Average Runs Scored Given Vegas Over/Under Odds

When you look at the Over/Under, often referred to as the "Run Total" for a major league baseball game at a Sports Book you will see the run total given with a number like "7 runs" with juice looking something like -120/100 with the -120 being the pay out for the over and the +100 being the pay out for the under. Juice looking like -120/100 is telling you that the Sports Book thinks it is a little bit more likely that the game will go over than under. In fact, the Sports Book is telling you there is a 52.38% chance that the game goes over and a 47.62% chance that the game goes under. Here is my algorithm and calculator showing you how to convert from a Sports Book odds (Example: -120/100) to a percentage.

How about a game where the Sports Book thinks there is a 50/50 chance of the game going over or under (-110/-110)? If the run total was "7 runs" on such a game how many runs would you expect there to be scored if this game was played thousands of times? You might think the answer would be 7, but it is not. Seven runs would be the median or the the run total where you would have the same number of overs as unders. But what about the mean or the average number of runs scored per game. Since run totals are skewed, such that the most likely final score for almost any game with a 7 run over/under is the home team winning by a score of 3-2 (5 total runs) we see a mean that is different than the median. How do you calculate the mean?

It's not easy to calculate, the best way is to look at the empirical data. Look at games and track the run total, over juice and under juice and see what the average number of runs scored for each game with the same values for each of the three parameters. Quickly, the problem you run in to is a sample size problem. There are just not enough games out there (162 per year). So this won't work very well. The solution is to create a larger sample size and the way I did this was to use my simulator to create games with an average of 5.5 up to 11.5 runs with gaps of 0.05 runs per game. For example I created two teams that averaged 5.5 runs per game when playing each other a million times. I then adjusted the two teams to create an outcome that averaged 5.55 runs per game, all the while recording the percentage that this game went over or under the nearest run total.

For example, I created a game and simulated it one million times that outputted an average runs scored per game of 5.9902. The run total that was closest to 50% on the over/under for this game was 5-1/2 runs. The chances of this game going over was 48.64% and going under was 51.36%.

Once I get enough samples at each over/under I can get a best fit equation (y = mx + b) for each run total given that I know the chances that the game goes over and under. My simulator tells me this and in the Sports Book example the over/under odds tells me this. So once I have the equation built from the simulators empirical data, I can use those equations with the Sports Book odds once I calculate the over and under chances from the odds and juice.

So below is the table that shows you the equation for each Run Total. In the equation "x" is the percent chance (ie - 51.92) that the games goes "over".

Let's take the June 30th game between the Indians and Dodgers as an example. The Vegas Odds on the "Run Total" look like 7-1/2 +115/-125 which translates to an over chance of 45.45% and an under chance of 54.55%.

The equation for a game with a Run Total of 7-1/2 is: y = (0.087176)(45.45) - 3.87196653

Which tells us the average number of runs for this game (given that the Vegas Odds are true odds) is... 7.59 runs

An interesting side note is that let's say you have a Run Total of 7-1/2 runs with Vegas giving us a 50/50 chance of both the over and under hitting, that would give us an average run total of 7.99 runs.

Steps
1. Get Vegas Run Total
2. Use the table below to determine your slope(m) and offset(b)
3. Use Vegas odds on the Run Total to determine percent chance the game goes over(x)
4. Calculate average runs scored per game by running data through the equation y = mx + b


Equation To Calculate Average Runs Scored per Game

Run Total	Slope(m)	Offset(b)
5.5	0.080769	-3.441105344
6	0.075334	-3.300033236
6.5	0.085624	-3.943390956
7	0.076109	-3.405558745
7.5	0.087176	-3.87196653
8	0.082359	-3.752582135
8.5	0.088259	-4.16674672
9	0.079836	-3.677004771
9.5	0.094069	-4.284308333
10	0.084646	-3.923914961
10.5	0.091977	-4.398507575
11	0.0816	-3.78090425
11.5	0.095217	-4.329096995

.

Best Lineup - Boston Red Sox

Next up on my look at each teams most efficient lineup is the Boston Red Sox.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using ZIPs projections which are available on Fangraphs. The lineup results will only be as good as the projections.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.  In fact, I know that many of the results will not happen due to manager philosophies and veteran favoritism but these are the most optimal lineups that the simulator spit out.  In some cases the top couple of lineups had very small differences in results. The starting nine players were taken from MLBDepthCharts website.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians | Athletics | Astros
NL: Mets | Cubs | Padres | Marlins | Reds | Giants | Brewers | Dodgers

                 Red Sox 2014 ZIPS Hitting Projections

	K%	BB%	AVE	OBP	SLG	OPS	wOBA
Shane Victorino	13.4%	6.6%	0.269	0.331	0.420	0.751	0.331
Dustin Pedroia	11.1%	9.3%	0.285	0.352	0.425	0.777	0.340
David Ortiz	15.5%	12.9%	0.296	0.386	0.552	0.938	0.377
Mike Napoli	30.5%	12.2%	0.241	0.342	0.466	0.808	0.350
Xander Bogaerts	23.6%	8.0%	0.267	0.331	0.429	0.760	0.333
Daniel Nava	20.8%	8.8%	0.257	0.344	0.384	0.728	0.322
Jonny Gomes	26.9%	11.4%	0.236	0.335	0.408	0.743	0.327
Jackie Bradley	23.3%	8.4%	0.245	0.322	0.375	0.697	0.308
Will Middlebrooks	26.0%	5.2%	0.249	0.291	0.425	0.716	0.312
A.J. Pierzynski	15.4%	2.9%	0.267	0.297	0.430	0.727	0.312

See the results after the jump

Best Lineup - Houston Astros

Next up on my look at each teams most efficient lineup is the Houston Astros.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using ZIPs projections which are available on Fangraphs. The lineup results will only be as good as the projections.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.  In fact, I know that many of the results will not happen due to manager philosophies and veteran favoritism but these are the most optimal lineups that the simulator spit out.  In some cases the top couple of lineups had very small differences in results. The starting nine players were taken from MLBDepthCharts website.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians | Athletics
NL: Mets | Cubs | Padres | Marlins | Reds | Giants | Brewers | Dodgers

                 Astros 2014 ZIPS Hitting Projections

	K%	BB%	AVE	OBP	SLG	OPS	wOBA
Dexter Fowler	28.3%	13.7%	0.247	0.354	0.382	0.736	0.328
L.J. Hoes	16.7%	8.4%	0.271	0.337	0.366	0.703	0.313
Jason Castro	24.9%	10.8%	0.256	0.337	0.439	0.776	0.335
Chris Carter	33.8%	11.4%	0.228	0.319	0.461	0.780	0.340
Marc Krauss	30.1%	10.3%	0.213	0.298	0.369	0.667	0.296
Robbie Grossman	27.1%	11.2%	0.228	0.321	0.330	0.651	0.289
Jonathan Villar	27.8%	7.3%	0.235	0.295	0.356	0.651	0.287
Jose Altuve	12.5%	5.1%	0.285	0.323	0.384	0.707	0.308
Matt Dominguez	15.8%	5.3%	0.249	0.294	0.395	0.689	0.300
Jesus Guzman	22.8%	8.5%	0.249	0.318	0.416	0.734	0.320
George Springer	31.1%	9.9%	0.237	0.319	0.439	0.758	0.335

See the results after the jump

Best Lineup - Los Angeles Dodgers

Next up on my look at each teams most efficient lineup is the Los Angeles Dodgers.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using ZIPs projections which are available on Fangraphs. The lineup results will only be as good as the projections.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.  In fact, I know that many of the results will not happen due to manager philosophies but these are the most optimal lineups that the simulator spit out.  In some cases the top couple of lineups had very small differences in results.  For NL teams it is always better to bat your pitcher eighth but I am not even going to go there in this exercise as I know there is a 0% chance of a MLB manager actually doing that.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians | Athletics
NL: Mets | Cubs | Padres | Marlins | Reds | Giants | Brewers

Dodgers 2014 Hitting ZIPS Projections:

	K%	BB%	AVE	OBP	SLG	OPS	wOBA
Matt Kemp	24.8%	8.6%	0.274	0.339	0.473	0.812	0.342
Yasiel Puig	19.7%	8.5%	0.284	0.354	0.485	0.839	0.359
Hanley Ramirez	17.3%	8.6%	0.276	0.342	0.486	0.828	0.357
Adrian Gonzalez	17.0%	8.0%	0.282	0.339	0.453	0.792	0.335
Carl Crawford	16.5%	5.2%	0.266	0.308	0.412	0.720	0.314
Alexander Guerrero	14.4%	7.5%	0.259	0.324	0.386	0.710	0.313
Juan Uribe	20.5%	6.1%	0.242	0.293	0.390	0.683	0.297
A.J. Ellis	18.3%	11.2%	0.244	0.337	0.367	0.704	0.306
Andre Ethier	19.5%	9.8%	0.261	0.340	0.405	0.745	0.319
Scott Van Slyke	25.1%	9.7%	0.249	0.325	0.420	0.745	0.325

See the results after the jump

Best Lineup - Milwaukee Brewers

Next up on my look at each teams most efficient lineup is the Milwaukee Brewers.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using ZIPs projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians | Athletics
NL: Mets | Cubs | Padres | Marlins | Reds | Giants

See the results after the jump

Best Lineup - Oakland Athletics

Next up on my look at each teams most efficient lineup is the Oakland Athletics.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using ZIPs projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians
NL: Mets | Cubs | Padres | Marlins | Reds | Giants

See the results after the jump

Best Lineup - San Francisco Giants

Next up on my look at each teams most efficient lineup is the San Francisco Giants.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays | Indians
NL: Mets | Cubs | Padres | Marlins | Reds

See the results after the jump

Best Lineup - Cleveland Indians

Next up on my look at each teams most efficient lineup is the Cleveland Indians.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays
NL: Mets | Cubs | Padres | Marlins | Reds

See the results after the jump

Best Lineup - Cincinnati Reds

Next up on my look at each teams most efficient lineup is the Cincinnati Reds.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible, therefore I didn't attempt to let Joey Votto and Jay Bruce hit back to back.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins | Blue Jays
NL: Mets | Cubs | Padres | Marlins

See the results after the jump

Best Lineup - Toronto Blue Jays

Next up on my look at each teams most efficient lineup is the Toronto Blue Jays.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins
NL: Mets | Cubs | Padres | Marlins

See the results after the jump...

Best Lineup - Miami Marlins

Next up on my look at each teams most efficient lineup is the Miami Marlins.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays | Twins
NL: Mets | Cubs | Padres

See the results after the jump...

Best Lineup - Minnesota Twins

Next up on my look at each teams most efficient lineup is the Minnesota Twins.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays
NL: Mets | Cubs | Padres

See the results after the jump...

Best Lineup - San Diego Padres

Next up on my look at each teams most efficient lineup is the San Diego Padres.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest.  For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers | Rays
NL: Mets | Cubs

See the results after the jump...

Best Lineup - Tampa Bay Rays

Next up on my look at each teams most efficient lineup is the Tampa Bay Rays.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting too many LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers
NL: Mets | Cubs

See the results after the jump...

Best Lineup - Chicago Cubs

Next up on my look at each teams most efficient lineup is the Chicago Cubs.  In this exercise the methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers.  I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting LH back to back when reasonably possible.  Keep in mind, the results are not intended to match what a certain teams manager is most likely to do during the season.

Previous teams:
AL: Angels | Rangers
NL: Mets

See the results after the break.

Best Lineup - Texas Rangers

Next up on my look at most efficient lineups is the Texas Rangers.  I used my baseball simulator to run millions of games through various different possible lineup scenarios to see which lineup it spit out as the most likely to win a game vs a RH and LH pitcher.  Each lineup was simulated in 2.5 million games.

Please keep in mind that 2014 Steamer Projections were used as input, so if you don't like some of the results take it up with them.

Previous teams:
AL: Angels
NL: Mets

See the results after the break.

Best Lineup - New York Mets

Next up on my look at most efficient lineups is the New York Mets.  I used my baseball simulator to run millions of games through various different possible lineup scenarios to see which lineup it spit out as the most likely to win a game vs a RH and LH pitcher.  I tried my best to not stack left handed hitters and I always batted the pitcher 9th because no MLB manager will bat his pitcher 8th which is where most should hit.

Please keep in mind that 2014 Steamer Projections were used as input, so if you don't like some of the results take it up with them.

Previous teams:
AL: Angels
NL: None

See the results after the break.

Best Lineup - Los Angeles Angels

Not sure if this is going to be a series for all teams or just some teams, but I am going to kick things off with the best lineup for the Los Angeles Angels. The methodology is to use my simulator to find out which lineup wins the most games vs RH and LH pitchers. I do this by making the team of interest the "away" team, playing against a "make believe" team whose stats don't change from one sim to the next. In fact no stats (or input projections) change for either team, the only difference from one simulation to the next is the lineup of the team of interest. For player projections, I am using Steamer projections which are available on Fangraphs. The lineup results will only be as good as the projections.  I am not a subject matter expert on every teams personnel but I try to use MLBDepthcharts as a guidance as to which players are starters and I tend to avoid hitting LH back to back when reasonably possible.  Two million simulations make up the sample size.

See the results after the break.

Dodgers Best Lineup

With Hanley Ramirez starting the season on the DL, the Dodgers will have to make some changes to their starting lineup and with these changes comes the question of what their most productive lineup is.  I used my simulator to figure out just that.  I used 2013 Bill James projections as input and for this exercise I had the simulator come up with the most productive lineup against RHP.  I assumed that the Dodgers would start Nick Punto at 3B against RHP and I am not about to project Puig as a starter yet.  Here is the best lineup that it found.

1. Carl Crawford  (L)
2. Matt Kemp
3. Adrian Gonzalez  (L)
4. Andre Ethier  (L)
5. Luiz Cruz
6. Mark Ellis
7. Nick Punto  (S)
8. A.J. Ellis
9. Pitchers Spot

I was surprised to see that batting the pitcher 8th was no longer the best option.  I suppose having a weak hitter like Nick Punto in the lineup put a damper on that strategy.

The Better Offense - Rockies or Dodgers

So there is this Buster Olney guy who gets paid money to write about baseball.  Recently, he put up an article where he ranked the best offenses in baseball.  More than a few Dodgers fans were up in arms when Buster ranked the Rockies offense a few spots ahead of the Dodgers offense.  I was asked by a couple followers on twitter to run the numbers through my simulator where I can take into effect things like the enormously friendly park that the Rockies hit in.

This is a pretty easy exercise for me to run in my simulator.  What I did is get park neutral offensive stats for both the Rockies and Dodgers lineups.  I took the 8 starting hitters for each teams, as listed at MLBdepthCharts website and gave each team what the simulator thought was its most efficient lineup.  I then gave each team the exact same starting pitcher, bullpen, bench and made all park factors league average.  I then ran five million individual game simulations, pitting the two teams together.  I let each team be the away/home team and repeated the above process for both a right handed and left handed starting pitcher.

So the only difference is the two hitting lineups, everything else is held constant.  The metric to determine the better offense can now be measured in how many of the five million games each team won.  Here are the results...