Baseball Totals

[DougOzzzz]

The average AL team in 2004 scored 5.01 runs per game. In the NL, the figure was 4.64. Combined, the average is about 4.83 RPG. All games from 2004 averaged a total of about 9.65 RPG.

If you go to pinnaclesports.com and look up the over/under lines, most totals are set at 9 runs or fewer. Today, the average line is 8.625 with slightly more juice on the over (-108 vs. -102).

If baseball totals are set more than a full run below the average run scoring, wouldn't it make sense to bet the unders consistently?

To test this theory, I set up an Excel spreadsheet. Using a formula from Baseball Prospectus 2005 (developed by Tangotiger), I estimated the frequency of 0, 1, 2, 3, 4, 5.... 20 run innings based on the number of runs per game for each team. The formula is very accurate when compared to actual statistics. I then "simmed" 200,000 games using these figures. The game ended if the home team was ahead after 8.5 innings, or if any team led after 9+ complete innings. If a home team happened to have a "big" inning in the 9th or later and won by more than 2 runs, I changed the runs scored so that 1 run wins outnumbered 2 run wins by a ratio of 5 to 1, and 3+ run wins were nonexistant (they do happen occasionally, but are rare). It's not perfect, but it does give a pretty adequate representation of the distribution of run totals for each team.

Both teams were set at the league average figure of 4.83 runs per game. The home team ended up scoring a bit less than that (since some big innings were taken away from them), while the road team scored a bit more than that. Interestingly enough, the home team still won 52% of the games - I cannot see a reason for this.

Anyways, a few conclusions based on the results (these should not be anything new to those who are familiar with betting on baseball totals):

1. 54.6% of all games ended with a total runs scored of 9 or fewer. You'd expect that number to be significantly less, considering the average is 9.65.

2. On average, a total of 9 would return 44.5% wins, and 45.4% losses. Thus, the totals according to this should be set slightly BELOW 9 runs on average. This is consistent with the lines at pinnaclesports.com, though this particular testing would probably assign an average line of ~8.9 runs rather than 8.625.

3. Odd run totals are significantly more frequent than even run totals. Again, this should be no surprise to anyone familiar with baseball totals. Odd run totals accounted for 58.95% of the possible outcomes - about 43.6% more often than even run totals.

4. The home team averaged .06 fewer RPGs than the road team. This doesn't sound right to me. About 20% of games should end after 8.5 innings, meaning the home team should lose about .2 innings per game. That should be equal to .11 runs, not .06.

5. The reason that these games usually have 9 or fewer total runs is obvious. There is no upper limit for total runs, yet there is a lower limit (1 run). Thus, there needs to be a greater frequency of low scoring games to balance the higher scoring games. About 4.45% of games ended up with 18 or more runs scored. These accounted for 187,793 runs, or 0.938965 runs/game (or about 9.7% of the total runs). Subtracting that from 9.65, we get 8.71 - which is much closer to the break-even point than 9.65.

Anyways, just thought this was interesting. If you think 2 teams are likely to average X amount of runs per game, yet the line is set BELOW X, it may not be profitable to bet the over. If anyone has actual data relating to this, I'd be interested to see how close my numbers match up.

[tech]

Averages (means) are worthless, especially when dealing with discrete data such as baseball totals.

[lastsamurai]

I agree... and with the player all natural this year...i see alot of HR totals down from last year.

[DougOzzzz]

[ QUOTE ]
Averages (means) are worthless, especially when dealing with discrete data such as baseball totals.

[/ QUOTE ]

I don't understand how this is true. Averages (means) have the advantage of being (relatively) easy to project. You take a teams expected RS (based on the lineup and season stats), you adjust for opposing pitching/defense and park effects, and you get a figure. You do this for both teams, then plug it into the formula, and see how often the totals fall above/below X amount of runs.

I fail to see how that is not useful, unless my formulas are incorrect. I concede that they are not perfect - a team can't be expected to have the same number (mean) of runs per inning in the 1st inning compared to the 2nd, or the 8th (against a reliever), etc. But I think overall it comes pretty close.

[Tboner7]

There were 9 games yesterday with run differences of 3 or more. That's not rare.

[tech]

I'm not saying your method is worthless -- I really haven't looked at it enough to know. My point is that you need to use a different statistic. Use medians, modes, frequency distributions, whatever. But the means are going to mislead you here. One or two outliers is going to throw you off significantly with a sample size of only 20 or so games.

[DougOzzzz]

Of course I agree with that. The whole thing is based on coming up with ACCURATE projections for future runs per game. Twenty games, or even 80 games, isn't enough.

As for coming up with these projections - I'm not quite there yet. But it will probably be a combination of PECOTA projections and current season stats.

[sportypicks.com]

Tech is right,

Averages are the lazy man's way of handicapping sports and they are totally misleading.

[DougOzzzz]

[ QUOTE ]
Tech is right,

Averages are the lazy man's way of handicapping sports and they are totally misleading.

[/ QUOTE ]

I am surprised by the responses I have gotten. I am trying to take a mathematical approach to computing baseball totals. I have yet to see anyone make a single argument against my approach.

I make no claims that the approach is easy, or "lazy". It is not. As I said before, the whole thing succeeds or fails based on how accurate your projections for RS/game are for each team. Obtaining an accurate projection in a single game is no simple matter - besides each team's offensive level, other factors include:

1) starting pitcher's strength
2) team defensive strength
3) park factors
4) strength of bullpen
5) umpire strike percentage
etc.

What I find to be the most appealing thing about this approach is that it is entirely based on mathematics. Each factor can probably be shown to have a certain amount of effect on RS/game. A team that averages 5.5 RPG for instance, against a pitcher with an EqERA 10% better than league average, against a defense that allows runs at 2% higher than league average, in a park that suppresses runs by 5%, with an umpire that calls strikes 1.5% less frequently than normal, with a bullpen that allows runs at 7% above league average - all that results in a figure for RPG. Using that, and simming the games, you can accurately predict the run distribution - which is what baseball totals is all about.

The other approaches seem awfully subjective to me, and based on small sample sizes. If the over is 15-8 at a particular park that season, how do you include that into your ratings? If a team has a median of 10 RPG (both scored and allowed), how do you adjust for the fact that they are playing on the road against an above average pitcher and a below average offense?

With my method, these adjustments are easy - provided that you can make accurate evaluations.

[sportypicks.com]

Doug,

I think you misunderstood me. I didn't say YOU were lazy, I was talking about people who just pick up the paper and read batting averages and era's and then bet on a game.

I probably should have conveyed myself better. I think you are definitely on the right track as far as producing accurate total numbers. All of those factors you mentioned above do come into play when handicapping totals.

My question for you is...How do you measure pitcher's strength? By just looking at his ERA (pitching avg) that would be the wrong way to go. One bad outing where he gets pulled after 1/3 of an inning giving up 5 runs can really distort an ERA. That is what Tech was talking about. Instead of taking an average, compile a distribution based on number of innings and runs allowed during these innings. I think you will fare much better in your simulations.