Flava4455
Joined: Apr 26, 2019
• Posts: 4
April 26th, 2019 at 7:55:12 PM permalink
Hi all and thanks for the help in advance. I may be overthinking this but figured I would run it by some math wizards here. I'm trying to calculate the chance of a run being scored in the first inning based off percentages. For example Tampa Bay vs Houston Astros. Tampa Bay season to date has scored a run in the 1st inning 60% of the time. Houston Astros have scored a run in the first inning 28% of the time.

Do you simply take the average of the 2 and say there is a 44% chance that a run will be scored in the first inning? Or is there different formula that takes into account multiple events, etc?

One step further, on average the opponent of Tampa Bay scores a run in the first inning 16% of the time and an opponent scores a run against the Houston Astros 48% of the time in the first inning.

How would you calculate the chances of a run be scored in the first inning using all variables? (Tampa Bay 1st Inning Runs Scored 60% of the time and opponent gets a Run 28% of the time. Houston Astros Score a Run 28% of the time in the first inning and their opponents score a run 48% of the time)
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4032
April 26th, 2019 at 8:02:41 PM permalink
I would treat the two half-innings as independent events. The Rays don't score in the first inning 40% of the time, and the Astros don't 72% of the time, so the two of them combined would have a 40% x 72% = 28.8% of not scoring in the first inning, or a 71.2% that at least one of them does.

Of course, there's far more involved than this - the specific pitchers, for one.
Flava4455
Joined: Apr 26, 2019
• Posts: 4
April 26th, 2019 at 8:33:54 PM permalink
Thanks, still wrapping my head around this. What is the reason you used the chance of this not happening to start the calculation? 72% and 28.8%. Calculating the other way 60×28=16.8% just doesn't sound right but not sure of the logic behind your calc
Rigondeaux
Joined: Aug 18, 2014
• Posts: 2537
April 26th, 2019 at 8:37:49 PM permalink
Quote: Flava4455

Hi all and thanks for the help in advance. I may be overthinking this but figured I would run it by some math wizards here. I'm trying to calculate the chance of a run being scored in the first inning based off percentages. For example Tampa Bay vs Houston Astros. Tampa Bay season to date has scored a run in the 1st inning 60% of the time. Houston Astros have scored a run in the first inning 28% of the time.

Do you simply take the average of the 2 and say there is a 44% chance that a run will be scored in the first inning? Or is there different formula that takes into account multiple events, etc?

One step further, on average the opponent of Tampa Bay scores a run in the first inning 16% of the time and an opponent scores a run against the Houston Astros 48% of the time in the first inning.

How would you calculate the chances of a run be scored in the first inning using all variables? (Tampa Bay 1st Inning Runs Scored 60% of the time and opponent gets a Run 28% of the time. Houston Astros Score a Run 28% of the time in the first inning and their opponents score a run 48% of the time)

If I were to attempt handicapping this, I'd include more factors. Most notably the starting pitchers. If Verlander is pitching, does it really matter how often Cole or any other Astros SP gives up runs in the first inning?

You might also look at righty/lefty splits for the first part of the order.
Flava4455
Joined: Apr 26, 2019
• Posts: 4
April 26th, 2019 at 8:40:35 PM permalink
Most definitely agree there are more factors to look at and factor in but really trying to lock down a solid starting point using 1st first inning stats. You can break down the starting stats like that by pitcher too...
Flava4455
Joined: Apr 26, 2019
• Posts: 4
April 26th, 2019 at 9:11:10 PM permalink
Quote: ThatDonGuy

I would treat the two half-innings as independent events. The Rays don't score in the first inning 40% of the time, and the Astros don't 72% of the time, so the two of them combined would have a 40% x 72% = 28.8% of not scoring in the first inning, or a 71.2% that at least one of them does.

Of course, there's far more involved than this - the specific pitchers, for one.

After some more searching found a good probability calculator. ThatDonGuy you were right, here is alittle more in depth for anyone else checking this out. Thanks!

Tampa 60% and Astros 28%

Probability of A NOT occuring: P(A')0.4
Probability of B NOT occuring: P(B')0.72
Probability of A and B both occuring: P(A∩B)0.168
Probability that A or B or both occur: P(A∪B)0.712
Probability that A or B occurs but NOT both: P(AΔB)0.544
Probability of neither A nor B occuring: P((A∪B)')0.288
Probability of A occuring but NOT B:0.432
Probability of B occuring but NOT A:0.112

Steps

P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.6 + 0.28 - 0.168
= 0.712
RisingDough
Joined: Oct 4, 2016