runner from 3rd crosses home plate
2. On a ground rule double all runners advance 2 bases.

Odd since wouldn't that also apply to a HR? Game over as soon as the runner from 3rd crosses? While the game is technically over (see Mets Walkoff Grand Slam), I was under the impression the game did allow for advancement if the advancement was procedural (completing an earned base).
Of course a runner can cross home plate and the game ISN'T over, if a force out occurs after said crossing.

But now that I think of it, you are probably right, since they don't count two runs if there's an overthrow into the stands in the bottom of the 9th. Probably just an exception for HR then. But I'm going to keep trying to think of a way more than 1 run can score :)

Once upon a time, the odds of scoring one or more runs in an inning were 27.5% http://www.nssl.noaa.gov/users/brooks/public_html/feda/datasets/expectedruns.html

I don't have a link handy, but in a walk-off out of the park home run, all of the runs can be allowed to count. In most other situations, the game ends as soon as the first run scores.

Quote: cclub79

Odd since wouldn't that also apply to a HR? Game over as soon as the runner from 3rd crosses? While the game is technically over (see Mets Walkoff Grand Slam), I was under the impression the game did allow for advancement if the advancement was procedural (completing an earned base).

Only in the specific case of an over-the-fence home run. In all other "awarded bases" situations, the "minimum number of bases needed for the winning run to score" rule takes precedence.

You are right that is it a possible trick question. Nowhere does it say that the home team wins only in the bottom of the 9th inning, so I would say that having the game go into extra innings is certainly a possiblity.

However there is only one way in which more than one run would be able to be scored in the bottom of the ninth as per the rules of baseball. That is a home run. Also it is possible that once the winning run scores, that the person who hit the home run could stop at any time after hitting first base. They would be given credit for the last base reached only. I recall this happening in exactly one occasion, and it was the Mets it happened to. I recall Robin Ventura hitting a walk off home run to win a game in the bottom of the ninth, but he was swarmed after rounding second base, and never proceeded to actually touch home plate. I do not remember the date, aside from it being early 2000s and I do not remember the final score (6-4 I believe if I were to guess).

To boil it down since I am not a statistical genius like others, it would be these likely possible scenarios happening.

A) Visiting team wins in extra innings 5-4
B) Visiting team wins in extra innings over 9.5 runs scored
C & D) Home team wins in either the 9th extra innings 5-4 (lose)
E) Home team wins via walk off home run in the 9th scoring more than one run
F) Home team wins in extra innings over 9.5 runs scored (the c/d scenario covers the losing scenario of this)

IF, and that is a big if, they are just as likely to happen, then the answer would be 4 losing scenarios and 2 winning scenarios.

Quote: Newtostats

In baseball, if the score is tied at 4 midway through the ninth inning, and the home team wins, what is the approximate likelihood of the total being higher than 9.5?...

The questioner is asking for only the approximate likelihood. My answer would be approximately 0.