We hear a lot about streaky players. Announcers talk about players who are on a hot streak. Players discuss “getting out of a funk” or if they are “swinging a cold bat”. We even call some hot streaks “patented”. The “streak” explanation has become almost completely ingrained in the way we think and talk about hitters.

There’s just one problem: hot streaks are an illusion.

Past Research

With almost thirty years of research on the subject, there is very little evidence to support a serial correlation (previous events influence future events) for at-bats. This is not to imply that streaks don’t exist: The A’s won 20 games back in the early 2000s and Dimaggio’s 56-game hitting streak are both examples of series of positives outcomes. But what we are interested in is whether this is somehow different than what we would expect given a players existing talent level.

To make this more concrete: if we flip a coin four times, we would expect 2 heads and 2 tails. Yet we also know there is a chance, although less likely, that we would get three heads and 1 tail. And even less likely still, there is a chance that we get 4 of the same type of outcome. Just because we get 3 heads in a row doesn’t mean that there is a greater chance that we will get the 4th in our next flip. We would say that flipping a head once is “not serially correlated” with the next coin flip.

In the area of sports, Tversky and Gilovich (1989) discuss the “hot hand” theory (the idea that a player is more likely to make a shot if they have just made a previous shot or shots) in basketball:

“First, the frequency of streaks (i.e., moderate or long runs of successive hits) must exceed what is expected by a chance process with a constant hit rate. Second, the probability of a hit should be greater following a hit than following a miss, yielding a positive serial correlation between the outcomes of successive shots”

The authors do not find evidence that previous hits or misses have an effect on future shots, providing further evidence that “…research indicat[es] that people’ intuitive conceptions of randomness do not conform to the laws of chance”.

That’s a really important line because the authors are implying that, instead of seeing randomness in a series of outcomes, people try to craft stories to understand events. Instead of remembering all the times a hitter fouls off a high fastball, we say they are a good fastball hitter if they crank a home run on a high heater. This is what is known as positive confirmation bias: we tend to remember the good moments as evidence of what we believe and discount evidence to the contrary.

The Tversky and Gilovich article is in the area of basketball which differs from baseball in several substantial ways (one being that baseball is enjoyable). Using a dataset of 501 baseball players who had 500+ at bats between 1987 and 1990, Albright (1993) finds no evidence of positive hitting streaks in professional baseball:

The data analysis performed here, on 501 plus-500-at-bat records over the four seasons from 1987 to 1990, has failed to find convincing evidence in support of wide-scale streakiness. In fact, the evidence is more in line with a model of randomness. It is certainly true that some players exhibit significant streakiness during a given season, but this would be expected under a model of randomness, just as one would expect a certain proportion of people flipping fair coins to produce streaky sequences of heads and tails.

This is a large body or research ranging from basketball (Shaw Dzewaltoski and McElroy, 1992), baseball (Vergin, 2000; Siwoff et al. 2000), to general psychology in sports (Adams, 1992). The large majority of studies have come to the same conclusion: hot streaks are an illusion.

Jay Bruce, “Streaky” Hitter?

No player has been more maligned with the “streaky” label than Jay Bruce. The argument goes like this:

Jay Bruce will carry his team for a month, maybe a little more, but all the other times he is a normal or below-average hitter. If only Jay could “figure it out” he would be a great player.

The “Bruce is streaky” argument begs the question: does Jay Bruce’s month-to-month production vary more than other players? Or, put another way, if we were to take each month of Bruce’s offensive production (say, in wRC+) and compared it to other players’ month-by-month production, would Bruce’s distribution have two “spikes” – one during his hot streaks and one during his “cold” streaks? Let’s find out.

Here are about 5 years worth of wRC+ data (note: injuries were excluded for obvious reasons) for the following players: Zack Cozart, Joey Votto, Jay Bruce, Todd Frazier, Devin Mesoraco and Brandon Phillips. These are the wRC+ histograms for each player, (in 10 wRC+ increments).



(I have to admit, this picture was the inspiration for this article.)











These graphs suggest that hitters’ productivity is fairly normally distributed around a central talent level, which is consistent with previous research on the subject. Readers of the Nation know that there is a relationship between hard hit balls and batters’ batting average on balls in play (BABIP). Yet within BABIP, there is also a healthy amount of variation. Put another way: sometimes a high popup falls in for a hit, sometimes a screaming line drive finds a glove. Many times it’s out of a hitter’s control.

Players will also go through periods where they face better and worse teams; they play in ballparks that are more or less hitter friendly; sometimes they are sick, or injured, and play poorly; sometimes they are feeling great and play well. In the end, however, the distribution of hitting outcomes conforms rather well to what we would expect given their level of skill.

From the data above, I calculated some measures of “central tendency” (or, how closely grouped together these values are). Each of these measures will provide different insights into how “streaky” these players are: mean wRC+ will show a player’s average production; the standard deviation will show if players frequently diverge from their average production (or if they are likely to have very productive months and then very unproductive months); and the middle 50% will show where a player spends half of their career.

These are not full careers but fall between 2010-2015, none of which included rookie seasons because it would create unrelated variation in the data. I removed some months when players were injured or clear outliers – such as when a player had three at bats and their wRC+ was in the 200s. Month-by-month groupings are imperfect because they do not possess the same number of games, but these generally fall between 21 games and 29 games per month. It’s not perfect; this is just a starting point.

Player Mean wRC+ Standard Deviation Variation – Middle 50%
Joey Votto 158.38 37.3 51.25
Brandon Phillips 98.9 35.5 52.5
Zack Cozart 77.6 22.8 36
Devin Mesoraco 119.16 60.3 70.75
Todd Farzier 113 49 54.5
Jay Bruce 121.35 39.2 51.25

These numbers indicate a few things: first, there is a close grouping in the standard deviation column. Mesoraco is probably an outlier because he only has 18 months of data and is pretty young. Cozart is in the low 20s because if his numbers varied any further, he would be out of the league. Votto, Bruce, and Phillips all have roughly the same standard deviation in their offensive production. Frazier had such a strange second half of 2014 and start to the second half of 2015 that his standard deviation is abnormally large.

This suggests that the only relevant difference is a player’s average level of production (a proxy for skill). Around that average level of production we witness some normal variation, party due to playing more or less skilled pitchers, playing with minor injuries, and the expected variation in a probabilistic distribution.

It does seem that it is harder to maintain a higher level of play than it is a lower level (or, Joey Votto going 0-for-4  has a much bigger effect on his wRC+ than Zack Cozart), so more skilled players seem to have a bit larger variation around their average production level than less skilled players. Or stated with an economic rationale: more skilled players have more room for variation because when they have a downward swing in their production, they don’t fall out of the league.

What About Game-By-Game Variation?

Assuming these numbers have a gravity toward some central underlying skill level, the more plate appearances in each unit (in this case, months, ~60PA), the more likely these numbers will be to cluster around a central skill level. The work I’ve done here is on a month-to-month basis, which may hide day-to-day variation (or week-to-week). Bill Petti (link) created the statistic “hitter volatility” to measure players’ variance from game-to-game in order to see if some hitters are more likely to follow a great performance with a poor one.

Petti article argues that, in general, walking is a more stable method to create value than hitting for power. In the three years covered in that article (2011-2013), Bruce’s day-to-day variation is calculated to be 4% higher than league average, tied with Chris Young, David Murphy, B.J. Upton, Pablo Sandoval, and Stephen Drew. This “volatility” is largely driven by Bruce’s reliance on power to create runs. The most volatile hitters from 2011-2013 (Pujols, +11% more volatile; Alfonso Sororiano, +9%, Matt Weiters +9%, etc.) trade power for consistency. All but the few of the most talented players are able to avoid this tradeoff. Petti’s prime example of such a player? Joey Votto.


This is not to imply that changes in ability or talent will not cause deviations from a player’s previous performance. Recently, Joey Votto said that he changed his swing mechanic during the All-Star break. These mechanical changes may cause hitters to perform better (or worse) than before, but this is because a change in approach, not some mythical “hot streak”. The same can be said about injuries — we only need to look at Jay Bruce’s performance last year to see that his decline was due to injury, not talent. With Jay now up to 119 wRC+ on the season, it appears that, once again, the long view is superior to the short view.

So while players will experience variation in their performance, attributing these changes to some mythical “streak” cheapens the discussion: instead of focusing on tactical or mechanical changes, fans are bombarded with the “streak” explanation. Yet if a player actually does bounce between high and low levels of performance, is it due to injury? changes in his swing? changes in ballpark? are pitchers approaching him differently?

For a long time we’ve chalked up changes in performance to “streaks” instead of looking for the underlying reasons. Most of the time these changes are just random variation, but if there is an underlying change, discussing these technical and/or tactical changes in a player’s plate approach would be a fruitful conversation.

As far as Jay Bruce is concerned, he’s not a streaky hitter. In fact, he’s surprisingly normal.

76 Responses

  1. Jason

    He just doesn’t hit when it matters

    • Kurt Frost

      Can we see your data to back up that statement?

      • Jason

        Yeah sit down and watch a game baseball isn’t rocket scientist otherwise you would need a PhD to play

    • gaffer

      Clearly that is not the case, as he has no control over everyone else. If he only gets a hit with 2 out and no one on that if the fault of others for not getting on base. He is also not in control of how our pitchers pitch. If we win a game 2-1 and he gets the game scoring run how does that matter more than if Bruce hits a grand slam but we have Kevin Gregg give up 4 runs in the 8th? The idea of “clutch” hits have been disproven.

    • Steve Mancuso

      Interesting comment about a guy who has two game-winning homers in the past couple weeks.

      • Scot Lykins

        The problem is he bats .190 then .350. He bats .190 much longer than the .350.

      • charlottencredsfan

        The only problem is, this isn’t factual. I thought the same but some gum shoeing proved otherwise. It’s easy to look up.

      • Steve Mancuso

        The 1800 word post here shows Bruce doesn’t have greater month-to-month variation than most players.

      • Jason

        The season has been pretty much over for the past two months though

    • charlottencredsfan

      I don’t know. It is anecdotal but let’s just say that, IMO, Jay is not at his best in high pressure situations. He appears a little tense to me.

      I heard about an interview with Joe Maddon and he said he wants his guys to relax more, that they are not curing cancer (life & death). Just paraphrasing Maddon, but I think Jay Bruce would be a perennial All-Star if he played under him. I like JB a lot and think the best is likely to be seen.

      Buy, sell or hold? BUY!

      • Jason

        The playoffs were essentially locked up it was just a matter of time

    • jdx19

      Something for all posters to keep in mind is that pitcher quality is generally higher in high-leverage situations than in low-leverage situations.

      I’m pretty sure no one does as good against Chapman as they do against a league-average pitcher, yet, Chapman (in some instances) is pitching high-leverage 9th innings.

      Also, bringing in a lefty-specialist to face Bruce (or anyone with a platoon split) in a high-leverage situation will give the illusion that he doesn’t do as well in high-leverage situations.

      If you think about it through that lens, almost all players should hit well less often in high-leverage situations than in low-leverage situations.

  2. charlottencredsfan

    Really good stuff, Michael.

    Reviewing Jay’s month-by-month stats, it appears Jay has one really, really great month and one awful one but is a picture of consistency the other 4.

    To me, he is the most overrated and underrated position player on the Reds. IMO, he is just a smidgen under elite status but a really fine player. Looking at 2015, every month his wRC+ has increased:
    Mar/Apr: 93
    May: 110
    June: 127
    July: 154

    Tell you what, I’m “not” trading this guy. If 2014 never existed, he would be considered a fantastic hitter who may be getting better and better and closing in on “elite”. Hold this hand, Reds. Heck, extend him right now!

  3. wdwrolen2713

    Legitimate question, couldn’t there be some mental or psychological truth to streaks? In other words, if a player randomly has a succession of hits or good games their confidence begins to boost. Also vice versa, if player has succession of bad games, couldn’t attitude technically stall them in slump? I feel the mental side of a player could add some to streaks, though I understand theres no physical proof of this.

    • wdwrolen2713

      Meant to say “add some TRUTH to streaks.”

    • Steve Mancuso

      What you call physical is a product of what you call mental. The theory about confidence is disproven by the numbers that show that streakiness is a myth.

      • jdx19

        (Not specifically a reply to you, Steve, but I’m posting here anyways!)

        And also if you think about it another way, variation in a player’s mood or confidence from day-to-day, even if there was such a thing, would even out given a large enough sample. So, even if streakiness due to mental state were true, I’d expect it to even out anyways and thus, not be streaky.

        What an interesting topic!

    • Michael Maffie

      The studies cited in the article are pretty good at testing the “psychological boost” explanation of streaks. The lab experiments match the real world data on sports performance and do not find evidence of for a “hot hand” (or hitting streak).

      As Steve said below, if a player changes their physical approach because they feel they are not hitting well (or have gone a long period of time without a hit), that’s not really a streak, that’s a physical adjustment.

      • charlottencredsfan

        At the same time, there are players who admit to pressing too much.

        In general I’m in agreement with you. I think guys mechanics do get tangled up at times. Jay has a big swing that may led him to having a bit more of an issue than a guy who’s swing is short and direct to the ball – Rose, Carew, etc. But then, Jay would give up much of his power. He is alright the way he is and there is evidence he is getting better.

        One of the best analysis at RLN and that is saying a lot.

      • Michael Maffie

        Thanks, Charlotte! You’ve put your finger on one of the most heated debates in this area: how do researchers model the changes players make during a contest. Early on there were arguments that basketball players with a “hot hand” would face a tougher defense or try more difficult shots because they were “feeling it”. Pairing lab studies with real world data helped to control for these effects and demonstrated that randomness was a better method of explaining shooting patterns.

      • jdx19

        Interesting point about what the players say themselves. Shouldn’t the players, after all, know better than an observer what is going on? Very interesting.

        Perhaps they are all learned responses from hearing other people say similar things. Better to have something fixable (pressing) to blame your variance on rather than saying “I have no idea what’s going on” when describing your variance at the plate.

        Good stuff!

  4. RedFuture

    I’ll allow that Bruce’s current streak is over a more extended time than most. I certainly hope this the beginning for a maturing hitter. It would be a shame to trade him away just when he became less streaky and more of a mature hitter. That said, the streaks that Bruce has had in the past did not last a month, they seemed to be 2 weeks max. These were also preceded and followed by cold streaks. Therefore the monthly figures don’t tell the story. The monthly stats will be “smoothed” and not show the streak extremes like the 10 day streaks. Do the same study over the course of 2 weeks or 10 games even.

    • charlottencredsfan

      I was under the same impression but don’t think serious study bears it out. When Bruce is “red hot”, he can carry a club and not many can make that claim. It doesn’t necessarily mean that he is “ice cold” the rest of the time. After thinking about it some, my opinion is those intense hot steaks cloud our (my) objective thinking about the non-hot streaks. In all honesty, Jay Bruce would be the last Red I’d recommend trading and is at the top of my list of offering an extension.

      I also disagree if you trade Frazier you must trade Bruce. TF is probably at the top of his game and could bring in a haul. I don’t believe we have seen Bruce’s best. He and Joey are the building blocks.

    • Michael Maffie

      Week-by-week studies tested if hitters who are on a “hot streak” (bat .450 or better) or on a “cold streak” (.150 or worse) are likely to follow up those weeks with “hot” or “cold” weeks. The results found that hitters were equally likely to follow “hot” weeks with another “hot” week or “cold” weeks with another “cold” week.

      If there is no serial correlation between at-bats, then it doesn’t really matter what timeframe you pick, these events do not influence each other.

  5. Ben

    I admire your approach on this, but I don’t like that you focused so much on calendar months. Your approach would miss a streak that straddled two months — a ten game hot streak could be measured in your data as 5-game blips in each month, which would register as small bumps on each monthly average and not show that for ten games this guy was pretty dang hot.

    The problem with statistics (or maybe with people’s expectations of statistics) is they are MUCH better at understanding what has already happened than they are at predicting what’s to come. So yea, you can’t say “he’s hit safely in the last 8 games, he won’t have an 0-fer today” but you can definitely say “his OPS the last three weeks has been 150 points higher than his season average, that’s a nice little hot streak.”

    That said, great writeup. Baseball is the perfect sport for stat geeks and articles like this are why.

    • Michael Maffie

      Thanks, Ben. I agree that month-by-month would not pick up smaller “streaks” if there is a pull toward a central performance level. Other studies have done week-by-week tests and come to the same conclusion. If there isn’t a serial correlation between at-bats, then it doesn’t really matter the timeframe selected. I picked months because the data is reasonably easy to collect from places like fangraphs and baseball reference and because the Jay Bruce narrative usually focuses around a month timeframe.

  6. WVRedlegs

    Excellent research Michael. You knocked it out of the park like a Jay Bruce HR.
    Jay Bruce has made some significant adjustments within the last year. He is hitting to LF more. He is hitting LH pitchers better. Historically, July is his worst month of hitting, a .230 BA. But this July he has put up a very solid month, .306 BA.
    I want to keep saying, “We’ve got Jay for that.” Do not trade him.

  7. HerpyDerp

    Couldn’t you just take every games batting average, and show the moving average over each season? I know it’s not terribly accurate, but it’s easy to digest.

    • Michael Maffie

      the Petti article pretty much does that for wOBP from game-to-game (that’s the core of his stat, “Hitter Volatility”). Since power stats are not linearly related to scoring runs, making the trade of power for consistency generally makes sense (hence why many of those players at the top of the hitter volatility leaderboard are great run producers, like Albert Pujols).

      The “volatility” here is intentional because those are the players can take an 0-3 night because they can go 2-3 with a double and a home run another night.

  8. Vanessa Galagnara

    If Jay is so fantastic then why aren’t clubs throwing top prospects to get him? Seager for Bruce. The dodgers would say no. Take any top 50 prospect and there is a good chance that the team with the prospect would turn down the offer. And yet we say Bruce is great and is paid a cheap salary. If that is true why aren’t the Dodgers, Yankees, Red Sox throwing the farm at the Reds in order to get him?

    • charlottencredsfan

      Mainly? Probably his knee. His value is going up as we speak but still would be a sell low target.

    • Michael Maffie

      1) you trade contracts, not players. Seager’s contract with LA is for 6 years at the beginning of his aging curve.

      2) Im not saying Jay Bruce is worth all the best prospects from every organization, just that when we label him “streaky”, it is a mischaracterization.

      • jdx19

        Admirable job of keeping your cool in the face of such ‘interesting’ posts.

    • lwblogger2

      Mostly because if you trade for Jay Bruce you have 1-2 years of team control at a reasonable but not minimal salary. With the prospect you’re holding on to, you may have a player who is nearly as good and you have that player for 6 years of control, 3 of them at a minimal salary and the other 3 likely at reasonable salaries. Bruce may still fetch a top 100 guy if traded because he’s a known quantity and prospects are not. It all depends on the right buyer. If the Reds could trade Bruce for a nearly ready top 100 outfielder then perhaps they should do it but if they got a top 100 it would more likely be a guy that’s got a later arrival date for MLB. Why? Because the teams that need Bruce may also see that top 100 who’s near MLB ready as a September or earlier callup that could perhaps still help this year. They are more likely to give up the player that wont help them this year… That’s a move the Reds should only make if they feel that they won’t compete until after 2017, at least in my opinion.

    • whodeythinkgonnabeatthemredlegs

      Agreed. Really interesting stuff.

  9. gaffer

    Bruce is on his way out the door. He will almost certainky be traded as the 1) reds need the $ and 2) he is the second best hitter on the market.

    • charlottencredsfan

      I’d trade anyone but it would have to be a very sweet deal.

      • lwblogger2

        Right, I’d only make the move in one of 2 scenarios:

        I get back a top 100 guy who’s near MLB ready


        I get back a top 100 guy who’s farther away but I don’t think my team will compete until after Bruce’s contract is up (2017)

  10. Playtowin

    Great job Michael. Your analysis makes a lot of sense. That said Bruce still appears to be streaky to me. I would not trade him either. He is still young. He is relatively inexpensive. I bet the Yankees make a run at him now or over the winter.

  11. zaglamir

    The statistics here are SEXY. Nice work. This makes me want to compute information transfer functions on the MLB at-bat data. Looking for outliers of people who have an over-arching, “this at-bat’s outcome is connected to the next at-bat’s outcome.” I imagine there would be some interesting data in this, especially if considering ranged input… such as, “how does “information” during the same game” or “versus the same pitcher” or “across games” or “does the at-bat 4 at-bats ago have the same transfer as the previous at-bat.” Basically, I’m saying your article has rendered me useless at work today while I think about baseball statistics.


    • i71_Exile

      I don’t know what this means, but am looking forward to the conclusion of your analysis.

    • Michael Maffie

      Two ideas:

      Are batters who face pitchers with 3 quality pitches more likely to have a positive information transfer then when they face pitchers who have 4 quality pitches? (I have to say, if this is the case, then it drastically changes when you take pitchers out of the game).

      I’ve also heard that leadoff hitters are instructed to take a bunch of pitches so they can report back to the dugout what the pitcher is throwing and how well they are able to get their pitches across. Has computer tracking changed this? If not, are there certain leadoff hitters that are able to identify pitches and transfer information better than others?

      Thanks for reading and happy Friday.

    • jdx19

      ZAGLAMIR… take this approach you’re alluding to and apply it to daily returns in the S&P now we’re in business! 😉

  12. zaglamir

    I’d like to also point out Votto’s “no longer elite” centroid of 155 wRC+. Holy cow, we’ve been watching one of the all-time greats. Too bad many of us won’t realize it until he’s gone.

    • jdx19

      You are correct. I’ve been trying to eductate folks on this (along with others here) for a long time.

      Earlier in the year I did an analysis on all players with 1500 PAs betwen 2010 and 2015. Votto was 1st in wRC+ with men on base (176, I believe). Next highest guy was Miguel Cabrera at 171, I think. I always think those things are intesting when we heard the narrative in 2013 that Votto wasn’t good when men on base (or men in scoring position; a subset of men on base).

      He’s Top 20 ALL-TIME (unless his .001 drop this year made him 21st) in OBP.

      He’s 4th ALL-TIME (Cobb, Hornsby, Carew) in BABIP (min 4000 PAs). This is the most impressive stat. It shows that he is truly one of the greatest strikers of the ball in MLB history. If he had a 10% K rate instead of 18%, I don’t think anyone would need convinving that he’s one of the all-time greats.

      It’s one of the worst travesties that many Reds fans can’t appreciate what we get to watch on a daily basis. We won’t see another Votto in Cincy for a long time, if ever.

  13. WVRedlegs

    May I propose a theory on why Jay Bruce’s name is being bandied about in trade rumors so much?
    I think the Reds have seen the starting pitching market going south with the underwhelming offers they are getting. They have decided to keep Cueto and Leake through the end of the season, give them the Qualifying Offer which both will turn down, and will take the two supplemental draft picks for them.
    Why do this? Well, with the Reds winning the Competitive Balance lottery with the first pick of those 10 teams. The first CB pick this past draft was #37 overall, last year it was #35 and in 2013 it was #34. The Reds should finish the season with around the 7th-10th overall pick in next years draft. Add the two supplemental picks for Cueto and Leake, which should be in the #26-#34 neighborhood, and presto, the Reds have FOUR of the top 35 or so picks in next years draft. That is the equivalent of FOUR first round picks. In what is being reported as a very deep top of the draft next year. Four top quality college picks, maybe.
    So then the Reds are left to shop Chapman, Bruce, Byrd, Phillips, Pena, and Schumaker.
    The Reds will take those four top draft picks, the prospects they get from the trades, and add them to the mix of Winker and Company. That will lead to a tsunami of Reds top prospects arriving in 2017 and before the 2018 season. The 2016 season will be a very lean year. But 2017 could be something special, and more so in 2018. A bigger and better version of the new Cubs, and getting there faster.
    It isn’t the road I would take as GM, but I could see the Reds front office taking this approach now. Getting four first round picks is enticing.

    • Vanessa Galagnara

      I think you are spot on. I am thinking that unless the Reds get top 10 caliber prospect offers they sit on both Leake and Cueto.

      • i71_Exile

        I agree with this. I did a little research using Baseball America’s top 100 lists for the Reds’ potential trade partners and after subtracting the “untouchables” found that the pickings were fairly slim—especially when compared to a well-scouted first round pick. If the Reds trust Dan Buckley, then a QO comp pick could be a better talent than what they are offered. Time is the key unless they go college and nab the next Mike Leake. Guys they receive in a trade should be closer than anyone they would draft.

    • jdx19

      Very interesting thought. You could be right.

      Ultimately, I hope you aren’t, though. Because four “first round” picks are not anywhere near as valuable as 2 guys who have proven they can play in AA, in my opinion. The amount of risk involved with guys who haven’t played above HS or college is significanly higher than guys who have proven they can handle some level of professional competition.

      I’d much rather get rid of everyone (who is going) now, save a little money, and get a few lower-risk (asusming sufficient upside) guys in high-A, AA, or even AAA, than spin the wheel in the amature draft.

      Either way, the next week should be interesting!

    • Tom Gray

      Like your optimism.

      The W totals I can see are 75 in 2015. 70 to 75 in 2016. 75 to 80 in 2017. 80 to 85 in 2018. Unless it’s a total fire sale (Cueto, Leake, Byrd, Bruce, Chapman) this month.

      Then 70 in 2015. 65 to 70 in 2016. 70 to 75 in 2017. 75 to 80 in 2018. Maybe less.

  14. Armflapper8

    IMO, do NOT trade Jay, let alone ANY of the core unless you’re just going to cave in to the idea that these 2010-2015 guys can never make it all the way. If you don’t think they can go all the way with this core, then we SHOULD blow it up completely and go with a full on youth movement.

    Basically, I think we should hold them all (except the free agents) and let the core of this team have one final go at it all while they’re all still in their prime. Sadly, the pitching staff is so young that they likely wont be good enough to even make the playoffs even IF the core remains intact and healthy. Still, I’d like to give it one more year because there’s some real talent with our starting 8.

  15. Armflapper8

    I’ll still never forget talking to my dad throughout the late 80s about how awful it would be never to get a championship out of Eric Davis’s talent. But then he won the big one.

    That’s how I feel about Jay, Joey, and Brandon. And now Todd and Billy as well. These guys are too talented to never make it to the series, and it’s going to break my heart if we don’t get to at least see them try for the next two years.

    But after that, I’m all for starting over again from scratch and firesaling them all.

    Still,I keep going back to this core being up on the Giants in the playoffs and…………so close.

    • IndyRedMan

      Dusty! Everyone could see Latos melting down in Game 5 but Dusty. He left him in to face Buster Posey….total collapse here we come!

      • Armflapper8

        Yep. Dusty. Liked the guy. Couldn’t stand the manager.

  16. jamesgarrett

    Great job Michael with the analysis on Jay Bruce.He has impressed me the last few months with his willingness to change his approach at the plate.I am really impressed when a major league player that has had success is willing to change when things aren’t going so good.To me that shows a team first and me second mentality.Hope he continues and others follow.

  17. IndyRedMan

    If Jay Bruce isn’t streaky then who was the guy I was jousting over online with his devoted followers in 2013 (or 2012?) because he hit like .190 from mid-May to early August. That’s not a brief slump…it was almost 3 months? Of course he got on a heater and his numbers were good by the end of the year. He’s a good player and a good guy and I would like to see him remain a Red….just preferably in the 6th hole.

    • jdx19

      The article pretty clearly states why Bruce isn’t ‘streaky.’

      At this point, we might just be dealing with people’s own definition of ‘streaky.’

      • IndyRedMan

        Same kind of number crunching nerds said Cozart was just unlucky last year because his batting avg w/balls in play was abnormally low.

        No….actually it wasn’t. His swing was flawed and he was popping everything up. It wasn’t some mathematical fluke.

  18. nllspc

    I’m undecided about this subject (more recent studies http://www.vox.com/2015/6/3/8719731/hot-hand-fallacy ) but the sample you’re using is comparing apples to an orange.

    I’d be more convinced if your sample included players more closely related to Bruce. Your data set for each player ranges from 2010 to 2015. Well Bruce’s experience level (plate appearances, age) in that range is different than Votto’s or Phillips, or Frazier’s, etc..

    The standard deviation approach sounds fine but as you mention,

    “It does seem that it is harder to maintain a higher level of play than it is a lower level (or, Joey Votto going 0-for-4 has a much bigger effect on his wRC+ than Zack Cozart), so more skilled players seem to have a bit larger variation around their average production level than less skilled players.”

    so wouldn’t it make since to choose from a group of players with similar wRC+ numbers as Bruce?

    I thought the “hitter volatility” section was interesting but I think that introduces another possible constraint on your sample — possibly only including power hitters.

    Anyways liked the approach but (disregarding sample size) I would’ve liked to have seen a random sample of players more closely related to the player they’re being compared to.

    • Michael Maffie

      agreed that a random sample would have been better, or perhaps limiting it to players who were around the same age / ability level as Bruce (~120 wRC+). I traded comparability for familiarity given the general gist of RN.

      I don’t really think its that big of a drawback, though. My data (month-to-month wRC+) was mostly an illustration of previous data and not really the underlying “backbone” of this article. The other literature cited above is much more comprehensive and statistically rigorous than lining up wRC+s for a few players who all happen to be on the same team. The literature pretty strongly implies that there isn’t a serial correlation between at-bats, so the sample size/comparability wasn’t something I wanted to spend a ton of time perfecting.

      The hitter volatility section from Petti includes all players from 2011-2013, but the players who ranked near the top of the league in terms of volatility were all power hitters. Given that Petti uses wOBP and a day-to-day timeframe, thats not really all the unexpected.

  19. jdx19

    Mike. This is perhaps the best article (or my favorite) written at RLN since I’ve been reading over the last 3 seasons. Kudos.

  20. User1022

    I think the main problem I find in this article is how it views the notion of a “streak”. Rather, it approaches a “streak” as though it is meant to be predictive. A case of this is indicated here:

    The authors do not find evidence that previous hits or misses have an effect on future shots, providing further evidence that “…research indicat[es] that people’ intuitive conceptions of randomness do not conform to the laws of chance”.

    The thing is, a “streak” is a descriptive outcome, not predictive. If a player goes something like 20-30 over the course of a week, you would say he’s on a “hot streak”. That week has no bearing on what that player is going to do in the future, it merely describes what happened. Likewise, if another player goes 5-30 in the same week, he’s in a slump or on a “cold streak”. It doesn’t matter if it’s because he’s injured, tired, his father is sick, he’s worried about trade rumors, the fact is, he had a bad week and that contributed to his “streak”. Basically, view a “streak” as batting average, not BABIP. You could also discuss how large of a sample size you need to consider something a “streak”. Basically, I think we can agree the idea of a “streak” is that a player produces at a level significantly higher or lower than their career averages for a sustained amount of time, but eventually revert to performing at their average level.

    Further, looking at the data a bit more, I think the graphs tell us something about where the notion of a “streak” comes from: It’s not so much the mean or median we should focus on (since those would just give us the average descriptive stats), rather it’s the RANGE.

    Think about this: Let’s say you are at a place where the average temperature over 10 day period is 60 degrees. The temperature varies by about 10 degrees each day, from 50 to 70, but it works out to 60. You would say the weather was quite consistent (and pleasant) over that stretch.

    Now, let’s say you are in another place and the weather also averages 60 degrees over a 10 day period. But the temperature is 90 5 of those days in a row, and 30 degrees on the other 5 days (also known as “May” in Cincinnati). We just had a streak of 5 blistering hot days followed by a streak of 5 pretty cold days.

    The median results would be the same, but how they arrived there was very different. One was caused by fairly consistent temperatures, while the other was caused by huge deviations (or streaks).

    Take a look at Jay Bruce’s chart as well as Todd Frazier’s, two hitters who are generally regarded as being fairly “streaky”. What do you notice? There is a significant distribution of data quite far away from their means, in both cases nearly 100 points positive and negative. Cozart has a much smaller range, only about 40 points in either direction, Phillips ranges about 70 points in either direction, although I suspect his range would be even smaller had you done this study before he had entered his decline years. Votto is an interesting case as he seems to have a smaller “peak” around the 200 area. I suspect if he hadn’t had so much productive time taken from him due to injury and recovery from that, his actual mean wRC+ would be about 20 points higher during this span, making his results a bit more evenly distributed around central point and it would also serve to eliminate some of the lower results, thus narrowing his range.

    The fact that Bruce and Frazier have such a wide range of results would seem to play into the notion that they are streaky hitters. And again, I think if you examined this on a weekly basis (I don’t consider a single game a large enough sample size to alone constitute a “streak”), you would find even greater variation among their ranges.

    The main takeaways are:

    1. A “streak” is a descriptive term, not predictive.
    2. A “streak” can be defined as a player producing at a level significantly higher or lower than their career averages for a sustained amount of time, but eventually revert to performing at their average level. No matter what caused these deviations, they do occur. (See #1)
    3. Jay Bruce and Todd Frazier are considered streaky because their results have a significantly wider range than what would be expected from normal, consistent production.

    • tct

      Agree with this. Loved the article, but I think in the end the debate about whether hot streaks exist is just arguing semantics. If a guy has a week where he goes 15-30 with 5 homers, did he have a “hot streak” or an “extremely fortuitous random distribution of events.” Does it even matter?

      The big takeaway for me in these studies is, as you say, hot and cold streaks are not predictive in any way. There is no way to know when they will begin or end. That is only apparent after the fact. So streaks have no value at all in the decision making process; for example, there is no benefit in moving a guy up or down in the lineup based solely on a streak.

    • Dave

      Bingo – streaks describe outcomes, whether caused by randomness in a model, mechanical changes, illness, or whatever. This article misses that point, saying in short that streaks don’t exist…then goes on to admit they do, but only by randomness *eye roll*.

      This misuse of statistical analysis is why a lot of the former players get annoyed with the SABR guys – a streak is sometimes hitting the ball hard and hitting it at people (just keep plugging away, they’ll start falling) or the inverse of soft hits dropping being “hot.” Hitting is something you have to constantly adjust and, regardless of your recent results, you should seek to minimize poor ABs/pitches every chance you get – it’s what makes the Vottos of the world get that extra hit ever week (.250 vs. .300, see Bull Durham, meat) and a 16-20 HR guy into a 30+ guy (one more dinger every two weeks). To look at the stats and say “streaks don’t exists, therefore I’m not in a slump, I’m fine, just keep swinging” robs you of the opportunity of improving.

  21. lost11found

    Both Batters and pitcher have much in common with golfers. A complex set of physical motions to achieve a result.

    Most would say streaks are caused by either repeating the succesful motions or by a breakdown of the same.

    In the end, the satement above that streaks are descriptive and not predictive has the most truth to it.

  22. sezwhom

    Jay Bruce? A take-off on Denny Green: he is what we thought he is…..

  23. The Next Janish

    Would losing your wallet count as a cold streak? Are some of us more prone to losing our wallets? Do some just lose their wallet and just don’t notice?

  24. Dave

    For a long time we’ve chalked up changes in performance to “streaks” instead of looking for the underlying reasons.

    Um, no, those of us that know the game have never done this, at all. Your original premise is flawed – a streak, by definition, is a “spell or run” (example given: luck). This has nothing to do with prior events influencing upcoming ones, but rather with the abnormal occurrence of events in sequence. In other words, a streak isn’t getting a hit in your 3rd and 4th time up BECAUSE you did it your first 2 ABs, as well, but rather it’s the stringing together of 4 consecutive hits. Or, in terms of a “hit streak,” it’s having consecutive games with at least one hit. That’s a streak – that exists, without question.

    You eventually arrive at a better place in terms of saying streaks exist, but are explainable within the context of randomness. And yes, DiMaggio and Rose are far more likely to run together consecutive games streaks than guys who get 140 hits on the year (as were Jeter and Ichiro, etc.). But the whole point to evaluating a streak is to seek the underlying reason for it – it’s why sometimes you hear a player say “it’s okay, I’m hitting the ball hard, they’re not falling in, they will” and not be worried about a “slump.” Other times, the player realizes the problem is mechanical or (far more often) approach-based and makes a change.

    The common theory is that when you’re going well, you start chasing anything and everything, leading to diminished results. You often then press and chase more and slump worse, until you correct your pitch selection and “start hitting” again. I’d be willing to bet the newer data on whiff% and chase vs. in-zone data confirm this (you hit strikes better than balls, as a general rule, for sure). There is likely a very strong positive correlation to chasing fewer balls and obtaining better results, from fewer whiffs to lower k% rates to harder exit velocity and higher BABIP.

    I agree Bruce is hardly any more streaky than anyone else – we just see that high ceiling and stretch his good days out beyond what they really were (correctly identified as confirmation bias). However, he, like everyone else who has ever played the game, has streaks, both good and bad. Sometimes he is injured/sick/whatever and other times its a matter of good or bad luck over a short period of time. The best hitters, however, like Votto and Ted Williams “don’t give away ABs,” focusing on pitch selection every time up and minimizing the number of times they produce lesser results (not just outs, but missing HRs to later walk or single on a tougher 2-strike pitch, hitting a strike for a well-struck out instead of swinging and missing, etc.). Bruce isn’t any streakier than most, but denying the existence of streaks in baseball is incorrect and, thinking a streak is defined by a prior event’s occurrence, robs people of the will to seek the truth as to why you’re having a good or bad week at the plate. It’s an example of misusing the stats (“streaks don’t exist,” rather than “they exist, but mainly due to randomness or a mechanical/pitch-selection issue”) to cheat people of proper, in-depth analysis that proves useful.

    • Armflapper8

      Wow. Mike, loved the post. But Dave’s reply here is exactly why I’ve been coming to Redleg Nation every day for 10 years. Every time I think I’ve heard it all, somebody else chimes in with something new to further my education on the greatest game ever devised by man!

      Thanks to all of you guys on this site for never letting the game get boring. I love baseball more and more everyday because of all the editors and commenters on this site. Again, thanks Chad!