Looking at Run Distribution | The Process Report

# Looking at Run Distribution

Through 37 games, nearly the first quarter of the season, the Tampa Bay Rays have scored 153 runs good for 23rd in Major League Baseball. However, they have only allowed 139, which would rank them sixth. You’ll note that this yields a positive run differential of 14 runs or if we convert that to a pythagorean win expectancy you would expect the Rays to have a record of 20-17. A big reason for why they have two fewer wins than expected is due to the outburst these past two games that saw the Rays raise their run differential 21 runs. These large run totals have skewed some of the overall run-based statistics so it makes sense to delve into this.

When blue (runs scored) is higher than red (runs allowed) you would expect the Rays to be faring pretty well. Unfortunately, that hasn’t been the case very often outside of an early stretch and then this most recent stretch. This seems to confirm the frustrating notion that when they pitch they don’t hit and vice-versa. The line of thought behind this is that the Rays do have the occasional outburst, but the majority of the time they are struggling to even get to the four run mark. Some might label this a classic fight between mean and median.

The mean tells us the average over the entire sample, but in a relatively few number of games such as this it is prone to being pulled by the larger numbers. The median would give us a notion of frequency. We can compare each team to see if this is a Rays-specific issue or something more systemic:

I have mapped each team’s median (vertical axis) and mean (horizontal axis) runs scored on the season with the dotted line indicating a perfect world 1:1 ratio between mean and median. The dashed line shows the actual trend between these teams. You can see that it does an effective job of mirroring our ideal, but it is a step down indicating that this is a systemic issue for all teams as EVERY team is going to see a bit of inflation due to the games where they blow up.

I have highlighted the Rays as the black dot and you’ll immediately notice that the team is amongst a group of teams that have the lowest median runs scored at three. You’ll also notice that the Rays are one of the teams that is furthest from our dashed line. The Dodgers are immediately to the right, which tells us that they have the strongest difference between the two measures at 1.3 runs per game. The Rays come in tied with the Reds and the Diamondbacks for the second largest difference at 1.1 runs per game. While this is something that all teams should be expected to see it does appear that the Rays show a larger variation in run scoring than nearly all other teams. We can look at this another way:

Starting with the rest of the league (red) we can see a fairly normal distribution with teams peaking at three runs per game. We see that is also where the Rays peak, but they’ve had nearly double the number of occurrences of scoring exactly three runs. This comes with a lower than league frequency of two and four runs per game, which would indicate that the Rays have traded some twos and fours for threes and have slightly more one-run games. Going to the higher side we can see that the Rays are below the league average all the way up to the highest scoring games where they do earn back some favor.

It would seem that the Rays have an abnormal habit of scoring three runs in a game, which is robbing equally from the games where they score plus or minus one more. We’d love to see some of those three-run games turn into four-run affairs, but I bet most folks wouldn’t trade the three-run games for an increase in two-run games. Of course, we’d also like to see a spike in scoring five or more runs per game, too.

The team could stand to score more runs, something they have done more often of late per the first chart, but isn’t guaranteed to continue. I’d expect some of this to smooth out, but it will take some time. I’d expect an equal number of those three-run games turning into twos and fours, which is both bad and good. What has happened is no guarantee of what will happen, but it looks like the Rays have been getting stuck on that three-run mark more often than most.