Defender leaderboard — four facets, 2023 World Championships

Every partnership with ≥40 defended boards in each division, ranked by F4 — their trick-taking on defence scored in IMPs against the field in the identical contract on the same deal. Both partners share every board; the two columns on the right split that IMP result by which partner made the opening lead.

Source Marrakech 2023 · RR + KO · peers = other tables in the same contract on that deal · leave-one-out · caveat: results can't fully separate great defence from declarer error — read vs the field

F1 · tricks vs DD

Double-dummy declarer tricks − actual. Positive = you held declarer below double-dummy.

F2 · tricks vs field

Held declarer to fewer tricks than other defenders in the same contract on the deal. Pure defence in tricks.

F3 · defeating vs field

Did you defeat it − the field's set-rate for that contract. Positive = you set ones the field lets through.

F4 · IMPs vs field · on lead

The ranking. F2's trick edge in IMPs from the defending seat. The two right-hand columns show F4 only on boards where that partner led.

Worked example — every board MOLENAAR / VERBEEK defended (Open), all four facets

The pair defended 111 boards together; 102 had another table in the identical contract from the same declarer seat (the default matching, needed for F2–F4). Both partners share every board — the two on-lead columns then split F4 by who actually made the opening lead.

F1 = DD decl tricks − actual  ·  F2 = mean(peer decl tricks) − actual  ·  F3 = set? − field set-rate  ·  F4 = IMP( your defenders' score − peers re-scored to the defending side of your contract )

The biggest single board — RR-r16 board 30, 6H by the opponents (W), VERBEEK on lead

Declarer took 11 (needs 12); double-dummy 12. 11 other tables were in 6H, 55% defeated it — the pair set it.
F1 = 12 − 11 = +1 (declarer vs double-dummy)
F2 = 11.6 − 11 = +0.64 (held below the same-contract field)
F3 = set (1) − 0.55 = +0.45
F4 = IMP( your +50 − field −424 ) = +10
Full ledger — all 111 defended boards
F1·DDF2·tricks vs fieldF3·defeating vs fieldF4·IMPs vs field
Boardcontractleddecl/DD=F1#prpeer trk=F2fld setresult=F3your $fld $=F4
RR-r1 b13NT EMOLENAAR12/9−378.9−3.1414%made−0.14−490−336−4
RR-r1 b24S WVERBEEK10/10+0179.3−0.7159%made−0.59−420−138−7
RR-r1 b32S WVERBEEK6/7+185.9−0.12100%set+0.00+200+213+0
RR-r1 b56Sx× EMOLENAAR9/10+1410.0+1.00100%set+0.00+500+300+5
RR-r1 b64C EMOLENAAR11/11+0711.0+0.000%made+0.00−150−150+0
RR-r1 b86NT EMOLENAAR12/13+1113.0+1.000%made+0.00−990−1020+1
RR-r1 b152S EMOLENAAR7/7+066.8−0.17100%set+0.00+50+58+0
RR-r1 b163NT WVERBEEK11/11+0611.0+0.000%made+0.00−660−660+0
RR-r10 b213D NVERBEEK9/8−138.3−0.6767%made−0.67−110+30−4
RR-r10 b222S NVERBEEK8/8+0128.1+0.080%made+0.00−110−112+0
RR-r10 b251NT NVERBEEK7/7+0177.1+0.1212%made−0.12−90−81+0
RR-r10 b263NT NVERBEEK8/8+0178.6+0.5953%set+0.47+100−233+8
RR-r10 b274H SMOLENAAR9/10+169.2+0.1767%set+0.33+50−98+4
RR-r10 b313D SMOLENAAR8/9+159.2+1.200%set+1.00+100−114+5
RR-r10 b324S NVERBEEK9/10+1138.6−0.38100%set+0.00+50+69+0
RR-r12 b194Sx× SMOLENAAR10/10+02010.5+0.500%made+0.00−590−640+2
RR-r12 b242H NVERBEEK9/9+049.0+0.000%made+0.00−140−140+0
RR-r12 b253D NVERBEEK9/9+089.0+0.0013%made−0.13−110−92+0
RR-r12 b262H SMOLENAAR8/7−177.9−0.1429%made−0.29−110−54−2
RR-r12 b273NT NVERBEEK9/9+029.0+0.000%made+0.00−400−400+0
RR-r12 b283NT NVERBEEK9/8−1228.9−0.0914%made−0.14−600−506−3
RR-r12 b305D NVERBEEK8/9+10···set····
RR-r12 b324Sx× NVERBEEK9/9+00···set····
RR-r13 b35C EMOLENAAR11/11+0111.0+0.000%made+0.00−600−600+0
RR-r13 b43NT WVERBEEK9/9+0229.0+0.000%made+0.00−600−600+0
RR-r13 b114D WVERBEEK9/9+039.0+0.00100%set+0.00+50+50+0
RR-r13 b124H WVERBEEK10/10+00···made····
RR-r13 b156Dx× WVERBEEK12/12+0712.0+0.000%made+0.00−1090−1090+0
RR-r14 b182NT WVERBEEK7/6−196.8−0.2278%set+0.22+50+34+0
RR-r14 b202D WVERBEEK7/7+018.0+1.000%set+1.00+100−90+5
RR-r14 b224H WVERBEEK10/9−1610.2+0.1733%made−0.33−620−395−6
RR-r14 b235H WVERBEEK10/10+00···set····
RR-r14 b262H WVERBEEK8/9+128.5+0.500%made+0.00−110−125+0
RR-r14 b273C EMOLENAAR9/9+0210.0+1.000%made+0.00−110−130+1
RR-r14 b292S WVERBEEK8/8+097.9−0.1122%made−0.22−110−67−1
RR-r14 b304H EMOLENAAR12/12+0312.0+0.000%made+0.00−480−480+0
RR-r14 b314S WVERBEEK9/9+079.1+0.1486%set+0.14+50−17+2
RR-r16 b173NT WVERBEEK12/10−2612.3+0.330%made+0.00−490−500+0
RR-r16 b181NT EMOLENAAR7/8+1167.4+0.440%made+0.00−90−103+0
RR-r16 b206Hx× WVERBEEK10/10+0111.0+1.00100%set+0.00+500+200+7
RR-r16 b213D EMOLENAAR9/9+049.3+0.250%made+0.00−110−115+0
RR-r16 b234C EMOLENAAR10/11+1210.0+0.000%made+0.00−130−130+0
RR-r16 b242S WVERBEEK9/9+099.0+0.000%made+0.00−140−140+0
RR-r16 b252D EMOLENAAR9/9+00···made····
RR-r16 b263NT EMOLENAAR8/8+0168.1+0.1394%set+0.06+100+54+1
RR-r16 b293NT EMOLENAAR8/8+0168.6+0.5650%set+0.50+100−247+8
RR-r16 b306H WVERBEEK11/12+11111.6+0.6455%set+0.45+50−424+10
RR-r16 b324S EMOLENAAR10/11+11910.8+0.790%made+0.00−620−644+1
RR-r18 b183D WVERBEEK9/10+158.6−0.4040%made−0.40−110−40−2
RR-r18 b204S WVERBEEK12/11−12211.8−0.230%made+0.00−680−673+0
RR-r18 b212Cx× WVERBEEK5/5+055.0+0.00100%set+0.00+500+500+0
RR-r18 b223NT EMOLENAAR12/10−259.2−2.8020%made−0.20−690−444−6
RR-r18 b232NT WVERBEEK6/7+136.7+0.67100%set+0.00+200+133+2
RR-r18 b251NT EMOLENAAR6/7+1147.0+1.007%set+0.93+100−79+5
RR-r18 b263H WVERBEEK9/11+2210.5+1.500%made+0.00−140−185+1
RR-r18 b273NT EMOLENAAR8/8+0178.3+0.2982%set+0.18+50−31+2
RR-r18 b283NT EMOLENAAR10/11+1111.0+1.000%made+0.00−430−460+1
RR-r18 b313NT WVERBEEK10/10+0239.7−0.260%made+0.00−430−422+0
RR-r19 b14S SMOLENAAR11/10−11210.6−0.420%made+0.00−450−437+0
RR-r19 b23NT NVERBEEK10/10+0110.0+0.000%made+0.00−630−630+0
RR-r19 b33NT SMOLENAAR10/9−1197.6−2.3758%made−0.58−430−95−8
RR-r19 b44D NVERBEEK9/9+00···set····
RR-r19 b54S NVERBEEK8/8+067.8−0.17100%set+0.00+200+217+0
RR-r19 b84S NVERBEEK10/11+12010.3+0.250%made+0.00−420−427+0
RR-r19 b104S NVERBEEK11/11+02210.6−0.360%made+0.00−650−639+0
RR-r19 b164Dx× SMOLENAAR8/8+018.0+0.00100%set+0.00+300+300+0
RR-r21 b183NT EMOLENAAR9/9+069.7+0.670%made+0.00−400−420+1
RR-r21 b214H EMOLENAAR10/10+0810.0+0.0013%made−0.13−420−362−2
RR-r21 b224D EMOLENAAR9/9+019.0+0.00100%set+0.00+100+100+0
RR-r21 b255C WVERBEEK10/11+11110.6+0.5545%set+0.55+100−282+9
RR-r21 b264S EMOLENAAR12/11−11311.4−0.620%made+0.00−680−662+0
RR-r21 b314S WVERBEEK11/11+01310.5−0.460%made+0.00−450−436+0
RR-r23 b193NT EMOLENAAR10/11+1610.5+0.500%made+0.00−630−645+0
RR-r23 b204S EMOLENAAR8/9+159.0+1.00100%set+0.00+200+100+3
RR-r23 b215Cx× WVERBEEK10/10+01710.3+0.3565%set+0.35+100−129+6
RR-r23 b232H WVERBEEK9/9+019.0+0.000%made+0.00−140−140+0
RR-r23 b244H WVERBEEK8/9+118.0+0.00100%set+0.00+100+100+0
RR-r23 b255D WVERBEEK9/9+039.3+0.33100%set+0.00+200+167+1
RR-r23 b295S WVERBEEK11/12+1211.0+0.000%made+0.00−650−650+0
RR-r23 b302Dx× EMOLENAAR4/3−10···set····
RR-r3 b53NT EMOLENAAR13/13+0113.0+0.000%made+0.00−520−520+0
RR-r3 b93NT WVERBEEK9/11+299.6+0.560%made+0.00−600−617+0
RR-r3 b113NT EMOLENAAR9/9+00···made····
RR-r3 b124H WVERBEEK10/10+02110.1+0.100%made+0.00−420−423+0
RR-r3 b133S WVERBEEK7/7+067.7+0.6783%set+0.17+200+110+3
RR-r4 b175Dx× NVERBEEK9/10+1410.0+1.00100%set+0.00+300+100+5
RR-r4 b182H SMOLENAAR7/8+178.3+1.2914%set+0.86+100−93+5
RR-r4 b203NT NVERBEEK8/8+0218.4+0.3862%set+0.38+100−163+6
RR-r4 b213NT NVERBEEK7/7+027.0+0.00100%set+0.00+200+200+0
RR-r4 b224S SMOLENAAR7/7+017.0+0.00100%set+0.00+150+150+0
RR-r4 b233NT NVERBEEK7/8+1157.5+0.5393%set+0.07+200+107+3
RR-r4 b244S SMOLENAAR11/11+01411.7+0.710%made+0.00−450−471+1
RR-r4 b254S NVERBEEK10/10+01410.0+0.007%made−0.07−420−389−1
RR-r4 b263NT NVERBEEK9/9+099.8+0.780%made+0.00−600−623+1
RR-r4 b294Hx× SMOLENAAR8/8+00···set····
RR-r4 b314H SMOLENAAR9/9+039.0+0.00100%set+0.00+100+100+0
RR-r4 b322Sx× NVERBEEK5/5+066.0+1.00100%set+0.00+500+300+5
RR-r6 b184NT EMOLENAAR10/10+0210.5+0.500%made+0.00−430−445+0
RR-r6 b202H WVERBEEK7/6−186.4−0.62100%set+0.00+100+163−2
RR-r6 b213Cx× EMOLENAAR6/6+026.5+0.50100%set+0.00+500+400+3
RR-r6 b224S EMOLENAAR9/10+1219.1+0.1476%set+0.24+100−62+4
RR-r6 b284H EMOLENAAR10/10+0310.0+0.000%made+0.00−420−420+0
RR-r6 b303NT WVERBEEK10/10+0159.9−0.070%made+0.00−430−428+0
RR-r9 b14Sx× NVERBEEK9/9+0108.8−0.20100%set+0.00+100+140−1
RR-r9 b24S SMOLENAAR9/9+0229.6+0.5545%set+0.55+100−293+9
RR-r9 b44C SMOLENAAR9/9+019.0+0.00100%set+0.00+100+100+0
RR-r9 b73C SMOLENAAR9/9+079.7+0.710%made+0.00−110−124+0
RR-r9 b83S SMOLENAAR10/10+0110.0+0.000%made+0.00−170−170+0
RR-r9 b91NT NVERBEEK9/8−1148.0−1.007%made−0.07−150−109−1
RR-r9 b115C NVERBEEK11/11+01011.0+0.000%made+0.00−400−400+0
RR-r9 b143H SMOLENAAR9/9+039.0+0.000%made+0.00−140−140+0
Reconciliation — matches the MOLENAAR / VERBEEK row in the Open table.
F1 +0.10 · F2 Σ13.4 ÷ 102 = +0.13 · F3 +0.04 · F4 Σ+86 ÷ 102 = +0.84
on lead: MOLENAAR +0.89 (n 45) · VERBEEK +0.81 (n 57)

How the on-lead split reads. Every defended board has exactly one partner on opening lead, so the two right columns partition the pair's boards and their board-weighted average is the pair's F4. A big gap between the two means one partner's leads (and the defences they start) are landing far better than the other's. Defence only; declaring and bidding are separate. Everything is vs the full division field, so a positive number beats a typical table at the championship.