I remember the first time I was blown away by how hard a pitcher threw. It was back in July of 1999, at the then young Camden Yards with the Orioles taking on the Toronto Blue Jays. A young kid by the name of Billy Koch came into the game in the ninth and began warming up. I loved going to Orioles' games like any good Baltimore youngster would. This would be the first time though that the pitching stole the show from my otherwise unfazed love of hitting.

Koch toed the rubber as Will Clark stepped to the plate. Clark lofted a single to left field on the first pitch, and I thought for a brief moment that we were in store for some of that patented Oriole magic. Fan favorite BJ Surhoff sauntered up to the plate, working the count full 3-2. Then Koch unfurled a fastball, that made Surhoff look like a little leaguer. My eyes darted to the scoreboard where one number lit up and blew my mind: 104 mph. Rich Amaral had pinch run for Will Clark and he was unceremoniously thrown out at 2nd base because stealing on a 104 mph fastball is generally ill-advised.

Koch would go on to find himself in a full count against Albert Belle. Before another heater, this time 103 mph, set Belle down and secured the win for the Blue Jays. It was disappointing for the Orioles fan in me, but seeing 103 and 104 mph on that scoreboard stuck with me forever.

Many years later I now know that those numbers likely weren't 100% accurate, but the concept of elite velocity has always intrigued me. Just last week I read an article that Jonah Keri and Neil Paine wrote on FiveThirtyEight about the growing trend of high velocity pitchers in the game. Their research identified a few trends to keep in mind as we dig deeper into the numbers later on:

- Relievers are becoming more specialized, throwing fewer innings per outing
- The percentage of pitchers throwing 95+ mph has roughly tripled since 2002
- Relievers have improved greatly at suppressing opposing offenses (as measured by OPS+ against RPs and SPs)

All of this made sense, and I think fits nicely with the subjective trends that we've noticed throughout baseball. I felt though, that it left me wondering about the connection between velocity and performance. The idea came to me from the Orioles, which launched this early post about the O's soft-tossing bullpen. They have the best bullpen in baseball by WPA, but rank 27th in MLB for fourseam fastball velocity. For this study I'll be using WPA as my stat of choice because it helps clarify the type of outing the pitcher is being used in, that is, it's going to tell us how confident a manager is in a given pitcher and how said pitcher performs in that outing (good means adding WPA, bad means subtracting it).

Since then I've worked with Bryan Cole to refine the method and now have a better grasp on what the data suggests. First, a few caveats:

- Data is up-to-date through 8/18
- Data includes only RPs who have thrown 10 or more IP this season (n=280*)
- Velocity is for fourseam fastball only. I know this limits things, but rather than sorting out which fastball every reliever uses the most, this will do.
- Full data can be found here on Fangraphs and our spreadsheet is here.

*13 RPs have not thrown a fourseam fastball, and have been excluded from the study

So what does it look like? Well, the average fourseam fastball from relief pitchers this season has been ~92.15 mph. That comes with a standard deviation of roughly 2.575, which leaves us with the following break points:

3 STDDev Below | 2 STDDev Below | 1 STDDev Below | Mean | 1 STDDev Above | 2 STDDev Above | 3 STDDev Above |
---|---|---|---|---|---|---|

84.42 | 87.00 | 89.57 | 92.15 | 94.72 | 97.30 | 99.88 |

Those are the velocity breakdowns for fourseam fastballs. Essentially what that let me do was group the pitchers by how many standard deviations they were from the mean. Here is what the sample distribution looks like, with the bars showing the sample size and the line showing the WPA for that group as a whole:

As you can see, it's similar to a standard distribution, but there's definitely a skew to the left. In fact only 2 pitchers are 2 or more standard deviations above the mean: Carter Capps (97.7 mph) and Aroldis Chapman (100.3 mph). What's interesting is that the WPA seems higher at either extreme than it does for those pitchers closest to the middle. There could be a few explanations for this, but we'll delve into that later.

Below is the raw data for that chart, so you can clearly see the WPA posted by each group:

3+ Below | 2-3 Below | 1-2 Below | 0-1 Below | 0-1 Above | 1-2 Above | 2-3 Above | 3+ Above | |
---|---|---|---|---|---|---|---|---|

WPA | 0.32 | 2.56 | 11.86 | 11.72 | 6.33 | 30.91 | 0.18 | 1.08 |

n= | 1 | 6 | 39 | 85 | 109 | 38 | 1 | 1 |

WPA/Pitcher | 0.320 | 0.427 | 0.304 | 0.138 | 0.058 | 0.813 | 0.180 | 1.080 |

Now, looking at all the pitchers in groups is a bit misleading, as there are going to be high and low performers in each group. Essentially it looks like there's a dearth of WPA-providing relievers within one standard deviation from the mean (89.57 mph - 94.72 mph). The hard throwers have provided more win probability added to their squads, generally, than the soft-tossers. Both groups however have out-performed the group within a few mph of the mean though, which is interesting.

It should be noted that since the sample sizes get smaller as you move away from the mean (n=86 for pitchers 1+ standard deviations from the mean versus n= 194 for pitchers between 0 and 1 standard deviations), so the WPA for each group is the output of a much smaller sample size than the majority of pitchers who fall in the middle. Here's what the data looks like as a scatter plot, showcasing where individual pitchers fall on the continuum:

There's a pretty distinct look to that data, so let's dig a little deeper. Across the top there's a row of pitchers that have produced a lot of positive value for their teams, largely regardless of their velocity. These are 12 of MLB's top 14 relievers for WPA (Huston Street and Pat Neshek are excluded as they do not throw a fourseam fastball). This list includes soft-tossers like Koji Uehara (88.0 mph), Darren O'Day (87.6 mph), and Joe Smith (89.7 mph) and flamethrowers like Dellin Betances (96.6 mph), Jake McGee (96.6 mph), and Wade Davis (95.5 mph). These are essentially your elite relievers, and are used as such. Interestingly, some of these pitchers are closers, but many are not.

The size of the bubbles in the above chart is based on inLI, basically how how leverage the situations are that the pitcher generally encounters upon entering the game. This overlaps slightly with WPA as higher leverage situations can result in larger swings in WPA, but I used it here to get an idea of manager confidence. After all, if a particular pitcher's bubble is very large (e.g., Koji Uehara's bubble the highest and largest bubble to the left) then that means that their manager trusts them in high leverage situations very often. As you can see from Uehara's excellent WPA (3.66) he has rewarded Farrell's trust handsomely.

So what can be seen in this data? Well, beyond that elite class of relievers who have dominated regardless of velocity, there are some other interesting things worth noting. Most of the very bad relievers hover just above or below that mean of 92.15 mph. In fact, there is only one pitcher, Jose Veras (87.7 mph, -1.57 WPA), that has posted worse than -1 WPA among the 86 pitchers more than one standard deviation from the mean. To build further on that, 30 of the 40 pitchers throwing 94.8 mph or higher (more than one standard deviation above the mean) have posted positive WPA figures this season. Conversely 30 of the 46, or roughly 10% fewer, of those throwing 89.5 mph or slower (more than one standard deviation below the mean) have posted a positive WPA. These pitchers have also generally been used in less high leverage situations: 0.81 inLI for soft-tossers vs. 1.08 inLI for flamethrowers.

Below is one last chart, this time showing where the break points are for the various groupings:

As you can see, nearly all of the negative WPA pitchers are grouped in between the large-dashed lines, especially if you look only at the very negative numbers (-1.00 or worse). Hopefully this last chart helps bring everything mentioned above together, into one cohesive image.

So what does this all mean? Well, I think that velocity certainly helps relievers, for a lot of reasons that most of us already knew. Having plus velocity means that you can get away with more mistakes because the hitter has a much smaller margin for error against a 97 mph fastball than they do against an 89 mph one. This can be seen in that there are very few negative WPA producers once you get to 94.8 mph or above. Those that are negative are generally pretty close to 0, so by the end of the season it's possible that they could bring that figure back into the positives.

It's also likely that the data is skewed on the soft-tossing side by some survivor bias. If a pitcher is throwing 88 mph, they are likely to have a shorter leash than a guy throwing high-90s. So the soft-tossers that are still in the big leagues are likely the guys that have utilized other tools to get batters out, whether it be funky mechanics (O'Day) or a dominant secondary pitch (Uehara), these guys have proven to be well above average relievers despite their lack of velocity.

Another interesting takeaway that I'd be remiss if I excluded it is my previous mentions about the manager's confidence level in the various pitchers. It appears that the average leverage index upon entering the game has been higher for the flamethrower group than for the group that's closer to the mean. This does in fact seem to be the case with those within one standard deviation from the mean having an average inLI of 0.90, lower than the flamethrower group but higher than the soft-tossers. This brings about an interesting point, whether managers are irrationally favoring guys in the 90-94 mph range over soft-tossers that have better results. After all, the first chart in this post shows that the soft-tossers have posted higher WPA/pitcher than the group closer to the mean. Why would this be?

Well there are a couple of possible explanations. Number one that middle group could include guys that used to be flamethrowers, but are now just average velocity guys. A perfect example of that would be Jonathon Papelbon who has averaged just 91.3 mph on his fastball this season, a far cry from his average of well over 94 mph in his Boston seasons. Another example could be guys that have some promise of being high velocity guys, but for whatever reason sit more in the mid-90s regularly. An example here could be Brad Brach of the Orioles, a pitcher who has hit over 96 mph this season, but more regularly sits between 92-94.

One possible solution, a salvo possibly at MLB managers' disposal could be that nearly all of the effective soft-tossers are currently being employed by clubs. This seems far-fetched to me, but theoretically is possible. If there are no more effective soft-tossers to be found, MLB managers are then forced to pitch harder throwing relievers because they lack a better option.

The most likely reasoning here is that MLB managers simply overrate average velocity and/or underrate guys with below average velocity that can still be effective. I'm sure Zach Putnam doesn't instill fear in the heart of opposing hitters with his 88.5 mph fastball, but his 1.32 WPA for the White Sox has shown that he's pretty darn good at providing value to his team.

Finally, there's pretty clearly an elite class of relievers that are incredibly successful regardless of velocity. This list is maybe 10-15 names long, but those guys are the cream of the crop so far this season. I'm sure that year over year that list changes, but it's worth noting that in 2014 there is a group of elite relievers that throw anywhere from 88 mph to 97+.

At the end of the day, it seems to be that there is some correlation between a reliever's velocity and their ability to provide value for their club (Correlation = 8.66%). However, that's not to say that low-velocity hurlers can't provide value. Rather, the soft-tossers can provide plenty of value on their own, it just happens that they do so in a different way than the flamethrowers do. If anything, there seems to be more correlation (22.10%) between velocity and the average leverage index that managers use their relievers in. That is that managers perhaps disproportionately favor high-velo guys in high leverage situations. Of course, it's possible that given those opportunities the soft-tossers would fail to post better WPAs either.

This one study won't provide all the answers about velocity and whether or not, but there are definitely interesting takeaways. Chief among them the glaring lack of poor performers at either extreme, the elite class of relievers regardless of velocity, and the serious over saturation of poor relievers that throw between 90 and 94 mph. If nothing else, this study can help us begin to understand this trend towards greater velocity in major league bullpens.

*Special thanks to Bryan Cole for his help with crunching the numbers and interpreting the data*

*All statistics courtesy of Fangraphs, Brooks Baseball, and Baseball-Reference.*

*Jeff Long is a writer at Beyond The Box Score and Baltimore Sports and Life. You can follow him on Twitter at @BSLJeffLong.*