Jonathan Broxton’s Declining Fastball
Jonathan Broxton, known to Dodger fans as “The Ox,” lost his closer role in August this past season after a 7.45 ERA and 1.76 WHIP in July. After a 2.26 FIP in 2008 and a 1.97 FIP in 2009, Broxton fell dramatically in 2010 with a miserable post-All Star performance. His home run rate remained relatively unchanged, while his walk rate increased by a little less than one walk per nine innings. Of the rate statistics, Broxton’s strikeout rate changed the most, decreasing from 13.5 K/9 in 2009 to 10.54 K/9 in 2010. But the largest difference in Broxton’s pitch results was how often he got hit (and how hard he got hit). Batters hit .270/.351/.367 off Broxton in 2010 (as opposed to .203/.276/.289 in 2007-2009).
The decline in Broxton’s fastball speed was properly publicized throughout the summer, and I wanted to take a look at how much that decline was. Broxton’s fastball averaged 97.5 mph in 2009 compared to 95.3 mph in 2010. I made a density plot of Broxton’s fastball speeds in 2009 compared to that of 2010 to show how drastic of a change this was. Take a look at Broxton’s fastball speed distribution below:
I plotted the first and third quartiles of each density plot, represented by the dotted lines. The first quartile is the 25 percentile mark which is larger than 25% of the sample, while the third quartile is the 75 percentile mark. Here are the values of those values along with the medians of each sample.
2009 fastball speeds:
1stQ: 96.6 mph
Med: 97.7 mph
3rdQ: 98.6 mph
2010 fastball speeds:
1stQ: 94.2 mph
Med: 95.5 mph
3rdQ: 96.5 mph
What I find particularly significant is that the first quartile of the 2009 sample (96.6 mph) is greater than the third quartile of the 2010 sample. Essentially, a 96 mph fastball would have been in the bottom fourth of Broxton’s 2009 fastballs, but faster than about 75% of his 2010 fastballs.
Broxton actually started off hot in 2010, holding a 0.00 ERA in April and striking out 35 in 23.1 innings over the first two months. But what’s confounding is that Broxton’s fastball speed was also diminished during that time frame, averaging 95.6 mph on his fastballs over those two months.
Although not nearly as significant, Broxton’s slider speeds also showed a decrease. Here’s his slider speed distribution for both seasons:
The bulk of Broxton’s sliders in 2010 were under 88 mph (about 75% of them), which matches the median speed of his sliders in 2009. Broxton mixes about 75% four-seam fastballs and 22% sliders though. In general, a rule of thumb is to keep sample size in mind when looking at any reliever’s secondary pitch. Still, there’s clearly diminished speed in Broxton’s slider, which is usually accompanied by a change in breaking movement. Broxton’s changes in distributions of slider horizontal movement and slider vertical movement suggest that his 2010 slider was more of a breaking ball with less cutter-like spin than his 2009 slider.
Frankly, Broxton wasn’t the same pitcher in 2010, and it showed up pretty blatantly in both of his main pitches as well as his performance. There are all sorts of reasons why this may have happened whether it’s conditioning, a change in mechanics, or an injury. What’s clear is that, fundamentally, Broxton has been a different pitcher, particularly in his four-seam fastball. If come late March, reports of Broxton’s fastball speeds indicate no improvement, expect his struggles to continue into 2011.
Albert Lyu (@thinkbluecrew, LinkedIn) is a graduate student at the Georgia Institute of Technology, but will always root for his beloved Northwestern Wildcats. Feel free to email him with any comments or suggestions.
I agree with your conclusion.
We don’t know why he lost velocity on ALL his pitches, but perhaps 2009 was his last great year.
As far as the reasoning for his 2nd half fade when velocity remained the same throughout the season, it’s just hitters adjusting………and realizing his fastball wasn’t as intimidating as it used to be. Three miles is ALOT when you’re talking about MLB hitters.
I’m wondering how easy it would be for you guys to run the statistics to show a confidence level in the differences you are seeing. That would at least save you from typed something to the effect of “beware of small sample sizes” so many times. Just a thought. Thanks for the article.
I notice that the player page only lists percentages with no sample size for pitches. Clearly there is a pitch-by-pitch data base somewhere, and it would be trivial to compute standard deviations and confidence intervals from that. It is amazing to me that a website so devoted to “statistics” makes the elementary error of reporting sample statistics without computing confidence intervals on the underlying parameter of interest.
For proportion measures (batting average, OBP, strikeout %, etc.) all you need to add is the sample size; the margin of error for a 95% confidence interval is 1.96*sqrt(p*(1-p)/n), where p is the observed (sample) proportion and n is the sample size. We see that in 2009 Broxton faced 300 batters, walking 1 intentionally, so he pitched to 299 and struck out 114. That’s 38.1% (.3813), so for a margin of error we have 1.96*sqrt(.3813*.6187/299) = .0551. Our 95% confidence interval is thus 38.1 +/- 5.5, so we estimate with 95% confidence his true talent level in 2009 was to strike out between 32.6% and 43.6% of batters pitched to.
Repeating for 2010, we get 73/266 = .2744, and MOE = 1.96*sqrt(.2744*.7256/266) = .0536, so a strikeout rate of between 22.0% and 32.8% . There is a small overlap in the ranges here; we should compute a formal estimate of the difference (the math is somewhat more extensive) but we can be comfortable saying we are highly confident the difference was real and not a fluke of sample size.
For interval measures (things that can’t be expressed as a percentage) we need sample size and standard deviation, and basically use standard deviation in the formula instead of p*(1-p). We also must use a t-value which varies with the sample size instead of the fixed 1.96; for 2010 (265 “degrees of freedom, or n-1) this would be 1.969.
These calculations are trivial to do in Excel, and the authors on this web site should do so for every statistic reported. If anyone needs help, email me at paul hightower 84 at hot mail dot com .
Slight correction: for interval measures, the margin of error is given by t*s/sqrt(n), where t depends on the confidence level desired and sample size and s is the sample standard deviation. I can’t give an example since we have no standard deviations reported in the Fangraphs or Baseball Reference data.
Well in spring training prior to 2010 Eric Gagne was giving Broxton tips, one of which was that he didn’t need to throw his hardest all of the time, and that taking a little off the fastball could help him if he gained command in the process. I can’t find a link to the old article, but at the start of 10 this was the explanation many Dodger fans had, of course nobody was worried at the time because Broxton had such great success.
Wat about his outing against the Yanx this year?
That bomb Burrell hit off of him was pure sex.
you’re talking about Pat Burrell? FYI he has never played for the Yankees
wow, now that’s class…
Albert,
Why are you picking on the Dodgers (First Kemp, now Broxton) ? Leave that to the Giants and Giant fan base.
This must be a long winter for the faithful of Chavez Ravine 🙂
Go Giants!
I was thinking the same thing, haha.
Sadly the Dodgers 2010 season has given plenty of ammo for people who want to write articles on “what went wrong for X in 2010?”
But I say why not write about how awesome Kuo was in 2010? That would sure be great 😀
Kuo should be closer. He’s filthy.
Kuo isn’t considered physically capable of going back-to-back days much, let alone three in a row if need be. I imagine he’ll close as much as he is able next year, but the Dodgers will likely designate a second closer for the games where Kuo can’t go.
Yeah, the knock on Kuo is that he doesn’t have the ability to go back-to-back games with regularity because of his high number of arm surgeries, which I believe is at 4 now. But Broxton is still here for another year, and I think he should have no problem being a reliable option as fulltime closer again. I know this article shows that his fastball speeds were down all this year, but he still managed to be either the best or second best closer until the middle of June, so I don’t have any problem seeing him being AT LEAST above average in 2011 as closer.
If not, I have no problem as well going with a closer by committee with either just Broxton and Kuo, or the three of Broxton, Kuo, and Jansen.
Good stuff as usual, Albert. Pretty graphs!
agree…
btw, the OP must be some kind of statistics genius….
Actually, the third and fourth graphs (referring to the horizontal and vertical movement on his slider) has a misnamed x-axis as it says “fastball velocity” when it should be the inches that his slider breaks.
I did not catch that. Thanks.
Like a lot of the hard throwing relievers of yore, Broxton may not be able to last over the long haul. The hardest throwing RP of the ’60’s was a guy named Dick “The Monster” Radatz who had 3 of the greatest seasons for a RP ever. Pitching for the Red Sox, Radatz K’d a relief record 181 batters in 157 IP in 1964. He had 29 SV and 16 W with a 2.29 ERA. In his rookie season (1962), Radatz led the AL with 24 SV, and relief wins (9). He went 15-6 in ’63 with 25 SV and a 1.97 ERA. He became the first ever to record consecutive 20 SV seasons. But all that largess was short-lived as Radatz was hurting toward the end of the 1965 season and though he recorded 9 W and 24 SV, he was never the same again. Let’s give Broxton credit for 4 1/2 years of meritorious service. That’s more than most of us have in a lifetime!
Another guy, though he didn’t throw as quite as hard as these 2 was Billy Koch. He was out of the game before the age of 30 after amassing 144 saves in his first 4 seasons. Not everyone can be Mariano Rivera and throw one pitch! he’ll be around, George, after they shovel the dirt over you, I’m sure. I love rotoimbeciles, your sight, it’s one of my first reads in the morning along with the obits in the daily paper. Keep up the great work.
i’m not sure you’ve made the case between cause & effect, albert.
broxton’s BABIP was .369 last year, or 84 points higher than last year’s figure. his BABIP last year was also 40 points higher than his career figure. drilling down to batted ball profiles, his LD%, GB%, HR/FB%, etc. from 2010 were all in line with his career figures.
i think 2010 was just a bad outlier year for broxton. relievers only pitch a few innings per month, so when you look at a “high ERA in July” or performance below expectations during the “post all-star break period,” you’re just cherry-picking from small sample sizes.
I agree. His reduced fastball speed is only back to 2006-7 levels and he wasn’t exactlly a terible pitcher then. He can obviously be effective with a 95mph heater if his BABIP drops back to .320-odd. One thing I did note is that he has thrown the fastball more and more over the years as its speed has crept up. With the fastball more hittable, he may need his slider a little more.
maybe part of Broxton’s problem is that his slider speed was concentrated in such a small distribution in 2010, while he had a much wider range in ’09. I would think that it is easier for a hitter to hit a guy who throws at basically two speeds, vs a whole range of speeds.
As a Dodger fan and fantasy owner of Broxton, I can attest to having watched most, if not all of his appearances last year. What struck me as different was Broxton’s command over the course of the year, particularly after a stretch in which Torre had used Broxton 4 times in 5 days (3 of which could’ve been handled by just about any other reliever). The last of those 4 appearances was the shellacking at the hands of the Yankees in which Torre allowed Broxton to throw over 40 pitches. While I did see some dip in Broxton’s velocity, I wonder how much of this was merely due to a sore/tired shoulder.
What does the distribution look like if you break out the fastball speeds by month?
Good piece, Albert
“If come late March, reports of Broxton’s fastball speeds indicate no improvement, expect his struggles to continue into 2011.”
I wouldn’t exactly call a 2010 xFIP of 3.32 struggling…”less dominant” is more accurate.