Sports Metrics-Tracking Wearable Sleeve

Dept. of CIS - Senior Design 2013-2014 ∗

Ibrahim Ayubibayub@seas.upenn.edu

Univ. of PennsylvaniaPhiladelphia, PA

Adam Colomboacolombo@wharton.upenn.edu

Univ. of PennsylvaniaPhiladelphia, PA

Max Ehrlichmax.ehrlich.design@gmail.com

Philadelphia UniversityPhiladelphia, PA

Tom Musemuseth22@gmail.comUniv. of Pennsylvania

Philadelphia, PA

Sawyer Waughswaugh@seas.upenn.edu

Univ. of PennsylvaniaPhiladelphia, PA

ABSTRACTWearable devices capable of computation are increasing ininfluence and functionality. Furthermore, their use has beenextended from purely academic and technical fields to otherarenas. The devices can be configured into various packages,such as watches, wristbands, and headbands. Regardless oftheir presentation, these devices are equipped with the base-line functionality of interacting with the user’s surroundingsor preferences and providing feedback. We propose a newdevice dedicated to sports and health. Utilizing a wearabledevice while practicing sports can provide substantial datafor users that can optimize their routines. Our solution, Re-flex, aims to identify and analyze data to allow athletes toeffectively train and to enhance their future practice sessionsby providing data-driven recommendations as well. Notably,Reflex is the first device to apply bayesian data analysis in asports analytics context. Our solution outlines novel modelspecifications which provide better analytics than current of-ferings.

1. INTRODUCTIONReflex is packaged as a lightweight wearable sleeve that

is designed to be used while the user is engaged in a prac-tice session. The inner lining is a polyester blend for sweatresistance, covered by an outer elastic silicone shell. Op-posing sides of the band contains sensor pads with pressuresensors. By touching either the left or ride side, the usercan log a successful or a failed repetition on the band. Thissimple mechanism can be applied to all sports, from prac-ticing shooting a basketball to putting in golf. The devicewill communicate data received to the user’s iOS device viaBluetooth. Here the user will be presented with the ana-lytics of the collected data, which includes visualizations ofprevious training sessions as well as recommended routinesfor the future.

2. BACKGROUNDWearable technology enables users to monitor and record

real-time data about their personal lives and daily activities.Devices are currently concentrated in healthcare and fitness.For the former, applications include monitoring heart rate,

∗Advisor: Kostas Daniilidis (kostas@cis.upenn.edu).

blood pressure and blood sugar, tracking weight, sleep pat-terns, and diet. Services dedicated to fitness record the dura-tion, frequency, and intensity of exercises as well. Advancesin manufacturing capabilities including the development ofwoven fabric sensors are leading to more applications as well.Despite gathering this data, these devices fail to addresskey needs for athletes seeking to improve in their respectivefields. In the context of sports, success is largely based onan athletes’ ability to effectively practice and have success-ful repetitions of routines fundamental to their given sport.Tracking practices and repeated movements is a difficult andtedious task for athletes. There is no product that providessophisticated analytics for teamsport atheletes. Reflex ad-dresses these issues to optimize athletic performance.

3. RELATED WORKThis section outlines related work in the areas of wearable

technology and sports performance. There are two maincategories of devices relevant to Reflex, health and fitness.After exploring these products, we discuss related analyticsin the arena of sports.

3.1 Health and Fitness DevicesWe briefly describe relevant health and fitness devices in

this section, followed by an explanation of why our imple-mentation is distinct and valuable.

NIKE FUELBAND [10] This wristband enables usersto track their physical activity, daily steps taken, and dailycalories burned. The information is integrated into the Nike+online community and phone application, enabling users toset their fitness goals, monitor their progress, and comparethemselves to others in Nike’s social platform.

FITBIT FLEX [4] This band tracks daily steps, sleepduration, and calories burned. It also offers Bluetooth syn-chronization to the user’s mobile device as well as visualiza-tions of the data.

JAWBONE UP [8] This device tracks movement andsleep and offers a corresponding mobile application that dis-plays the data and also allows for user input on meals andmood.

LARKLIFE [1] This wristwatch tracks patterns of dailyexercise, diet, and sleeping throughout the day. It then offersfeedback in real-time to the user.

MISFIT SHINE [11] This device acts as a pedometer,utilizing a three-axis accelerometer to track movement. Thisproduct is also equipped with Bluetooth for synchronizingdata with iOS devices.

LIT [9] The LIT bracelet tracks common activities such aswalking and running as well as movements unique to actionsports such as surfing, skateboarding, and snowboarding.This device also allows users to share their information onsocial media platforms as well.

These devices, while similar in nature to the structure andunderlying technology of Reflex, differ in that they are fo-cused on overall daily well-being. As such, they track dailymovements do not provide sports analytics. The last exam-ple, LIT, incorporates sports but they concentrate on ac-tion sports and letting users share their best statistics withfriends. Thus, Reflex is unique in the sense that while itis also tracking movement and user input, it is analyzingthe data ultimately to enhance practice and athlete perfor-mance.

3.2 Sports Tracking DevicesUnlike the devices listed in the previous section, there

are a few products dedicated solely to sports. They arebriefly described below followed by an explanation of thedistinguishing components of Reflex.

SHOT COACH [3] This device automatically trackssuccessful and failed shot attempts, logs the location of wherethe shot was taken, records wrist movement, shot arch, andball velocity, and transmits this information via Bluetoothto the user’s smartphone. The Shot Coach includes a wear-able sweatband and a module that attaches to the bottom ofthe basketball rim. The band contains sensors that commu-nicate with the module, and the information collected fromboth is then sent to the smartphone.

HOOP TRACKER [5] Hoop Tracker consists of twophysical components, a wristwatch and a magnetic shot de-tector that is mounted on the rim of the basket. Throughouta practice session, shot percentage, shot location, and otherinformation is displayed on the watch.

The devices described above are too complicated to beeffective for most athletes due to an excessive number ofcomponents. Both Shot Coach and Hoop Tracker requirehardware to be placed on the basketball hoop itself. Thisfeature requires an the user to be the sole person using thatparticular basketball hoop. In contrast, Reflex may be usedwhile sharing a basketball hoop with any other number ofathletes. Last, unlike Reflex, neither leverages the collecteddata to provide optimized workouts for the user or customanalytics.

3.3 Sports Performance AnalyticsIn regards to analytics, all related work has been focused

on in-game performance, and a variety of insightful metrics

have been developed.

Player Spread [7] In a presentation at the Sloan SportsAnalytic Conference, Kirk Goldberry developed this metric.It decomposes an athlete’s shooting performance into 1 of1,284 scoring cells. The player’s spread is the measure of thenumber of cells that were used and the associated frequen-cies.

Skill-Acquisition Learning [12] Manuel C. Voelkle et.al. have published work analyzing various skill acquisition-learning curves, identifying different levels of learning andprogress.

This work is relatable to REFLEX in determining and re-fining the underlying algorithms to be developed for athleteperformance and recommendations.

In particular is the idea that sports skills like musical oreven driving a car are in the psychomotor region of skills,requiring the most practice and constant upkeep of practicein order for the skill to be maintained. This is relatable toREFLEX in that it will help determine the constant upkeepnumbers these skills require.

4. SYSTEM MODELThis section explains the underlying design and structure

of Reflex. This service consists of a wearable device andmobile application that optimizes an athlete’s practice andtraining. The device monitors the wearer’s performanceover each training session. The athlete’s progress is ana-lyzed statistically and presented visually through a series ofa graphs. Using this data, along with user-defined parame-ters (including height, weight, age, and goals), Reflex createscustomized workouts for athletes.

4.1 Reflex System ComponentsReflexSleeve is a lightweight wearable sleeve worn on

the forearm. The sleeve is lined with a moisture-wickingpolyester blend for sweat resistance and maximal comfort.The outer shell is composed of elastic silicone for physicalrobustness. Figure 1 shows a rendering of the CAD file whichis used in fabricating the sleeve.

Figure 1: CAD Rendering

Within the sleeve is a microcontroller to process the datareceived. Limited, onboard memory allows us to run a sim-ple program for tracking workouts and interacting with I/O

devices. The microcontroller is connected to pressure sen-sors, bluetooth antenna, and battery. The pressure sensorsare large and covered with tactile rubber nubs for ease ofuse. By touching either the left or ride side, the user can loga successful or a failed repetition. The bluetooth antenna isused to communicate with the user’s iOS device as well asthe two other iOS devices to triangulate the user’s position.

ReflexPOS is the system used to triangulate the user’slocation on the basketball court. Using bluetooth to connectthe ReflexSleeve with two other iPhones, the user’s positioncan be identified.

ReflexStat is the central component to the Reflex sys-tem. It receives and sorts data streams from the ReflexSleeveand ReflexPos components, and communicates with the server,ReflexServe. Finally, ReflexStat performs analytics and presentsmeaningful feedback to the user with a clean, simple graph-ical user interface.

ReflexServe is an applicaton server which serves the Re-flex API.

ReflexDB is a relational database. The database holdsinformation about users, user workouts, user progress, andshooting. The exact schema is still being developed.

5. SYSTEM IMPLEMENTATIONFigure 2 shows the interactions between the Reflex com-

ponents. All workout session data is collected by the Re-flexSleeve and the ReflexPos components. This data is thentransmitted wirelessly to ReflexStat where it is stored tem-porarily. At the conclusion of a workout, the temporary datalog is pushed to a table, workouts, in ReflexDB. ReflexStatthen queries workouts in ReflexDB for the updated data set.The data set is analyzed and the results are pushed back toa different table in ReflexDB, analytics, for storage. Thiscommunication occurs over WI-FI or a cellular connection.When a user accesses ReflexStat to review his progress, theapplication queries analytics for the most recent entry. Theinformation in analytics is used to populate the graphicaland statistical models within the application. Each compo-nent of Reflex will now be explained in detail.

Figure 2: System Overview

5.1 API ServerReflex’s servers are hosted on Amazon’s Elastic Compute

Cloud (EC2). We serve data for our mobile application andwebsite using a Node.js process. Amazon’s EC2 was cho-sen to host the server because EC2 provides Reflex with the

ability to readily scale by distributing the server load acrossmultiple instances if necessary. Furthermore, EC2 is a re-liable server with extensive support. Node.js is a softwareplatform that is increasingly used to power I/O-intensive ap-plications. Thus, Node.js was chosen for the servers becauseReflex is I/O bound rather than CPU bound, which is ad-dressed by Node.js. Furthermore, Node.js provides ease inquickly incorporating new features and expanding Reflex’sservices in the future.

5.2 DatabaseUser data is stored on a PostgreSQL instance on Amazon’s

Relational Database Service (RDS). PostgreSQL has sev-eral benefits over MySQL for the purposes of Reflex. First,PostgreSQL has a simpler method for creating user-definedfunctions, which are necessary in generating analytics. Ad-ditionally, PostgreSQL has various features including ACIDcompliance and an Array data type that aid both in ensur-ing data consistency and in modeling the event data that iscollected.

5.3 Mobile Application

5.4 ReflexSleeveReflexSleeve is controlled by a Microduino microcon-

troller. Microduino is a smaller variation of the open-sourceArduino hardware, approximately 2.5cm by 2.5cm. Thiscompact frame is more user-friendly, as it is lighter and re-quires less space in the ReflexSleeve. Apart from the slimform-factor, the Microduino also provides Wi-Fi, bluetoothconnectivity, and a large selection of compatible I/O devices.

5.5 ReflexPOSReflexPOS is a system that is used to compute relative

position on a playing field or court using bluetooth technol-ogy. We use Apple’s Core Bluetooth framework to networkwith the bluetooth antenna in ReflexSleeve. Apple’s CoreBluetooth framework is used to measure the received signalstrength indicator (RSSI) from ReflexServe. The value ofRSSI serves as a proxy for distance because RSSI increasesas the bluetooth source moves closer and decreases as itmoves away. With a total of three bluetooth receivers (iOSdevices) we are able to calculate three distance measures.Using these distance measures we are able to use trilatera-tion to find relative position on the court. When Reflex isstarted, the user is prompted to specify where they are lo-cated on the court. This allows Reflex to establish an origincoordinate from which to base future positions.

6. ANALYTICSReflex offers two types of player analytics. The first, Re-

flex Workout Analyzer, analyzes practice sessions, scorespast performance and predicts future performance. The sec-ond, Reflex Workout Creator, uses past workouts and perfor-mance to construct optimized workouts for the player goingforward.

6.1 Workout AnalyzerReflex’s Workout Analyzer uses Bayesian data analysis to

provide accurate predictions of future workouts and gives

players a powerful tool to evaluate their performance.The core of the Workout Analyzer is a Beta-Binomial

model. The Beta-Binomial model is similar to a Binomialdistribution except that instead of having a fixed probabilityp of success in each Bernoulli trial, p varies according to aBeta distribution. We have the following:

p(X = x|n, p) =

(n

x

)px(1− p)n−x,

p ∼ Beta(α, β)

In order to remove the dependence on p which is unknown,we integrate over all possible values of p:

p(X = x|n) =

∫ 1

0

(n

x

)px(1− p)n−x · p

α−1(1− p)β−1

B(α, β)dp,

p(X = x|n) =

(n

x

)B(n+ α, n− x+ β)

B(α, β)

In order to apply this model we first partition the play-ing surface into sections. For basketball we have chosen todivide the area around the hoop on each end of the courtinto six zones, two rows with three zones in each row. Foreach zone, we establish a prior distribution for use in theBeta-Binomial model. The prior distribution specifies apri-ori knowledge about player performance in any particularzone. Since these prior distributions are used for customerswhom we have not collected data on, they are constructed inorder to represent the base case player. It is also importantto note that prior distributions were constructed for eachparticular player position; we expect shooting guards to adifferent shot distribution than power forwards.

Figure 3 shows a heat map of NBA player Kobe Bryant’sshots from 2006 through 2011. In the image, brighter colorsindicate a higher probability of successful shot and the sizeof the boxes indicate a higher number of shots taken fromthat location. This heat map, combined with knowledge ofbasketball affected the development of the prior distribu-tions.

Figure 3: Heat Map

Figure 4 shows the prior distribution used in the top leftzone on the heat map. Kobe Bryant is a shooting guard andthis distribution represents how we believe shooting guardswill perform from the top left zone (around three point line)on the court. The distribution shown in 4 is the distributionthat p is drawn from. One way of interpreting this distribu-tion is that we expect on any given day, you will make on

average 37.5% of shots from this zone. We can also see thatit is highly unlikely that you will make more than 60%.

Figure 4: Top Left Prior

Figure 5 shows the prior distribution for the bottom leftzone. This helps to illustrate the variance in performancethat the Beta-Binomial model captures across the differentzones.

Figure 5: Bottom Left Prior

The power of the Workout Analyzer is that it allows Re-flex to learn about customers as they use the product. Reflexaccomplishes this task by using bayesian inference to makemore and more refined statements about a customer’s abil-ity. Too explain how Reflex accomplishes this, a brief reviewof Bayes Law is required.

Bayes Law is a law of probability that relates conditionalprobabilities.

p(x|y) =p(y|x) · p(x)

p(y),

=p(y|x) · p(x)∫p(y|x) · p(x)dx

This allows us to create an updated distribution of param-eters given some observed data, which is called the posteriordistribution. The posterior distribution is:

p(p|x, n) ∼ Beta(α+ x, n− x+ β)

With each workout, Reflex collect n & x (total numberof shots and number of made shots); Reflex is then able toupdate the distribution for p to more accurately reflect aparticular customer’s ability. This distribution takes intoaccount all previous workouts and is entirely customized ona per player basis.

To evaluate the performance of the Workout Analyzer,live tests were done. In one test, practice was simulated byhaving a player take 20 shots from the top left zone. Theplayer ’practiced’ over three workouts. Results showing theWorkout Analyzer’s predictions and actual performance areshown in Table 1.

Workout Analyzer Testingα β # Attempts # Expected

Successes# Actual Suc-cesses

6 10 20 7.5 1016 20 20 8.88 1228 28 20 10 836 40 20 9.47 -

Table 1: Workout Analyzer Test

These results are shown plotted in Figure 6.

Figure 6: Workout Analyzer Test

Figure 6 shows the bayesian update process in action. Re-flex’s model responds to performance and updates predic-tions accordingly.

6.2 Skill DecayThe Beta-Binomial model is well documented in the field

of bayesian data analysis. In keeping with the psycho motorprinciple of skill decay, the basic Beta-Binomial model wasmodified the model in order to take into account the timebetween workouts. The full model, including skill decay isspecified below:

p(X = x) =

(n

x

)B(α′+ x, β′+ n− x)

B(α′, β′),

α′ = α0 + α · λ, β′ = β0 + β · λ

, λ =1

1 + e(t−t0),

t0 = 8

In the full model, λ represents skill decay, t is the timebetween workouts in days, and t0 is a parameter that governshow quickly that decay happens. If an athelete works outwithin 8 days of his/her previous workout, there is littleno no skill decay (λ is close to 1); however, if an atheletewaits more than 8 days, λ begins to drop to 0. In thismodel, α0 and β0 represent the parameters for the aprioriprior distributions when Reflex knows nothing about thecustomer. As λ drops towards 0, the parameters α′ andβ′ regress to their initial values, representing the fact thatsince it has been so long since the player practiced, Reflexis again unable to make any specific predictions about theirperformance.

6.3 Workout & Player EvaluationReflex’s Workout Analyzer provides a valuable tool for

players to evaluate their own performance. For example,Reflex may predict that a player will make 15 out of 20shots from a certain location. This becomes a metric thatthe player can use to judge their own performance. Reflex’sWorkout Analyzer also enables players to compare them-selves to other players that Reflex has data on.

We know that for two players P1 and P2, their values of pare distributed according to beta distributions with param-eters α1, β1 and α2, β2.

p1 ∼ Beta(α1, β1),

p2 ∼ Beta(α2, β2)

There is a closed form solution for P (p1 > p2) howeverit is computationally intensive. Instead these distributionsare sampled from in order to approximate this probability.This allows Reflex to give players reports on how they com-pare to their friends or any other athelete. This is anothernovel way that Reflex analytics allow players to evaluatetheir performance.

6.4 Workout CreatorThe basis of the analytics for users in a created Reflex

workout is that they can be seen as stochastic systems, eachworkout may result in a random shooting percentage, butoverall there is a positive growth towards higher numbers asplayers improve through practice. After again using the heatmap to eight most common gametime shooting positions byplayer type, the analytics involved use an iterative formula

Figure 7: Chosen Shot Spots for SG

to determine the number of attempts the user should takefrom any one position in the following workout.

Workoutxn,t+1 = β1 ·xn,tmin

FGP (xn,t)+ β2 ·

xn,t−1min

FGP (xn,t−1)−

β3 · (FGP (xn,t)− FGP (xn,t−1)) + β4ed

The equation takes into account the last two workouts ofthe user to determine the next one, and has four weightedparts the effectiveness in workouts one and two, improve-ment in two from one, and again skill decay is brought in asthe last subsection. Therefore as time goes on the equationmore closely matches the skill of the user and will give morepersonalized and efficient workouts to have the user improvehis skill at the fastest rate possible. Finally the psychomo-tor skill ideas surrounding sporting skills is also taken intoaccount as a preset minimum number of shots the user musttake from any position regardless of algorithm output in or-der to avoid any skill decay. On the opposite end there arealso preset maximums so that the workouts are timely asthe desired user is an amateur who has limited time

7. RESULTSFigure 8 shows ReflexBand during development.ReflexBand was able to communicate both positioning

and make and miss inputs to the user cell phone(s).Analytically, Reflex shows promising results when simu-

lated in the preset workout feature as it does start to adjustto the users growth rate by about the fifth workout session.This is important because while in the first two or three ses-sions the number of attempts from any position may jumpdrastically, after a while the user expects a more coherentoutput that makes sense based on the prior workouts with-out providing too big of a jump in attempts. This mentalreassurance only further drives the user to want to use Reflexmore as the user is rewarded with fewer attempts and fasterworkouts. The fact that Reflex has also shown the result topersonalize with simulated users of various skill levels alsohelp point to its flexibility to personalize future workouts.

Also looking at the simulation, it is evident that beyondjust personalizing future workouts to each user, Reflex trulydoes maximize practice efficiency as it does highlight the

Figure 8: Hardware Device

zones where the user is either a poor shooter either by per-centage, or by improvement rate, and the analytics do havethe user proportionally take more shots from those regions.For some of the higher rated simulations (those that shoot

at 45 percent, considered to be the NBAaAZs best) theywere reaching the minimum shooting attempts in under tenworkouts at some positions. This data shows that Reflexcan truly track user process as well as not waste user time.

Finally the results from the analytics in a non preset work-out also show the same promise. The workout analyzer as-pect of the Reflex tool provides equally relevant and infor-mative data and analyses and was done in the workout gen-erated half. The Bayes analysis while starting from a Reflexdecided baseline, does indeed in simulations approach thetrue mean of the shooting percentage in a reasonable lengthof time (10-15 uses). The skill decay function was also testedin simulation and also displayed promising results as it dis-plays rougher results though ones that are more accurate asthe simulated actor did lose skill in the simulation.

8. FUTURE WORKThe Reflex service is currently focused on workout opti-

mization for basketball, however this model can be adaptedfor other sports as well. The intuitive and user-friendly Re-flexSleeve can be worn without interrupting the user whileengaged in many activities, such as baseball, golf, football,soccer, archery, and hunting. In general terms, due to thebinary input design of ”success” or ”failure,” Reflex can beadapted to any exercise where users are monitoring perfor-mance in this binary fashion. Additionally, changing thecontext from a basketball court to a different environmentis not trivial, but can readily be modified and still leveragethe underlying formulas and analysis.

The current Reflex model is also designated for one user.However, future work can expand its functionality to accom-modate teams as well. In doing so, users and coaches alikecan better understand performance and growth both on anindividual and on a team basis. This would require a morecomplex system model, where ReflexSleeves can identify andcommunicate with one another. While the current analysis

of an individual’s performance may not need to be altered,additional analytics would be needed to model and monitoran athlete’s interaction with teammates.

9. ETHICSOne potential concern stems from the ‘recommended work-

outs’ that Reflex provides to its users. These workouts areintended to help the athlete improve in their particular ath-letic domain; such improvement requires a particular degreeof intensity. While the Reflex algorithms do consider age,weight, physical fitness and athletic skill, there exists a smalllikelihood that a user will be prescribed a workout exceed-ing his physical capabilities. Any form of excessive physicaleffort, particularly those involving repetitive motions, caninduce overexertion [2]. To mitigate the risk of a Reflex useroverexerting himself, cautionary information will be madeavailable to the user. Reflex products will come packagedwith materials warning of the dangers of overexertion, itssymptoms, and suggestions for treatment. Another way tomitigate risk is to include additional sensors in the Reflexsleeve that monitor particular aspects of a user’s health. Theuser would be considered safe within some range of valuesfor each health metric; any activity outside of that rangewould immediately alert the user and end the workout. Thewearable technology market is currently flooded with de-vices that give such biofeedback, including heart rate, bloodpressure, caloric exertion, blood sugar, blood oxygen level,and breathing rate [6]. By integrating some or all of thesebiosensors into Reflex, we would both mitigate risk and in-crease its value.

10. CONCLUSIONThis paper outlined a new type of wearable device geared

towards providing sophisticated analytics to team sport atheletes.Specifically, Reflex outlines:

1. A wearable device designed for a team sport practiceenvironment

2. An analytics package able to provide custom analyticsfor atheletes

3. An application and service that provides a user inter-face which makes it easy for athletes to access andinterpret analytics

11. REFERENCES[1] Lark life. http:

//www.lark.com/products/larklife/features/.

[2] Overexertion.http://www.nsc.org/nsc_events/Nat_Safe_Month/

Documents/PreventingOverexertion.pdf.

[3] The shot coach. http://theshotcoach.com.

[4] Brian Bennett. A most versatile, feature-packedtracker.http://www.cnet.com/products/fitbit-flex/2/,2013.

[5] Ben Coxworth. Hoop tracker keeps tabs on basketballplayers’ makes and misses. http://www.gizmag.com/hoop-tracket-basketball-watch/28854/.

[6] Samuel Gibbs. Ces 2014: The best wearablesmartwatches and fitness gadgets. http://www.theguardian.com/technology/2014/jan/07/

ces-2014-wearable-smartwatches-fitness-gadgets.

[7] Kirk. Goldsberry. Courtvision: New visual and spatialanalytics for the nba. Proc. of MIT Sloan SportsAnalytics Conference, 2013.

[8] Jawbone. Up. http://jawbone.com/up.

[9] NZN Labs. Lit: An activity tracker ready for action.http://www.indiegogo.com/projects/

lit-an-activity-tracker-ready-for-action.

[10] NIKE. Nike fuel band.http://www.nike.com/cdp/fuelband/us/en_us/.

[11] Scott Stein. Misfit shine review.

[12] Manuel C. Voelkle, Werner W. Wittmann, andPhillip L. Ackerman. Abilities and skill acquisition: Alatent growth curve approach, learning and individualdifferences.