Best Left-Backs in the La Liga (Jun 2026)
Ranked by Analytical Strength Index
Market Overview: La Liga Left-Backs 2026-27
Our database tracked 34 La Liga Left-Backs in the 2026-27 season, representing 20 clubs with a combined market value of €298.2M. The average market value for La Liga Left-Backs was €8.8M, with the average age at 28 years old.
The most valuable left-back in the La Liga was Álvaro Carreras, worth €60.0M and played for Real Madrid at 23 years old. The top 5 Left-Backs averaged €34.0M in market value, including Alejandro Balde and Gerard Martín.
Age distribution showed the youngest tracked left-back was Alejandro Balde (22 years, FC Barcelona, €60.0M), while the oldest was Yuri Berchiche (36 years, Athletic Bilbao, €1.2M). Research shows Left-Backs typically peak at age 27.
Historical analysis showed 12 Left-Backs (35%) increased in market value over the following 12 months based on age-curve trajectories, then-current performance trends, and playing time analysis. The La Liga market for Left-Backs remained actively developing with emerging talent in the 2026-27 season.
💡 Use the search bar below to find specific players, or apply filters to narrow results by club, age range, or market value. Click the chart icon next to any player to view their historical value trajectory and forecast.
Explore Market Size by Position in La Liga
Interactive bubble chart showing predicted 2-year growth vs current age for all La Liga Left-Backs. Identify undervalued assets and track market momentum across 20 clubs with €298.2M combined value.
Age Distribution: La Liga Left-Backs
The La Liga LB market shows 4 distinct age segments, with the largest cohort in the 30+ bracket (12 players, 35% of market). The 21-23 age group holds the most value at €141.0M, averaging €28.2M per player.
Top Left-Backs by Age Bracket
21-23 Years (5 players)
24-26 Years (11 players)
27-29 Years (6 players)
30+ Years (12 players)
Market Value Distribution
Elite Tier Concentration
The top 4 Left-Backs (12% of players) control €155.0M
Market Tiers
Market structure shows distributed value with elite (€50m+) tier representing 6% of the La Liga LB pool.
Elite (€50M+)
High (€15-30M)
Mid (€5-15M)
Club Distribution: La Liga Left-Backs
Among 20 La Liga clubs, Real Madrid leads with 3 Left-Backs worth €83.0M (averaging €27.7M per player). The top 10 clubs account for 62% of tracked Left-Backs.
Real Madrid (3 Left-Backs)
FC Barcelona (2 Left-Backs)
Real Sociedad (2 Left-Backs)
RCD Espanyol Barcelona (2 Left-Backs)
Player Rankings
Ranked by Analytical Strength Index. Click any player to view full profile, or click the chart icon to see value history.
Álvaro Carreras
Real Madrid • 23 years old
€51.9M
€60.0M
+15.6%
Expected: €66.9M
91.5
Alejandro Balde
FC Barcelona • 22 years old
€51.9M
€60.0M
+15.6%
Expected: €66.1M
90.8
Gerard Martín
FC Barcelona • 24 years old
€17.3M
€20.0M
+15.6%
Expected: €20.5M
73.7
Matteo Ruggeri
Atlético de Madrid • 23 years old
€13.0M
€15.0M
+15.6%
Expected: €16.1M
70.4
Carlos Romero
RCD Espanyol Barcelona • 24 years old
€13.0M
€15.0M
+15.6%
Expected: €15.4M
70.1
Sergio Gómez
Real Sociedad • 25 years old
€13.0M
€15.0M
+15.6%
Expected: €14.7M
69.5
Fran García
Real Madrid • 26 years old
€13.0M
€15.0M
+15.6%
Expected: €15.4M
69.2
Pep Chavarría
Rayo Vallecano • 28 years old
€12.9M
€10.0M
-22.6%
Expected: €8.8M
60.6
Sergi Cardona
Villarreal CF • 26 years old
€8.6M
€10.0M
+15.6%
Expected: €10.3M
60.4
Ferland Mendy
Real Madrid • 31 years old
€10.3M
€8.0M
-22.6%
Expected: €6.6M
58.3
Gabriel Suazo
Sevilla FC • 28 years old
€9.0M
€7.0M
-22.6%
Expected: €6.1M
56.2
Manu Sánchez
Levante UD • 25 years old
€5.2M
€6.0M
+15.6%
Expected: €5.9M
54.5
Junior Firpo
Real Betis Balompié • 29 years old
€7.7M
€6.0M
-22.6%
Expected: €5.0M
54.4
Javi López
Real Oviedo • 24 years old
€4.3M
€5.0M
+15.6%
Expected: €5.1M
52.7
José Gayà
Valencia CF • 31 years old
€6.5M
€5.0M
-22.6%
Expected: €4.1M
52.3
Abel Bretones
CA Osasuna • 25 years old
€3.9M
€4.5M
+15.6%
Expected: €4.4M
50.9
Álex Moreno
Girona FC • 33 years old
€4.5M
€3.5M
-22.6%
Expected: €3.1M
48.1
Javi Galán
CA Osasuna • 31 years old
€4.5M
€3.5M
-22.6%
Expected: €2.9M
47.9
Aihen Muñoz
Real Sociedad • 28 years old
€4.5M
€3.5M
-22.6%
Expected: €3.1M
47.5
Adama Boiro
Athletic Bilbao • 23 years old
€2.6M
€3.0M
+15.6%
Expected: €3.2M
43.2
Scout Tools
Advanced analytics for scouting and recruitment decisions. Each tool provides unique insights into player value, potential, and market dynamics.
Pre-Peak Value Efficiency (PPVE)
Identifies pre-peak players offering exceptional value relative to their age bracket. Higher PPVE = better value.
Understanding Pre-Peak Value Efficiency (PPVE)
FC Barcelona's Alejandro Balde at 22 years old has the highest Pre-Peak Value Efficiency at 4.00×. That means Álvaro Carreras is valued 4.00× higher than the median player in the 21-23 age bracket-representing exceptional value before reaching peak age.
In second is Real Madrid's Álvaro Carreras, who is 23 years old, with a 4.00× PPVE. Third is Gerard Martín of FC Barcelona, who is 24 years old with a 3.33× PPVE.
How PPVE is calculated: PPVE compares a player's current market value to the median value of all players in their age bracket. A PPVE of 4.00× means the player is worth 300% more than typical players their age-making them high-value targets before they reach peak value.
PPVE by Age Bracket
| Rank | Player | Age | Bracket | Current Value | Bracket Median | PPVE |
|---|---|---|---|---|---|---|
| #1 | Alejandro Balde FC Barcelona | 22 | 21-23 | €60.0M | €15.0M | 4.00× |
| #2 | Álvaro Carreras Real Madrid | 23 | 21-23 | €60.0M | €15.0M | 4.00× |
| #3 | Gerard Martín FC Barcelona | 24 | 24-26 | €20.0M | €6.0M | 3.33× |
| #4 | Sergio Gómez Real Sociedad | 25 | 24-26 | €15.0M | €6.0M | 2.50× |
| #5 | Carlos Romero RCD Espanyol Barcelona | 24 | 24-26 | €15.0M | €6.0M | 2.50× |
| #6 | Matteo Ruggeri Atlético de Madrid | 23 | 21-23 | €15.0M | €15.0M | 1.00× |
| #7 | Manu Sánchez Levante UD | 25 | 24-26 | €6.0M | €6.0M | 1.00× |
| #8 | Javi López Real Oviedo | 24 | 24-26 | €5.0M | €6.0M | 0.83× |
| #9 | Abel Bretones CA Osasuna | 25 | 24-26 | €4.5M | €6.0M | 0.75× |
| #10 | José Salinas RCD Espanyol Barcelona | 25 | 24-26 | €2.8M | €6.0M | 0.47× |
| #11 | Victor Parada Deportivo Alavés | 24 | 24-26 | €2.0M | €6.0M | 0.33× |
| #12 | Jesús Vázquez Valencia CF | 23 | 21-23 | €3.0M | €15.0M | 0.20× |
| #13 | Adama Boiro Athletic Bilbao | 23 | 21-23 | €3.0M | €15.0M | 0.20× |
Return-to-Peak Potential (RPP)
Recovery potential from current value to forecasted peak. Shows how much upside remains for players approaching their prime.
Understanding Return-to-Peak Potential (RPP)
FC Barcelona's Alejandro Balde at 22 years old has the highest Return-to-Peak Potential at +25%. That means Alejandro Balde is projected to appreciate 25% as they reach their peak age in 4 years-representing significant upside before entering their prime.
In second is Valencia CF's Jesús Vázquez, who is 23 years old, with a +20% RPP (3 years to peak). Third is Adama Boiro of Athletic Bilbao, who is 23 years old with a +20% RPP (3 years to peak).
How RPP is calculated: RPP compares a player's current market value to their forecasted peak value, calculating the percentage appreciation potential. A 25% RPP means the player is expected to gain 25% value as they enter their prime-making them excellent growth investments.
Recovery Potential by Player
| Rank | Player | Age | Years to Peak | Current | Peak Forecast | RPP % |
|---|---|---|---|---|---|---|
| #1 | Alejandro Balde FC Barcelona | 22 | 4 | €60.0M | €80.2M | +25% |
| #2 | Jesús Vázquez Valencia CF | 23 | 3 | €3.0M | €3.7M | +20% |
| #3 | Adama Boiro Athletic Bilbao | 23 | 3 | €3.0M | €3.7M | +20% |
| #4 | Matteo Ruggeri Atlético de Madrid | 23 | 3 | €15.0M | €18.6M | +20% |
| #5 | Álvaro Carreras Real Madrid | 23 | 3 | €60.0M | €74.6M | +20% |
| #6 | Javi López Real Oviedo | 24 | 2 | €5.0M | €5.8M | +14% |
| #7 | Victor Parada Deportivo Alavés | 24 | 2 | €2.0M | €2.3M | +14% |
| #8 | Gerard Martín FC Barcelona | 24 | 2 | €20.0M | €23.1M | +14% |
| #9 | Carlos Romero RCD Espanyol Barcelona | 24 | 2 | €15.0M | €17.3M | +14% |
| #10 | José Salinas RCD Espanyol Barcelona | 25 | 1 | €2.8M | €3.0M | +7% |
| #11 | Sergio Gómez Real Sociedad | 25 | 1 | €15.0M | €16.1M | +7% |
| #12 | Manu Sánchez Levante UD | 25 | 1 | €6.0M | €6.5M | +7% |
| #13 | Abel Bretones CA Osasuna | 25 | 1 | €4.5M | €4.8M | +7% |
Risk-Adjusted Upside (RAU)
Upside potential weighted against forecast uncertainty. Higher RAU = better risk-reward profile.
Understanding Risk-Adjusted Upside (RAU)
Real Madrid's Álvaro Carreras has the highest Risk-Adjusted Upside at 42.8. That means Álvaro Carreras has 11% upside potential with only 0% forecast uncertainty-representing excellent risk-reward for value appreciation.
In second is FC Barcelona's Alejandro Balde with a 38.4 RAU (10% upside, 0% uncertainty). Third is Matteo Ruggeri of Atlético de Madrid with a 27.5 RAU (7% upside, 0% uncertainty).
How RAU is calculated: RAU divides upside potential by forecast uncertainty (RAU = Upside % ÷ Uncertainty %). A RAU of 42.8 means the upside is 42.8× greater than the uncertainty-making it a high-confidence growth opportunity. Target RAU ≥2.0 for balanced risk-reward.
Risk-Adjusted Upside by Player
| Rank | Player | Expected | Range | Upside % | RAU |
|---|---|---|---|---|---|
| #1 | Álvaro Carreras Real Madrid | €66.9M | €58.8M-74.9M | +11% | 42.8 |
| #2 | Alejandro Balde FC Barcelona | €66.1M | €58.2M-74.0M | +10% | 38.4 |
| #3 | Matteo Ruggeri Atlético de Madrid | €16.1M | €14.1M-18.0M | +7% | 27.5 |
| #4 | Jesús Vázquez Valencia CF | €3.2M | €2.8M-3.6M | +7% | 27.5 |
| #5 | Adama Boiro Athletic Bilbao | €3.2M | €2.8M-3.6M | +7% | 27.5 |
| #6 | Diego Pampín Levante UD | €1.2M | €1.1M-1.4M | +3% | 12.0 |
| #7 | Sergi Cardona Villarreal CF | €10.3M | €9.1M-11.5M | +3% | 12.0 |
| #8 | Fran García Real Madrid | €15.4M | €13.6M-17.3M | +3% | 12.0 |
| #9 | Carlos Romero RCD Espanyol Barcelona | €15.4M | €13.5M-17.2M | +2% | 9.8 |
| #10 | Victor Parada Deportivo Alavés | €2.0M | €1.8M-2.3M | +2% | 9.8 |
| #11 | Javi López Real Oviedo | €5.1M | €4.5M-5.7M | +2% | 9.8 |
| #12 | Gerard Martín FC Barcelona | €20.5M | €18.0M-22.9M | +2% | 9.8 |
Roster Pressure Index (RPI)
Squad depth pressure based on Z-score distribution. Negative RPI = thin depth, positive = deep roster.
What This Shows
Z-Score explained: Measures how many standard deviations a player's strength is from the position average. Z-Score = 0 means average, +1.0 is one standard deviation above average, -1.0 is below average.
How to use: RPI < -1.0 indicates critical depth shortage. These positions need immediate reinforcement. RPI > +1.0 suggests strong depth, allowing selective, high-value additions only.
Current market: left-back position shows strong depth (avg Z-score: 0.00). RPI: 0.00.
Position Depth Analysis
Highest Z-Scores
Lowest Z-Scores
Age-Share Concentration (ASC)
Identifies players capturing disproportionate value relative to age group representation. Positive ASC = value concentration.
Understanding Age-Share Concentration (ASC)
Atlético de Madrid's Matteo Ruggeri in the 21-23 age bracket has the highest Age-Share Concentration at +32.6%. That means Álvaro Carreras captures 47.3% of total market value while representing only 14.7% of players in their age group-showing dominant elite status.
In second is Valencia CF's Jesús Vázquez with a +32.6% ASC (47.3% value share vs 14.7% player share in 21-23 bracket). Third is Alejandro Balde of FC Barcelona with a +32.6% ASC (47.3% value vs 14.7% players in 21-23 bracket).
How ASC is calculated: ASC = (% of total value) - (% of total players) in age bracket. A +32.6% ASC means the player captures 32.6% more market value than their numerical representation-indicating marquee status. ASC > +15% = elite dominance, ASC < -15% = potential value targets.
Value Concentration by Player
| Rank | Player | Age Bracket | Value Share | Player Share | ASC |
|---|---|---|---|---|---|
| #1 | Matteo Ruggeri Atlético de Madrid | 21-23 | 47.3% | 14.7% | +32.6% |
| #2 | Jesús Vázquez Valencia CF | 21-23 | 47.3% | 14.7% | +32.6% |
| #3 | Alejandro Balde FC Barcelona | 21-23 | 47.3% | 14.7% | +32.6% |
| #4 | Adama Boiro Athletic Bilbao | 21-23 | 47.3% | 14.7% | +32.6% |
| #5 | Álvaro Carreras Real Madrid | 21-23 | 47.3% | 14.7% | +32.6% |
| #6 | Juan Cruz CA Osasuna | 30+ | 10.5% | 35.3% | -24.8% |
| #7 | Álex Moreno Girona FC | 30+ | 10.5% | 35.3% | -24.8% |
| #8 | José Gayà Valencia CF | 30+ | 10.5% | 35.3% | -24.8% |
| #9 | Diego Rico Getafe CF | 30+ | 10.5% | 35.3% | -24.8% |
| #10 | Johan Mojica RCD Mallorca | 30+ | 10.5% | 35.3% | -24.8% |
| #11 | Mihailo Ristic Celta de Vigo | 30+ | 10.5% | 35.3% | -24.8% |
| #12 | Ferland Mendy Real Madrid | 30+ | 10.5% | 35.3% | -24.8% |
| #13 | Alfonso Espino Rayo Vallecano | 30+ | 10.5% | 35.3% | -24.8% |
| #14 | Alfonso Pedraza Villarreal CF | 30+ | 10.5% | 35.3% | -24.8% |
| #15 | Javi Galán CA Osasuna | 30+ | 10.5% | 35.3% | -24.8% |
| #16 | Yuri Berchiche Athletic Bilbao | 30+ | 10.5% | 35.3% | -24.8% |
| #17 | Ricardo Rodríguez Real Betis Balompié | 30+ | 10.5% | 35.3% | -24.8% |
| #18 | Toni Lato RCD Mallorca | 27-29 | 9.9% | 17.6% | -7.8% |
| #19 | Junior Firpo Real Betis Balompié | 27-29 | 9.9% | 17.6% | -7.8% |
| #20 | Gabriel Suazo Sevilla FC | 27-29 | 9.9% | 17.6% | -7.8% |
Buy-Now vs Wait-List Map
Categorizes players by age position and upside potential to guide timing of acquisition.
What This Shows
How to use:"Buy Now - High Upside" = immediate priority targets."Watch List" = monitor for 6-12 months."Peak" = pay premium for proven performers."Aging" = short-term depth only.
Current market: 0 immediate targets, 5 standard acquisitions, 0 watch-list prospects, 15 at peak.
BUY NOW - High Upside
No players in this category
WATCH LIST - High Upside
No players in this category
BUY NOW - Medium Upside
PEAK Players
Price vs Peer Z-Score
IQR-based pricing analysis relative to position peers. Identifies over/undervalued players vs market.
What This Shows
How to use: Z-score < -1.5 = significantly undervalued (potential bargain). Z-score > +1.5 = premium pricing (requires strong justification). Within ±1.0 = fair market value.
Current market: Position median is €60.0M. 0 undervalued, 2 premium.
Value Positioning vs Peers
| Player | Market Value | Position Median | Z-Score | Assessment |
|---|---|---|---|---|
José Gayà Valencia CF | €5.0M | €3.5M | -1.00 | Good Value |
Diego Pampín Levante UD | €1.2M | €3.5M | -0.64 | Good Value |
Mihailo Ristic Celta de Vigo | €800K | €3.5M | -0.54 | Good Value |
Alfonso Espino Rayo Vallecano | €1.0M | €3.5M | -0.38 | Fair Value |
Victor Parada Deportivo Alavés | €2.0M | €3.5M | -0.32 | Fair Value |
Junior Firpo Real Betis Balompié | €6.0M | €3.5M | -0.25 | Fair Value |
Juan Cruz CA Osasuna | €1.2M | €3.5M | -0.23 | Fair Value |
Diego Rico Getafe CF | €1.2M | €3.5M | -0.23 | Fair Value |
Yuri Berchiche Athletic Bilbao | €1.2M | €3.5M | -0.23 | Fair Value |
Javi López Real Oviedo | €5.0M | €3.5M | -0.20 | Fair Value |
Ferland Mendy Real Madrid | €8.0M | €3.5M | 0.00 | Fair Value |
Toni Lato RCD Mallorca | €1.5M | €3.5M | 0.00 | Fair Value |
Fran García Real Madrid | €15.0M | €3.5M | 0.00 | Fair Value |
Sergio Gómez Real Sociedad | €15.0M | €3.5M | 0.00 | Fair Value |
Gabriel Suazo Sevilla FC | €7.0M | €3.5M | 0.00 | Fair Value |
Léo Pétrot Elche CF | €1.5M | €3.5M | 0.00 | Fair Value |
Matteo Ruggeri Atlético de Madrid | €15.0M | €3.5M | 0.00 | Fair Value |
Manu Sánchez Levante UD | €6.0M | €3.5M | 0.00 | Fair Value |
Jesús Vázquez Valencia CF | €3.0M | €3.5M | 0.00 | Fair Value |
Alejandro Balde FC Barcelona | €60.0M | €3.5M | 0.00 | Fair Value |
How We Rank La Liga Left-Backs
Our Analytical Strength Index is calibrated specifically for left-backs, using position-specific age curves and playing time benchmarks. The model draws from academic research on player valuation (Franck & Nüesch, 2012) and age-performance curves (Dendir, 2016).
Scoring Components for LB
Historical Achievement Index (35%)
Peak career market value for La Liga left-backs, reflecting proven track record and reputation. Uses log-scale to account for exponential value distribution at elite level.
Current Performance Proxy (30%)
Present market value for La Liga left-backs, capturing recent form, injuries, and current performance level. Weighted to reflect age-related depreciation patterns.
Playing Time Utilization (18%)
Defenders with 2,500+ minutes score highest, indicating regular starting role and sustained performance.
Age-Adjusted Performance Curve (12%)
Defenders peak at 27 with 5.0%/year decline rate. Pre-peak players score higher on development trajectory.
Competition Level Adjustment (3%)
La Liga receives Top 5 European league premium for competitive intensity and quality of opposition.
Performance Expectations Multiplier (2%)
Players at clubs with Champions League pedigree face higher performance standards and tactical complexity, contributing to development and market validation.
LB Performance Benchmarks
Peak Age: 27 years (balance of physicality and tactical intelligence)
Decline Rate: 5.0% per year (moderate decline as positioning offsets pace loss)
Optimal Minutes: 2,500 per season (regular starter with rotation management)
1-Year Market Value Forecast
Probabilistic model combining age-curve depreciation, value momentum, and playing time factors:
• Age Factor: Defender -5.0%/year post-peak, +5%/year pre-peak
• Value Trajectory: Near career peak (>95% of peak value): +3% momentum | Moderate decline: -5%
• Playing Time Factor: Regular starters (+2%), Squad rotation (-2%)
• Forecast Range: ±10% confidence interval
Research Foundation
• Dendir (2016): Age-performance curves for left-backs
• Carmichael et al. (2011): Player depreciation in top leagues
• Franck & Nüesch (2012): Hedonic pricing models for talent valuation
• Szymanski, S. (2015). Money and Soccer: A Soccernomics Guide
Frequently Asked Questions
Common questions about La Liga Left-Backs in the 2026-27 season
Who are the most valuable Left-Backs in the La Liga in 2026-27?
The most valuable left-back in the La Liga in 2026-27 is Álvaro Carreras, who is worth €60.0M and plays for Real Madrid. The second most valuable is Alejandro Balde (€60.0M, FC Barcelona), followed by Gerard Martín (€20.0M, FC Barcelona). Our database tracks 34 La Liga Left-Backs with comprehensive market valuations updated for the 2026-27 season.
How are La Liga Left-Backs ranked?
La Liga Left-Backs are ranked by our proprietary Analytical Strength Index, which is specifically calibrated for Left-Backs. The score combines six factors: Historical Achievement Index (35%) measuring peak career value, Current Performance Proxy (30%) reflecting recent market signals, Playing Time Utilization (18%) tracking minutes played, Age-Adjusted Performance Curve (12%) using position-specific peak ages, League Quality Coefficient (3%) for La Liga competition level, and Club Tier Multiplier (2%) accounting for club prestige. This methodology is grounded in academic research including work by Dendir (2016) on age-performance curves and Franck & Nüesch (2012) on hedonic pricing models.
What age do Left-Backs peak?
Defenders typically peak at age 27, with a decline rate of 5.0% per year after peak. Research shows defenders balance physical attributes with tactical intelligence, allowing them to maintain high performance through their late 20s. The optimal playing time for peak performance is around 2,500 minutes per season.
How much does it cost to sign a top left-back from the La Liga?
Transfer fees for La Liga Left-Backs vary significantly based on market value, contract length, and club bargaining position. For the top-ranked left-back Álvaro Carreras (market value: €60.0M), estimated transfer fees would range from €48.0M to €84.0M depending on contract situation. Players with longer contracts (3+ years) command premium fees (1.2-1.4× market value), while those in the final year may be available for 0.8-1.1× market value. Our fee estimates are derived from historical transfer patterns and contract-clock modifiers validated against actual La Liga transactions.
What is the value forecast for La Liga Left-Backs?
Our 1-year forecast model projects market value changes for La Liga Left-Backs based on age-curve depreciation, historical trajectory, and playing time adjustments. The forecast combines three factors: age-based appreciation/depreciation (pre-peak players gain ~5% per year toward peak age, post-peak players decline at position-specific rates), market trajectory momentum (comparing current to peak value), and playing time confidence (regular starters receive +2% boost). Forecast confidence intervals account for position-specific volatility-defenders have ±10% volatility. Young players (under 22) and older players (over 32) receive 1.15× uncertainty multipliers due to unpredictable development or decline patterns.
Where does the La Liga left-back data come from?
Our La Liga left-back data is sourced from Football Analytics AI's proprietary Transfer Intelligence Database, which aggregates market valuations, player statistics, contract information, and transfer histories from multiple industry sources. Market values are updated regularly based on player performance, injuries, contract negotiations, and transfer market activity. We enhance this data with our proprietary analytics including position-specific scoring algorithms, age-performance curves calibrated to academic research, and statistical forecast models. All data is validated against official La Liga sources and updated monthly for the 2026-27 season to ensure accuracy for recruitment and investment decisions.