Pitchers for the Colorado Rockies might be wondering if their stadium humidor is broken. After a long stretch of good pitching after the humidor was installed in 2002, the ball is back to flying out of the Rockies home park.

There seems to be some fuzzy science behind offensive outbursts that avid baseball fans might not be able to channel Einstein on, but certainly can smell it as certain as the smell of BBQ.

The classic situation is the struggling pitcher starting an afternoon game on a hot and humid day - batters can't wait to hack. That is until the game reaches the time of day when the sun drops to create shadows between the mound and home plate - batters couldn't see a beach ball thrown by the team mascot - for about an hour.

Fans just know what time it is. Ah, science - the master of the universe, controlling whether the pitcher is lights out or gets lit up.

To put some numbers behind what we empirically already know, (raw data from RetroSheet.org), combined runs scored were tabulated based on game start time. The table below shows the percent of games during the hour for each combined run total. For example, games starting at 4pm, 22% of those games had a combined total of 7 or 8 runs.

Table: Percent of games with combined runs scored for each hour of the day. 14,571 games from 2006 thru 2011.

The chart below helps make sense of the average runs scored by hour of day. Keep in mind that a game generally last three hours, so the 4pm start time implies the game was played over the 4pm, 5pm and 6pm hours.

There are two points of interest in the chart - a high point at 2pm and a low point at 5pm.

Whatever the science involved, starting a game between 2pm and 3pm results in more runs scored, and starting a game between 5pm and 6pm results in less runs scored.

Chart: average combined runs per game start time

Lesson? Maybe if you are a team that projects to have below league average starting pitchers and an awesome bullpen, you would want to have game start times at either Noon or 5pm when the mysterious atmospheric conditions could hide your poor starting pitching while negating the opponent's better starting pitching. Or maybe the lesson is more basic, buy tickets for the 2pm game since chicks dig the long ball.

ADDED: Deeper Dive

The questions about sample size for the 2pm start time and if the data might be skewed by a few ballparks were addressed by determining that three teams contributed the most to the 2pm totals in the table above: Texas 39, Boston 23 and Chicago Cubs 19.

To see if the overall effect was still valid, the table/chart below used a larger data set (12 years, 2000-2011) and shows a comparison of league average, average of the three teams in question (Tex/Bos/Cub) and average of all other 27 teams.

Several things to note:

-based on the totals for Bos/Tex/Cub, you can predict every ballpark has a different profile
-the combined number for these three teams have higher run totals at all start times except 6pm (weird)
-the pattern for the combined other 27 teams show the same profile as when Bos/Tex/Cub are included in the league averages

The conclusion would be that there is a time of day effect in aggregate, while each ballpark would have their own pattern.

ADDED: Deeper-er Dive

In an effort to better understand the data in the previous tables, specifically why there is such a big difference in games started at 5pm and 6pm, re-ran the numbers with the simple-minded logic of assigning runs scored in the first three innings to the first hour, second three innings to the second hour and the last three innings to the third hour.

The table/chart below shows the runs scored during an hour, independent of game start time. For example, the 5pm data includes innings 7/8/9 from 3pm starts, innings 4/5/6 from 4pm starts, and innings 1/2/3 of 5pm starts.

What is interesting about this breakdown is the up/down spikes in the data were ‘averaged-out' in the previous analysis that focused on game start time. This chart better supports the cause-and-effect discussion. (Note: since the averages are computed with a different number of overlapping games, you can't simply add three numbers to match data in the previous tables.)

My thoughts are that 4pm is generally the hottest time of the day combined with the sun reaching angles that affect fielders. Then shadows move across the field making hitting difficult during the 5pm hour. Lots of science in the numbers.

Table: All games 2000-2011, Runs Scored by Time of Day

Chart: Average Runs Scored by Time of Day