Funneling Attempts on the Power Play

If you have vaguely followed the NHL in the recent past, arguably the most evergreen phenomenon is Alex Ovechkin shooting from the left face-off circle on a power play. Not familiar? Take a look at his shot attempt locations with the man advantage since the 2007-2008 regular season:

Distilling these locations into a contour map yields the following:

The Washington Capitals, in this time-frame, have ranked 3rd, 1st, 1st, 17th, 18th, 1st, 1st, 1st, 1st, 3rd, 6th, 14th, and 21st (this past season) in goals per 60 minutes on the power play. Over the entirety of the time between the 2007-2008 and 2019-2020 seasons, the Capitals have scored 7.94 goals per 60 minutes on the power play, 0.82 goals per 60 more than the second-place Bruins. The difference between the Capitals and Bruins is the same as the difference between Boston and Montreal, who ranks 17th. Recent struggles notwithstanding, the Capitals power play has consistently churned out goals despite the fact that everyone in the arena and on their couch knows where they want to move the puck. To boil down the Capitals power play to funneling Ovechkin the puck is a bit disingenuous, but one would think going to the well over and over again would lose effectiveness over time. One might argue that the Caps are seeing their predictable behavior come to haunt them in recent seasons, but I would argue that has more to do with relative effectiveness of some of the pieces as they age. For most of the last 13 seasons, the Capitals have had the best power play in the league. 

Ovechkin is a generational goal scorer and arguably the best of all time. Funneling shot attempts to a player of that caliber (to the tune of 38 percent the past three seasons) seems like a shrewd strategy. But what about other players? Can funneling the puck to a single player on the power play lead to overall effectiveness if that player is not Ovechkin? To investigate, I took every player who has played 100 minutes on the power play (specifically 5v4 power plays) over the past three regular seasons. Next I looked at each of those players' individual shot attempt rates, goal scoring rates, and expected goal scoring rates. I then paired those with their on-ice shot attempt, goal, and expected goal rates and took the percentage of each that the individual accounted for. 

Once I collected all the data, I first plotted the effects of funneling for all the players in the data set on their on-ice goal rates (my barometer for power play effectiveness): 

There looks to be not much of a relationship. At the tail end of the shot attempt and goal plots there appears to be a small negative relationship, so I filtered for players who I deemed the most used (at least 20% of shot attempt, goal, and expected goal share): 

Still nothing. For expected goals and goals, there seems to be some diminishing returns at around 28 percent, but this does not persist with shot attempts. Finally, I split the data by forwards and defenseman to see if funneling to a specific player type has any effect: 

Given the locations from where defensemen shoot, it is not surprising that funneling offense in their direction yields worse results. They are often shooting far from the goal line, above the face-off circles. For forwards, it is still difficult to come to any conclusion. 

In the future, I would like to dig into this deeper and see if funneling to specific locations for specific shot types can help explain the proficiency of a power play. Can a player like Mike Hoffman, who has a similar shot diet to Ovechkin but at the right face-off circle, prop-up a good power play? For now, I think we can safely say the following: funneling the puck to forwards is not an inherently bad strategy (without knowledge of specifics) and funneling the puck to defenseman is bad (which is not a revolutionary finding). 

For those who are curious, here are the most and least used players on the power play based on percentage of shot attempts: 

Shot location data via Moneypuck.com, all other data via Natural Stat Trick

Small Sample Strikeout Woes

Gary Sanchez, through his first 25 plate appearances in this abbreviated 2020 season, accumulated 12 strikeouts, a rate of 48 percent. Needless to say, there has been a lot of hand-wringing about this slow start to the year, including questions about his focus (which New York fans love to talk about with respect to Sanchez) and his overall ability (despite the massive sample of Sanchez being an excellent hitter, the best among catchers since his debut in 2016 on a rate basis).

I wanted to pen a quick post about narrative building off of small samples of plate appearances. Given the short season and the general nature of baseball fandom, it is difficult to put aside what you are watching on a game to game basis and have perspective on the range of outcomes for a player in small samples and what that player should be expected to do, on a macro-level (single or multiple seasons), in the future.

Inspired by Sanchez's strikeout-riddled start to the season, I looked at theoretical hitters with true strikeout rate talents from 20 percent to 40 percent in increments of two percentage points. For each batter I simulated 25 plate appearance samples 10,000 times each. I used a Monte Carlo method where a number below the strikeout rate talent level resulted in a "strikeout" while all other numbers were other plate appearance outcomes, which I was not concerned with for this study. The following are histograms for each theoretical hitter and the distribution of strikeout rates in each of the 10,000 25 plate appearance samples:

The horizontal axis represents the strikeout rate in the sample. The dashed line represents a strikeout rate of 50 percent, so any result past that would indicate the hitter struck-out in at least 13 plate appearances in the sample. As you would imagine, a true talent 20 percent strikeout rate hitter rarely records 13 strikeouts in 25 plate appearances. Also not surprising, a 40 percent strikeout rate hitter is rung-up at least 13 times more often than the hitter with a 20 percent talent. For more clarity on how often each hitter records a strikeout rate of 50 percent, I created another visualization using the distributions above: 

The 20 percent strikeout rate hitter recorded 13 strikeouts in just six of the samples, or 0.06 percent. The 40 percent hitter recorded the value of interest in 16.1 percent of the samples. Even a 40 percent true talent hitter rarely records this result and there are not even any of these types of hitters who regularly play in MLB. The average strikeout rate in MLB is 23 percent and a hitter of that talent level would be expected to record this result about 0.15 percent of the time. Let us now go back to Gary Sanchez. Depth Charts projections at FanGraphs have him at a 28.9 percent strikeout rate for the rest of the season, which we can consider that system's estimation of his true talent. We would expect a hitter of this caliber to strikeout at least 50 percent of the time about 1.2 percent of the time. What this means is that Sanchez is performing (with respect to striking out) at a level that certainly is within his range of possible outcomes, but an incredibly bad outcome at that. So I guess what you, the reader, should take away from this is maybe, just maybe, cut the guy a little slack. He has certainly been dreadful thus far, but I would not expect this level of performance to persist throughout the season. 

Gerrit Cole's First Couple of Starts for the Yankees

Now a little more than one week through the (mess that is the) 2020 MLB season, we have seen Gerrit Cole take the mound for the Yankees on two occasions. Cole was the biggest free agent on the market and as such he signed a 324 million dollar contract with New York, the largest ever for a major league pitcher. Cole is coming off of two seasons in Houston where, after making some meaningful changes to his pitch mix, he blossomed into an ace-level starting pitcher to the tune of a 37.3 percent strike-out rate, a 6.9 percent walk rate and accumulated 13.4 wins above replacement over 412 and two thirds regular season innings, per FanGraphs. 

Having seen both of his starts thus far, I thought it would be a fun exercise to dig through some of the pitch-level data, even with the season's future hanging in the balance and see if I can spot any differences in his pitch characteristics thus far between his tenure in Houston and his starts with the Yankees. Before I take a look, I should provide the caveat that looking at just two starts worth of pitches should be taken with a massive grain of salt, on account of the extremely small sample. 

First, here are his average velocities by pitch type and the standard deviation of those velocities: 

Not much of a change at all. Even the standard deviations are very close. Next, pitch usage both in total and by count: 

Cole has been much more reliant on his four seamer in the early going, especially in hitter's counts. This might be some indication that he does not trust his secondary pitches yet for high leverage pitches, which given the unusual circumstances around the start of the season is not especially surprising. Still, given his success the last couple of years, I would hope as the season (hopefully) progresses, he begins to lean on his slider and curve more often to keep hitters uncomfortable even when they have the advantage. 

To the eye, Cole has not been very sharp (relative to our enormous expectations) and sure enough he seems to have some issues commanding the fastball and curve.

He really seems to be making an effort to bury his curve, but given his whiff rates in the past on the pitch he would probably see some benefit to putting it more in the strike zone and forcing opposing hitters to swing. The fastball has been left over the plate way too often thus far, and his whiff rate has suffered as a result (37.6 percent last year, 22.0 percent through his first two starts. In 2018 it was 29.7 percent, so some regression from last year's figure is to be expected). The slider seems fine, but his curve ball is generally his breaking ball of choice against lefties. In order to turn over the lineup more than a couple of times effectively, he needs to be more effective with that curve. Maybe you can attribute some of this apparent lack of command to where he is releasing the ball?

Looks like he is releasing the ball closer to his head on average. There is still overlap between the release positions in Houston and New York, but there is a clear separation between the clusters. Here is the same information in tabular form: 

There is a difference, but it is too early to attribute this difference to a mechanical change versus just natural variance in his release points. In the release point plots above, there is more variation in his release points from his Houston days, but also more pitches facilitates a larger probability that various release points deviate from the mean. If you consider his release point data from Houston as a distribution of possible release points for Cole, it is feasible that the data from his pitches in New York would fit in that distribution, disproving the idea that this is a conscious mechanical change and instead is just a product of variance. Nevertheless, I would be interested in hearing whether or not he made this tweak on purpose or its just the product of a small sample of pitches. Finally I looked at Cole's pitch movement profile and found that nothing had really changed in his first two starts. 

And the data in tabular form: 

Given the movement has not changed nor has the velocity, as I explained above, the apparent lack of command through two starts is probably the main culprit of his strike-out rate falling 10 percentage points since compared to his time in Houston and going from 0.93 ground balls per fly ball to 0.35, per FanGraphs. His swinging strike rate is down (about 27 percent) as is the rate at which he puts away hitters with two strikes.

All of this is not cause for alarm. Cole has been very good through two starts, just not as dominant as we have been used to. But we are also talking about only two starts and two starts after a four month layoff. Given what has transpired in the world of baseball the last few days, I would be much more worried about seeing Cole pitch at all for the rest of 2020. 

Predicting NBA Team Scoring Rates with Splits

Using splits when analyzing sports is, generally, something that should be done with caution. Entire seasons worth of player and team performance are subject to noise so taking that data, breaking it into specific splits, and drawing conclusions leads to even noisier results.

With that being said....I am going to see if I can use team scoring rate splits to better predict next year overall scoring efficiency. The impetus behind my idea was that I thought certain splits may better isolate how effective an NBA offense is at scoring efficiently. For example, one of the splits I looked at was scoring efficiency on possessions that started with a dead ball. The theory is that by looking at just these possessions, I could get more signal about future offensive efficiency because this split is not reliant on the opponent missing a shot and the location of the rebound after the missed shot. The issue is, in general, teams have about one fourth to one third the possessions following a dead ball versus those that start after an opponent miss.

I looked how all situations scoring efficiency in year N can be predicted by scoring efficiency in all situations, off of a miss, after a dead ball, and after a steal in year N-1. I included scoring efficiency after steals to show how offensive value generated off of steals is not something teams should count on year over year since they are highly dependent on the opponent and transition efficiency in general is a noisy. I made five simple linear models to predict year N all situation offensive efficiency (measured in points per 100 possessions): scoring efficiency in all situations in prior year adjusted for minutes continuity between years N and N-1, scoring efficiency after opponent misses in prior year adjusted for minutes continuity between years N and N-1, scoring efficiency after dead balls in prior year adjusted for minutes continuity between years N and N-1, a model using all three of the splits adjusted for minutes continuity between years N and N-1, and a model to look at the change in overall scoring efficiency with just minutes continuity between years N and N-1. The minutes continuity data can be found here.

The following represents the adjusted R squared values for each linear model:

Of all the models, just using the prior year overall scoring efficiency is most predictive followed by the mixed split model and the model using efficiency after opponent misses. First, my assumption that performance after dead balls might give more signal into a team's "true" offensive efficiency seems to not hold much weight. That model was barely more predictive than the model using scoring effectiveness after steals. I would attribute this to the sample issues I alluded to above, where there were only about one fourth to one third of the possessions after dead balls relative to those after a miss for a given team season. Furthermore, not breaking the data down into splits proves to be the best way to handicap a team's offensive efficiency in the following year. Now keep in mind, this is a very simple way to approach such handicapping; the R squared between all situations scoring efficiency in years N and N-1 is still only 0.38 after adjusting for minutes continuity. What is missing in this analysis is a more granular look at minutes continuity; the way I accounted for minutes continuity does not account for the quality of the players nor does it account for changes in player ability by means of aging. This manifests itself in the model using just simple roster continuity having an adjusted R squared of just 0.012. Incorporating player value and performance (through one or a blend of the many RAPM variants out in the public) and player aging would yield a better correlation.

What can be gleaned from this study? This is a reaffirmation that using splits to predict team performance is not a worthwhile endeavor. Splits can be useful for describing team and player past performance, but their contributions to past performance (either positive or negative) is noise for the purposes of prediction and should be regressed heavily towards the mean. 

Considering a Nolan Arenado Trade

Over at Pinstripe Alley readers were asked to come up with a post about possible Yankees trade targets, including Nolan Arenado, a player general manager Brian Cashman has been rumored to covet. In a vacuum, I would think that any fan of the team would love to have Arenado don pinstripes. The issue is baseball players do not exist in a vacuum; players compete on the diamond and in return receive an agreed upon salary. The issue with Arenado is two-fold; his contract is large compared to most of his peers (he has been guaranteed the sixth largest contract amongst active contracts, per Cots Contracts) and he can opt out of his contract after the 2021 season. The opt-out clause makes valuing Arenado in a trade tricky. With that being said, I wanted to try to find a fair way to value Arenado and construct a deal with would potentially make sense for the Yankees, if possible.

As I alluded to above, Arenado is guaranteed a lot of money. To be precise from 2020 through 2026 he is set to receive 234 million dollars from the Rockies, per RosterResource. Now, using the methodology for valuing players I described here (a quick summation if you want to avoid the link: I use a simple aging curve combined with a Monte Carlo simulation of a players WAR total and cost of a win in free agency to get a distribution of possible dollar figures for a player) and using his Depth Charts win projection of about 4.86 WAR this coming year, I projected Arenado to be worth about 265.57 million dollars over the next seven seasons, so about 31.57 million dollars in surplus over seven years. The following is a distribution of his seven-year value, in millions of dollars:

The column headers correspond the percentiles. 95 percent of the time, he is expected to be worth at least 113.09 million dollars. Overall, Arenado’s contract is reasonable, without considering the opt-out clause.

I should note, if any of you may have forgotten, we are living in the middle of a global pandemic and the structure of the MLB season has been substantially altered to the tune of 60 games. As a result, Arenado will paid a prorated share of his 35 million dollar salary, which comes out to 12.96 million dollars. So, shave off 22.04 million dollars from 234 million and about 26.01 million dollars from his 50^th percentile outcome. From Craig Edwards research into prospect value Arenado would be worth either a 55 FV pitcher or 50 FV position player without the opt-out clause, or some combination of players that would yield a similar result if the Rockies value quantity over quality.

Without the opt-out clause, I would end the analysis here. But the option is arguably the most important and valuable component of the contract from Arenado’s side. Before I put a dollar value on the option, let’s first look at Arenado’s value assuming he opts out after the 2021 season. Under normal circumstances he would be due 70 million dollars over the next two years. Using the methodology from above, here is a snapshot of his distribution of possible outcomes:

On average, he would be worth 7.06 million dollars in surplus, or about a 45+ FV prospect for two seasons. Given the Arenado’s stature as a player, this is surprising and speaks volumes on how well Arenado and his representation made out in their negotiation with the Rockies. Like we saw above, we need to consider the circumstances of the pandemic and the fact that if the Yankees were to trade for Arenado at the deadline on August 31^st, they would only get him for about 30 games plus a potential playoff run. When accounting for his prorated salary over 30 games and his full salary next season, he is owed 41.48 million dollars over two years. The snapshot of his possible value distribution is as follows:

On average he will provide just a bit more than one million dollars in surplus. If the Yankees were to operate under the assumption that opt-out with 100 percent certainty, it would be hard to argue they should give up anything of substance to bring Arenado into the fold. Now, this fails to consider that the value of WAR is not linear and the value of the great players is higher because concentrating WAR into one roster spot gives teams the opportunity to be flexible with rest of the roster, but I did not think it was worth getting any more into the weeds.  

The real issue underlying all of this is the team cannot value Arenado as if he will definitely play out all seven years under contract nor can it assume he will definitely opt-out. Given the economic uncertainty brought on by the pandemic, I would tend to think Arenado would be more likely to opt in to the remaining five years on the deal. But let’s assume that the free agent market does not change as a result of the pandemic (which one might say is a foolish assumption, but I think provides a more interesting thought exercise). Let’s also assume that Arenado will opt out of his deal if he is projected to be worth more than 164 million dollars he is owed over the final five years of the deal starting at age 31. Using my Monte Carlo simulation function and assuming his projection is about half a win less at age 31 as it is at age 29, Arenado would be worth at least 164 million dollars about 57 percent of the time. There are two ways to account for this in the valuation of the contract. The first is to look at how much he is worth when he opts in, account for that in the valuation and take a weighted average of his surplus value when he opts in and out, where the weights are the percent chance he makes each decision. Using this methodology, if he opts in he would be worth on average 129.26 million over five years putting the contract 34.74 million dollars underwater at the end. Remember, over the first two years with the pandemic, he is worth 1.31 million in surplus. Taking the weighted average of the two figures yields a valuation of his contract being worth 14.15 million in the red.

The other way of accounting for the opt out clause is to isolate the value of the clause on Arenado’s end of the deal and add it to the total money guaranteed to get the value of the combination of the opt out clause and the guaranteed salary. When Arenado opts out of the deal, he is worth on average 208.14 million dollars on average. Since he opts out 57 percent of the time, you can value the opt out as the additional money he would make by hitting the open market multiplied by the percent chance he goes to the market. Since he would be worth 208.14 million over the five years, we will assume he would receive that amount on a contract. This would be a net gain of 44.14 million dollars (164 subtracted from 2018.14). Multiplying 44.14 by 57 percent and you get 25.16 million dollars. Add the 25.16 million to the 234 million he is owed and you get a seven-year value of 259.16 million dollars. Remember from the beginning, he is projected to be worth 265.18 million dollars over the seven-year period, not accounting for the pandemic, so the contract is worth 5.99 million in surplus, which is microscopic relative to the size of the deal. Obviously, I am not considering the pandemic in this scenario but not much changes when you do so. When accounting for his smaller prorated salary this year and the value he will provide in the shortened season, the total surplus does not change much.

So, what did we learn from all of this? Well Arenado and his agency (he was represented by Wasserman Media Group) did great work in negotiating this deal. They got him an opt out early which gives Arenado the chance to hit the free agent market if the Rockies do not move in a direction he is comfortable with and the opt out makes it difficult for the Rockies to move him for a decent return. When I consider the opt out clause and the probability that he exercises it, his contract is either a slight negative or a slight positive on the team end. Given the player-friendly nature of the deal (which I do not mean to paint as a negative, just a negative when looking to trade for Arenado. I love seeing players going out and negotiating deals in their favor) and the uncertainty derived from the player option, I would be weary of dealing anything of value for Arenado. If the Yankees are truly interested in his services, I would rather see the team wait a couple of seasons and try its luck in free agency.

Can Players Drive Goals Above Expected?

The main pillar of hockey analysis in the year 2020 expected goals, a concept first introduced in soccer and one that eventually made its way over to hockey. Expected goals attempts to gauge the probability that a shot attempt finds the back of the net. A shot attempt with an expected goal value of 0.09 should be expected to be converted 9% of the time, assuming that the expected goals model is well calibrated. The driving forces behind all expected goal models are the x and y coordinates of the shot attempt, which can be found in the play-by-play data from the NHL API. This should be intuitive, the closer a shot is to both the goal line and the center of the ice, the greater the chance that shot will be converted. Now, the shot coordinates are not the only couple of variables. Analysts, such as those at Evolving-Hockey, MoneyPuck, and Natural Stat Trick have incorporated variables such as the handedness of the shooter, the time between successive shots, how long players have been on the ice, etc. I would going to this link and reading about the model at Evolving-Hockey for some more background. Included in that write-up is a short history of expected goal models.

The premise of using expected goals to evaluate players is that players do not have too much control over either their individual shooting percentage, their teammates shooting percentage, and their on-ice save percentage. This is not totally true (forwards, especially compared to defenseman, have some control over the two former figures. With that being said, these percentages should be heavily regressed towards the mean), but mostly true, so knowing where the shots are coming from and the nature of the shots should be more valuable than either goals for and against or even just shot attempts for an against.

Now, as I alluded to above, there is some evidence that players can some, albeit little, ownership over some of the percentages that are mainly chalked up to luck in hockey analyst circles. The analysts over at MoneyPuck have done work to gauge shooting talent using goals above expectation and Bayesian statistics. I wanted to see if I could find any signal in on-ice goals above expectation. To do so, I looked at the the differences between actual and expected goal Regularized Adjusted Plus-Minus (RAPM), which can be found at Evolving-Hockey. RAPM is derived from linear regression, where the target variable (in our case goals and expected goals) is regressed against the skaters on the ice, the score and strength state, zone starts, whether or not the offensive team played a back-to-back, and whether or not the offensive team was the home team. RAPM looks to isolate each players individual impact on his team's target variable differential.

For my analysis, the variable of interest was the difference between actual and expected goal RAPM per 60 minutes of even strength play, which I will refer to as RAPM delta for the remainder of the post. The idea is to figure out whether differences in the two RAPM figures can be considered meaningful for a player and then contribute that difference to the ability to drive goals by means of skills not captured in expected goals (mainly by individual shooting talent and buoying teammate shooting talent).

I took every skater season pair from the 2007-2008 season through 2019-2020 where the skater played at least 50 minutes in each season at even strength (an example of a season pair is Connor McDavid from 2018-2019 to 2019-2020). First I wanted to get a sense of the stickiness of RAPM delta year over year.

This is almost completely noise. With weights corresponding to the average time on ice between the two seasons in the pair, this yields an R-squared of about 0.01. As I alluded to above, deviations from the mean in shooting talent or on-ice percentages need to be regressed heavily towards the mean, even for multi-year samples. So the fact that RAPM delta in year N effectively does not explain anything about RAPM delta in year N+1 is not surprising. To account for the need of a heavy dose of regression, I put together a similar linear regression, but instead of using years N and N+1 weighted by average time on ice, I used career RAPM delta up to year N and RAPM delta in year N, weighted by career time on ice up to year N. 

There are less data points here because I am just looking at non-rookie skaters from the 2019-2020. Surprisingly, there is not much more signal here compared to when I looked at just prior year RAPM delta. This regression yielded an R-squared of about 0.027, still almost entirely noise. 

My last resort was to look at all of the players in my data set. I created a model where the target variable was RAPM delta. Instead of using any prior RAPM deltas, however, I created a series of dummy variables for each player with a season pair in the data set and regressed all of these variables (1645 in total) against RAPM delta. 

Now we see some signal. This regression resulted in a R-squared of 0.2458, a much stronger correlation than the previous two models. The coefficients in front of each dummy variable represent the estimated effect of each player on goals above expectation per 60 minutes. The following is the distribution of those coefficients: 

The distribution looks normal, as was expected. The fact that it is centered at about -0.05 goals per 60 minutes can be attributed to expected goals slightly underestimating actual goals. 

So, there appears to be some merit to players being able to drive on ice goals above expected. Given the research done on player shooting talent over at MoneyPuck, I think this type of behavior can manifest itself at the on-ice level, but probably not as strongly as on the individual level (given the confluence of variables at the on-ice level). The next step would be to try to nail down an accurate figure or reasonable possible distribution of figures for each individual player.

I will leave you with a table with some estimates of player RAPM delta (i.e. the coefficients from the regression). I took the top 10 and bottom ten RAPM delta impacts for players who played at least 1,000 even strength minutes this year. I would take these with a heavy grain of salt, there is still not an especially strong correlation between the model predictions and actual results and I did no further regression to the mean for the uncertainty of players who do not have a lot of career minutes. 

Statcast Aging Curves: Looking at How Hitter Exit Velocity Behavior Changes

Recently I looked at aging curves in the NHL. In my last couple of posts, I used the delta method to determine how forward skills age and how overall player value changes. Now, I am moving to baseball and, more specifically, exit velocity aging curves from the Statcast data. Since 2015, MLBAM has made some of the data recorded by TrackMan (and in the future Hawk-Eye) available to the public through its website Baseball Savant.

I wanted to see how hitter batted ball profiles aged, so I pulled a few batted ball metrics from the leader-boards and developed an aging pattern. In this study, I weighted each delta by the average number of batted balls between two player seasons.

First, the most commonly cited metric from Statcast, average exit velocity. While I have some qualms with how average exit velocity is presented versus what it actually means in practice (average exit velocity gives no context to the spread of a hitter's exit velocities, so Christian Yelich and Franmil Reyes profile similarly). Nevertheless, here is how average exit velocity ages during a hitter's career:

Age, to reiterate the point I made in my first aging curve post, is the second age in a given bucket. So age 24 on the chart corresponds to the delta between age 23 and age 24. The peak is a bit later than I expected, given our understanding that generally peak performance generally occurs somewhere between age 24 and 27. Maybe average exit velocity over a season is not a good indicator of whether or not that season was successful, relative to that player's ability. Let us now look at how maximum exit velocity ages: 

This is more in line with the traditional aging curve for player performance. For the sake of easy comparison, I put the maximum and average exit velocity curves on the same chart, along with average line-drive/fly-ball exit velocity.

Average exit velocities in balls put into the air age similarly to total average exit velocity (i.e. a less robust curve and later peak). This makes me think that maximum exit velocity is a distillation of where a player is in his career than either total average exit velocity or air-ball exit velocity. This finding is similar to the conclusion Rob Arthur came too in a 2018 study at The Athletic (subscription required). This is despite the fact that the maximum exit velocity for a player in a given season consists of a sample size of one (because it is the maximum of a distribution) while the other two measures consider all balls put in play. Subjectively, I would think that maximum exit velocity is a better indicator of physicality than average exit velocity, the latter of which can remain relatively unchanged even if the maximum declines through the development of some of the "soft skills" of being a major league hitter (waiting for good pitches to drive, avoiding swinging at pitches outside the strike-zone, etc).