Major League Baseball Batting Leaders

Wins Above Replacement--all

<strong>Wins Above Replacement</strong><br>A single number that presents the number of wins the player added<br>to the team above what a replacement player (think AAA or AAAA) would add.<br>Scale for a single-season: 8+ MVP Quality, 5+ All-Star Quality, 2+ Starter,<br>0-2 Reserve, < 0 Replacement Level <br>Developed by Sean Smith of BaseballProjection.com

1. Trout • LAA 10.4
2. Betts • BOS 9.8
3. Altuve • HOU 7.8
4. Machado • BAL 7.4
5. Verlander • DET 7.4
6. Canó • SEA 7.3
7. Donaldson • TOR 7.3
8. Bryant • CHC 7.2
9. Correa • HOU 7.0
10. Beltré • TEX 6.9

WAR Position Players

<strong>Wins Above Replacement for position players</strong><br>A single number that presents the number of wins the player added<br>to the team above what a replacement player (think AAA or AAAA) would add.<br>Scale: 8+ MVP Quality, 5+ All-Star Quality, 2+ Starter,<br>0-2 Reserve, < 0 Replacement Level <br> Developed by Sean Smith of BaseballProjection.com

1. Trout • LAA 10.4
2. Betts • BOS 9.8
3. Altuve • HOU 7.8
4. Machado • BAL 7.4
5. Canó • SEA 7.3
6. Donaldson • TOR 7.3
7. Bryant • CHC 7.2
8. Correa • HOU 7.0
9. Beltré • TEX 6.9
10. Seager • SEA 6.8

Offensive WAR

<strong>Offensive Wins Above Replacement (everything but Fielding)</strong><br>The same statistic as Wins Above Replacement for Position<br>Players (WAR), but with the fielding value excluded.<br>oWAR + dWAR does not equal WAR.<br>Adding would count positions twice.<br>Contains the factor for batting stats, baserunning, a positional adjustment, and the replacement player adjustment.<br> Factors developed by Sean Smith of BaseballProjection.com

1. Trout • LAA 9.9
2. Altuve • HOU 7.9
3. Donaldson • TOR 7.3
4. Correa • HOU 6.4
5. Betts • BOS 6.4
Bryant • CHC 6.4
7. Canó • SEA 6.2
8. Dozier • MIN 6.0
9. Seager • LAD 5.9
10. Murphy • WSN 5.6

Defensive WAR

<strong>Defensive Wins Above Replacement for position players</strong><br>A defensive measure of wins above replacement, but given<br>only the defensive stats of the player and his position adjustment. For this calculation, we use a<br>replacement level on defense is the league average.<br>Based on Baseball Info Solutions defensive runs saved from 2003 on<br>and total zone rating developed by Sean Smith of BaseballProjection.com previously

1. Crawford • SFG 3.5
2. Betts • BOS 2.9
3. Simmons • LAA 2.9
4. Kiermaier • TBR 2.8
5. Machado • BAL 2.8
6. Pillar • TOR 2.7
7. Russell • CHC 2.5
8. Eaton • CHW 2.4
9. Beltré • TEX 2.2
10. Perez • KCR 2.1

Batting Average

<strong>Hits/At Bats</strong><br>For recent years, leaders need 3.1 PA<br>per team game played<br>Bold indicates either highest BA using current stats<br>or awarded title at end of year.

1. LeMahieu • COL .348
2. Murphy • WSN .347
3. Altuve • HOU .338
4. Votto • CIN .326
5. Blackmon • COL .324
6. Segura • ARI .319
7. Betts • BOS .318
8. Pedroia • BOS .318
9. Cabrera • DET .316
10. Trout • LAA .315

On-Base%

<strong>(H + BB + HBP)/(At Bats + BB + HBP + SF)</strong><br>For recent years, leaders need 3.1 PA<br>per team game played

1. Trout • LAA .441
2. Votto • CIN .434
3. LeMahieu • COL .416
4. Goldschmidt • ARI .411
5. Donaldson • TOR .404
6. Ortiz • BOS .401
7. Freeman • ATL .400
8. Altuve • HOU .396
9. Belt • SFG .394
10. Cabrera • DET .393

Slugging %

Total Bases/At Bats or
(1B + 2*2B + 3*3B + 4*HR)/AB
For recent years, leaders need 3.1 PA
per team game played

1. Ortiz • BOS .620
2. Murphy • WSN .595
3. Arenado • COL .570
4. Freeman • ATL .569
5. Cabrera • DET .563
6. Cruz • SEA .555
7. Bryant • CHC .554
8. Blackmon • COL .552
9. Votto • CIN .550
10. Trout • LAA .550

On-Base Plus Slugging

<strong>On-Base + Slugging Percentages </strong><br>For recent years, leaders need 3.1 PA<br>per team game played

1. Ortiz • BOS 1.021
2. Trout • LAA .991
3. Murphy • WSN .985
4. Votto • CIN .985
5. Freeman • ATL .968
6. Cabrera • DET .956
7. Donaldson • TOR .953
8. Bryant • CHC .939
9. Blackmon • COL .933
10. Arenado • COL .932

Games Played

Games Played or Pitched

1. Schoop • BAL 162
Springer • HOU 162
Escobar • KCR 162
4. Altuve • HOU 161
Canó • SEA 161
6. Arenado • COL 160
Carter • MIL 160
Longoria • TBR 160
Encarnación • TOR 160
10. Trumbo • BAL 159
Abreu • CHW 159
Suárez • CIN 159
Trout • LAA 159
Semien • OAK 159
Herrera • PHI 159

At Bats

At Bats

1. Betts • BOS 672
2. Canó • SEA 655
3. Bogaerts • BOS 652
4. Springer • HOU 644
5. Machado • BAL 640
Altuve • HOU 640
7. Segura • ARI 637
Escobar • KCR 637
9. Pedroia • BOS 633
Longoria • TBR 633

Plate Appearances

<strong>Plate Appearances</strong><br>When available, we use actual plate appearances from play-by-play game accounts<br>Otherwise estimated using AB + BB + HBP + SF + SH,<br>which excludes catcher interferences.<br>When <span class=tooltip>this color</span> click for a summary of each PA.

1. Springer • HOU 744
2. Betts • BOS 730
3. Bogaerts • BOS 719
4. Altuve • HOU 717
5. Canó • SEA 715
6. Eaton • CHW 706
7. Goldschmidt • ARI 705
8. Encarnación • TOR 702
9. Donaldson • TOR 700
10. Bryant • CHC 699

Runs Scored

Runs Scored/Allowed

1. Trout • LAA 123
2. Betts • BOS 122
Donaldson • TOR 122
4. Bryant • CHC 121
5. Kinsler • DET 117
6. Arenado • COL 116
Springer • HOU 116
8. Bogaerts • BOS 115
9. Blackmon • COL 111
10. Altuve • HOU 108

Hits

Hits/Hits Allowed

1. Altuve • HOU 216
2. Betts • BOS 214
3. Segura • ARI 203
4. Pedroia • BOS 201
5. Canó • SEA 195
6. Seager • LAD 193
7. Bogaerts • BOS 192
LeMahieu • COL 192
9. Machado • BAL 188
Cabrera • DET 188

Total Bases

<strong>Total Bases</strong><br>Singles + 2 x Doubles + 3 x Triples + 4 x Home Runs.

1. Betts • BOS 359
2. Arenado • COL 352
3. Canó • SEA 349
4. Machado • BAL 341
5. Altuve • HOU 340
6. Dozier • MIN 336
7. Freeman • ATL 335
Cabrera • DET 335
9. Bryant • CHC 334
10. Ortiz • BOS 333

Doubles

Doubles Hit/Allowed

1. Ortiz • BOS 48
2. Murphy • WSN 47
3. Ramírez • CLE 46
4. Freeman • ATL 43
Rizzo • CHC 43
6. Betts • BOS 42
Cabrera • CHW 42
González • COL 42
Altuve • HOU 42
10. Segura • ARI 41
Kipnis • CLE 41
Belt • SFG 41
Longoria • TBR 41

Triples

Triples Hit/Allowed

1. Owings • ARI 11
Hernández • PHI 11
Crawford • SFG 11
4. Lamb • ARI 9
Eaton • CHW 9
6. LeMahieu • COL 8
Dyson • KCR 8
Belt • SFG 8
Turner • WSN 8
10. Segura • ARI 7
Inciarte • ATL 7
Bradley • BOS 7
Fowler • CHC 7
Bourjos • PHI 7
Harrison • PIT 7
Panik • SFG 7
Wong • STL 7
Andrus • TEX 7
Revere • WSN 7

Home Runs

Home Runs Hit/Allowed

1. Trumbo • BAL 47
2. Cruz • SEA 43
3. Dozier • MIN 42
Davis • OAK 42
Encarnación • TOR 42
6. Arenado • COL 41
Carter • MIL 41
8. Frazier • CHW 40
9. Bryant • CHC 39
Canó • SEA 39

Runs Batted In

Runs Batted In

1. Arenado • COL 133
2. Ortiz • BOS 127
Encarnación • TOR 127
4. Pujols • LAA 119
5. Betts • BOS 113
6. Ramírez • BOS 111
7. Rizzo • CHC 109
8. Trumbo • BAL 108
Cabrera • DET 108
Kemp • 2TM 108

Bases on Balls

Bases on Balls/Walks

1. Trout • LAA 116
2. Goldschmidt • ARI 110
3. Donaldson • TOR 109
4. Votto • CIN 108
Harper • WSN 108
6. Belt • SFG 104
7. Santana • CLE 99
8. Zobrist • CHC 96
9. Freeman • ATL 89
10. Davis • BAL 88
Springer • HOU 88

Strikeouts

Strikeouts

1. Davis • BAL 219
2. Carter • MIL 206
3. Napoli • CLE 194
4. Upton • DET 179
5. Springer • HOU 178
Sanó • MIN 178
7. Villar • MIL 174
Espinosa • WSN 174
9. Freeman • ATL 171
10. Trumbo • BAL 170

Stolen Bases

Stolen Bases

1. Villar • MIL 62
2. Hamilton • CIN 58
3. Marte • PIT 47
4. Davis • CLE 43
5. Núñez • 2TM 40
6. Pérez • MIL 34
7. Segura • ARI 33
Turner • WSN 33
9. Goldschmidt • ARI 32
10. Altuve • HOU 30
Dyson • KCR 30
Trout • LAA 30
Strange-Gordon • MIA 30
Jankowski • SDP 30

Singles

Singles Hit/Allowed

1. Pedroia • BOS 149
2. Altuve • HOU 145
3. LeMahieu • COL 141
4. Betts • BOS 136
Bogaerts • BOS 136
6. Segura • ARI 135
Prado • MIA 135
8. Lindor • CLE 134
9. Hernández • PHI 130
10. Escobar • KCR 129

Adjusted OPS+

<strong>OPS+</strong><br>100*[OBP/lg OBP + SLG/lg SLG - 1]<br>Adjusted to the player&#x2019;s ballpark(s)

1. Trout • LAA 173
2. Ortiz • BOS 164
3. Votto • CIN 160
4. Freeman • ATL 157
5. Altuve • HOU 155
6. Cabrera • DET 155
7. Murphy • WSN 155
8. Donaldson • TOR 153
9. Cruz • SEA 147
10. Bryant • CHC 146

Runs Created

<strong>Runs Created</strong><br>A set of formulas developed by Bill James and others<br>that estimates a player&#x2019;s total contributions<br>to a team&#x2019;s runs total.<br>This is computed with the "technical" formula when possible.<br>If SB or CS data is missing, the "basic" formula is used.<br>If HBP, IBB, SH, SF, or GIDP data is missing, the "stolen base" version of the formula is used. <br>Team Runs Created is the sum of player Runs Created.

1. Trout • LAA 148
2. Votto • CIN 139
3. Freeman • ATL 138
4. Bryant • CHC 135
Altuve • HOU 135
6. Betts • BOS 133
Donaldson • TOR 133
8. Ortiz • BOS 130
9. Goldschmidt • ARI 127
10. Cabrera • DET 126

Adj. Batting Runs

<strong>Adjusted Batting Runs</strong><br>A set of formulas developed by Gary Gillette, Pete Palmer and others<br>that estimates a player&#x2019;s total contributions<br>to a team&#x2019;s runs total via linear weights.<br>0.0 is an avg performance, <0 is worse than avg and >0 is better than avg

1. Trout • LAA 64
2. Votto • CIN 55
3. Ortiz • BOS 53
4. Altuve • HOU 51
5. Freeman • ATL 51
6. Cabrera • DET 48
7. Donaldson • TOR 48
8. Murphy • WSN 43
9. Bryant • CHC 41
10. Cruz • SEA 39

Adj. Batting Wins

<strong>Adjusted Batting Wins</strong><br>A set of formulas developed by Gary Gillette, Pete Palmer and others<br>that estimates a player&#x2019;s total contributions<br>to a team&#x2019;s wins with his bat.<br>0.0 is an avg performance, <0 is worse than avg and >0 is better than avg

1. Trout • LAA 6.1
2. Votto • CIN 5.3
3. Ortiz • BOS 5.1
4. Freeman • ATL 4.9
5. Altuve • HOU 4.9
6. Cabrera • DET 4.6
7. Donaldson • TOR 4.6
8. Murphy • WSN 4.1
9. Bryant • CHC 4.0
10. Cruz • SEA 3.8

Extra Base Hits

<strong>Extra Base Hits</strong><br>Doubles + Triples + Home Runs

1. Ortiz • BOS 87
2. Freeman • ATL 83
3. Arenado • COL 82
Dozier • MIN 82
5. Longoria • TBR 81
6. Rizzo • CHC 79
7. Machado • BAL 78
Betts • BOS 78
9. Bryant • CHC 77
Murphy • WSN 77

Times On Base

<strong>Times on Base</strong><br>Hits + Bases on Balls + Hit By Pitch<br>Does not include Reached on Error or Catcher Interference.

1. Trout • LAA 300
2. Votto • CIN 294
3. Goldschmidt • ARI 289
4. Altuve • HOU 283
5. Donaldson • TOR 282
6. Freeman • ATL 277
7. Bryant • CHC 269
8. Cabrera • DET 267
Springer • HOU 267
10. Betts • BOS 265

Offensive Win %

<strong>Offensive Winning Percentage</strong><br>The percentage of games a team with nine of this player<br>batting would win. Assumes average pitching and defense.<br>This uses the Pythagorean win pct formula with the player's RC/G for runs scored and the league's R/9 as runs allowed.

1. Trout • LAA .800
2. Votto • CIN .779
3. Murphy • WSN .776
4. Ortiz • BOS .756
5. Freeman • ATL .753
6. Bryant • CHC .738
7. Blackmon • COL .735
8. Donaldson • TOR .732
9. Goldschmidt • ARI .719
10. Altuve • HOU .718

Hit By Pitch

Times Hit by a Pitch.

1. Guyer • 2TM 31
2. Dietrich • MIA 24
3. Espinosa • WSN 20
4. Bryant • CHC 18
5. Rizzo • CHC 16
Marte • PIT 16
7. Abreu • CHW 15
8. Eaton • CHW 14
Kang • PIT 14
10. Blackmon • COL 13
Kinsler • DET 13

Sacrifice Hits

Sacrifice Hits (Sacrifice Bunts)

1. Scherzer • WSN 13
2. Teheran • ATL 11
Hamilton • CIN 11
Straily • CIN 11
Cueto • SFG 11
6. Lester • CHC 10
Escobar • KCR 10
8. Hendricks • CHC 8
LeMahieu • COL 8
Dyson • KCR 8
Pérez • LAA 8
Maeda • LAD 8
Fernández • MIA 8
Guerra • MIL 8
Galvis • PHI 8
Hellickson • PHI 8
Bourn • 2TM 8

Sacrifice Flies

Sacrifice Flies
First tracked in 1954.

1. Lindor • CLE 15
2. Kemp • 2TM 12
3. Carter • MIL 10
Harper • WSN 10
5. Markakis • ATL 9
Abreu • CHW 9
Crawford • SFG 9
8. Goldschmidt • ARI 8
Jones • BAL 8
Duvall • CIN 8
Votto • CIN 8
Arenado • COL 8
Turner • LAD 8
Harrison • PIT 8
Posey • SFG 8
Encarnación • TOR 8
Murphy • WSN 8
Rendon • WSN 8

Intentional Bases on Balls

<strong>Intentional Bases on Balls</strong><br>First tracked in 1955.

1. Harper • WSN 20
2. Freeman • ATL 18
3. Goldschmidt • ARI 15
Ortiz • BOS 15
Votto • CIN 15
Cabrera • DET 15
7. Trout • LAA 12
Espinosa • WSN 12
9. Altuve • HOU 11
10. Arenado • COL 10
Braun • MIL 10
Mauer • MIN 10
Seager • SEA 10
Crawford • SFG 10
Murphy • WSN 10

Double Plays Grounded Into

<strong>Double Plays Grounded Into</strong><br>Only includes standard 6-4-3, 4-3, etc. double plays.<br>First tracked in 1933.<br>For gamelogs only in seasons we have play-by-play, we include triple plays as well.<br>All official seasonal totals do not include GITP's.

1. Cabrera • DET 26
2. Pedroia • BOS 24
Pujols • LAA 24
Prado • MIA 24
5. Ortiz • BOS 22
Molina • STL 22
Encarnación • TOR 22
8. Abreu • CHW 21
Kipnis • CLE 21
Escobar • LAA 21
Bautista • TOR 21

Caught Stealing

Caught Stealing

1. Villar • MIL 18
2. Hernández • PHI 13
3. Marte • PIT 12
Jankowski • SDP 12
5. Segura • ARI 10
Peraza • CIN 10
Altuve • HOU 10
Springer • HOU 10
Núñez • 2TM 10
Harper • WSN 10

SB %

Stolen Base Percentage
SB / (SB + CS)

1. Owings • ARI 91.30
2. Dozier • MIN 90.00
3. Hamilton • CIN 87.88
4. Davis • CLE 87.76
5. Kiermaier • TBR 87.50
6. Betts • BOS 86.67
7. Goldschmidt • ARI 86.49
8. Broxton • MIL 85.19
9. Turner • WSN 84.62
10. Kipnis • CLE 83.33

Power-Speed #

<strong>Power/Speed Number</strong><br>2 x (Home Runs x Stolen Bases)/(Stolen Bases + Home Runs)<br>The harmonic mean of HR and SB.<br>To do well you need a lot of both.<br>Developed by Bill James.

1. Trout • LAA 29.5
2. Villar • MIL 29.1
3. Betts • BOS 28.3
4. Myers • SDP 28.0
5. Goldschmidt • ARI 27.4
6. Altuve • HOU 26.7
7. Dozier • MIN 25.2
8. Segura • ARI 24.9
9. Upton • 2TM 23.0
10. Núñez • 2TM 22.9

AB per SO

<strong>At Bats Per Strikeout</strong><br>For career marks this only includes AB&#x2019;s for seasons where SO&#x2019;s were tracked.

1. Panik • SFG 9.9
2. Iglesias • DET 9.3
3. Murphy • WSN 9.3
4. Altuve • HOU 9.1
5. Ramírez • CLE 9.1
6. Beltré • TEX 8.8
7. Prado • MIA 8.7
8. Pedroia • BOS 8.7
9. Cabrera • CHW 8.6
10. Molina • STL 8.5

AB per HR

<strong>At Bats Per Home Run</strong>

1. Trumbo • BAL 13.0
2. Davis • OAK 13.2
3. Carter • MIL 13.4
4. Cruz • SEA 13.7
5. Gattis • HOU 14.0 **
6. Ortiz • BOS 14.1
7. Encarnación • TOR 14.3
8. Dozier • MIN 14.6
9. Frazier • CHW 14.8
10. Davis • BAL 14.9

Outs Made

<strong>Outs Made</strong><br>(At Bats - Hits) + Double Plays Grounded Into <br>+ Sac. Flies + Sac. Hits + Caught Stealing.

1. Escobar • KCR 506
2. Springer • HOU 499
3. Kemp • 2TM 485
4. Canó • SEA 484
5. Longoria • TBR 483
6. Betts • BOS 481
Bogaerts • BOS 481
Frazier • CHW 481
9. Kipnis • CLE 478
10. Jones • BAL 477
Galvis • PHI 477

Base-Out Runs Added (RE24)

<strong>Base-Out Runs Added</strong><br>Given the bases occupied/out situation, how many runs did the batter<br> or baserunner add in the resulting play.<br>Compared to average, so 0 is average, and above 0 is better than average

1. Trout • LAA 72.88
2. Ortiz • BOS 58.77
3. Freeman • ATL 48.95
4. Donaldson • TOR 48.36
5. Votto • CIN 47.58
6. Murphy • WSN 45.75
7. Bryant • CHC 45.72
8. Rizzo • CHC 43.31
9. Arenado • COL 41.72
10. Altuve • HOU 38.47

Win Probability Added (WPA)

<strong>Win Probability Added for Offensive Player</strong><br>Given average teams, this is the change in probability<br>caused by this batter during the game.<br>See <a href='https://www.baseball-reference.com/about/wpa.shtml'>Win Expectancy explainer</a> for details.

1. Trout • LAA 6.4
2. Donaldson • TOR 4.4
3. Ortiz • BOS 4.3
4. Goldschmidt • ARI 4.2
5. Votto • CIN 4.1
6. Beltré • TEX 4.0
7. Rizzo • CHC 3.9
8. Arenado • COL 3.8
9. Murphy • WSN 3.8
10. Yelich • MIA 3.7

Situ. Wins Added (WPA/LI)

<strong>Situational Wins (WPA/LI)</strong><br>It is the sum of WPA divided by the leverage index for each play.<br>WPA depends greatly on the context of the at bats.<br>This stat does not.

1. Trout • LAA 6.5
2. Freeman • ATL 5.1
3. Donaldson • TOR 4.9
4. Ortiz • BOS 4.8
5. Cabrera • DET 4.8
6. Murphy • WSN 4.7
7. Bryant • CHC 4.7
8. Goldschmidt • ARI 4.5
9. Cruz • SEA 4.5
10. Rizzo • CHC 4.4

Championship WPA (cWPA)

<strong>Championship Win Probability Added for Offensive Player</strong><br>Given average teams, this is the change in probability of winning the World Series, displayed in percentage points.<br>See <a href='https://www.baseball-reference.com/about/wpa.shtml'>Win Expectancy explainer</a> for details.

1. Ramírez • BOS 3.9
2. Ortiz • BOS 3.5
3. Betts • BOS 3.3
4. Donaldson • TOR 3.1
5. Murphy • WSN 2.7
6. Céspedes • NYM 2.6
7. Pedroia • BOS 2.3
8. Desmond • TEX 2.1
9. Yelich • MIA 2.1
10. Harper • WSN 2.1

Base-Out Wins Added (REW)

<strong>Base-Out Wins Added (REW)</strong><br>This is the number of wins above average the player was worth by their performance measured by the 24 <br>base-out situations across every play in the game.

1. Trout • LAA 7.1
2. Ortiz • BOS 5.4
3. Freeman • ATL 4.7
4. Donaldson • TOR 4.6
5. Votto • CIN 4.6
6. Bryant • CHC 4.4
7. Murphy • WSN 4.3
8. Rizzo • CHC 4.1
9. Altuve • HOU 3.8
10. Arenado • COL 3.7

rOBA

rOBA
A measure of a player's offensive contributions, weighted in proportion to each event's actual run value

1. Trout • LAA .435
2. Ortiz • BOS .423
3. Votto • CIN .421
4. Freeman • ATL .412
5. Murphy • WSN .411
6. Donaldson • TOR .409
7. Bryant • CHC .406
8. LeMahieu • COL .404
9. Cabrera • DET .402
10. Altuve • HOU .400

Rbat+

Rbat+
Batting runs as computed for WAR, but indexed to the environment the player played in, where 100 is league average.

1. Trout • LAA 182
2. Votto • CIN 167
3. Ortiz • BOS 166
4. Freeman • ATL 165
5. Murphy • WSN 160
6. Altuve • HOU 159
7. Bryant • CHC 158
8. Donaldson • TOR 158
9. Cabrera • DET 156
10. Cruz • SEA 152

A ** by the stat's value indicates the player had fewer than the required number of at bats or plate appearances for the BA, OBP, SLG or OPS title that year. In order to rank the player, the necessary number of hitless at bats were added to the player's season total. The value printed here is their actual value and not the value used to rank them, therefore some numbers may appear out of order.

For rate stats, generally a minimum of 3.1 Plate Appearances/Team Game (batting), 1.0 IP/Team Game (pitching), 0.67 Gm and Chances/Team Game (fielding), 0.2 SB att/Team Game (catchers), 0.1 SB att/Team Game (baserunners only since 1951), and 0.1 decision/Team Game (W-L%) is needed for single-season leaderboards. For pitcher fielding the minimums are reduced by a third. For LF, CF, RF fielding stats, we only have reliable data since 1898, so all leaders are since 1898. Explanation of min. requirements