The day defence of Germany changed so much in 1944 not sure an average can cover it.
As of January 1944 the Luftflotte 3 fighters were generally trying to defend occupied Western Europe rather than Germany, by the end of the year that role had disappeared.
Mid 1943 Fw190A-6, 2x7.9mm machine guns, 4x20mm high velocity cannon, the final standard firepower upgrade with the A-8 in February 1944 with 13mm replacing the 7.9mm machine guns. February 1943, Bf109G-6, standard firepower 1x20mm cannon and 2x13mm machine guns, already the earlier Bf109F had the option of a pair of underwing 20mm cannon, mostly thanks to the Red Air Force Il-2
The Luftwaffe had a chronic problem keeping aircraft serviceable, start with fewer spare parts = more new production, think of all those potential ground crew put into the Luftwaffe field divisions and then over Germany in 1943/44 a tribute to the bomber gunners, they certainly did not shoot down anywhere what was claimed but they kept putting holes in attacking fighters.
Carrying rockets or underwing cannon imposed a noticeable performance hit on the single seat fighters, the second half of 1943 solution for defending Germany was rebuilding the day twin engine fighter force, from none defending Germany in July to 9 Gruppe in December. A solution that became untenable when all USAAF raids became escorted. The performance of the P-47 and P-51 also made carrying underwing armament dangerous, generally making it hard to take on the USAAF fighters.
Next came the single engine Sturm units, a staffel formed in late 1943 initially with heavier armour rather than more firepower, later came upgunning and expansion to Gruppe strengths. Same result as twin engine type, able to inflict heavy damage on bomber formations, cut to pieces by escorts, escorting the Sturm units was fine in theory, hard in practice. The final Luftwaffe solution was replacing 20mm with 30mm cannon, that did little to performance while being much more effective against bombers.
E R Hooton, Eagle in Flames, single engine fighters
20 January 1943 Luftflotte 3 had 241 on strength, Mitte/Reich 163 on strength, total 404
20 April 1943 Luftflotte 3 had 232 on strength, Mitte/Reich 188 on strength, total 420
20 June 1943 Luftflotte 3 had 353 on strength, Mitte/Reich 343 on strength, total 696
20 September 1943 Luftflotte 3 had 222 on strength, Mitte/Reich 677 on strength, total 899
20 December 1943 Luftflotte 3 had 312 on strength, Mitte/Reich 572 on strength, total 884
31 March 1944 Luftflotte 3 had 166 on strength, Mitte/Reich 853 on strength, total 1,019
Alfred Price strength/serviceable
31 May 1944 Luftflotte 3 had 168/115 on strength, Reich 814/450 on strength, plus 53/37 and 198/82 twin engine fighters.
10 January 1945 Luftflotte 3 had 1,094/770 on strength, Reich 356/153 on strength.
Williamson Murray notes end June 1944, thanks to Overlord, the western front had 425 and Reich 370 single engine fighters, a situation that persisted into July.
No more specific break downs by Luftflotte so time for the aggregate figures given by September 1944 the Western Front was the German border, Alfred Price reports as of 31 May 1944 operational unit single engine fighter strength was 1,602/1,063,
RAF figures Luftwaffe operational single seat fighter strength/serviceable
31-May-44 1,683/1,111
10-Jun-44 1,483/1,037
20-Jun-44 1,609/1,067
30-Jun-44 1,523/895
10-Jul-44 1,453/951
20-Jul-44 1,759/992
31-Jul-44 1,937/1,193
10-Aug-44 1,804/1,066
20-Aug-44 1,766/1,156
31-Aug-44 1,610/1,043
10-Sep-44 1,990/1,501
20-Sep-44 1,952/1,377
30-Sep-44 1,984/1,413
10-Oct-44 2,376/1,756
20-Oct-44 2,816/2,081
31-Oct-44 3,055/2,487
10-Nov-44 3,117/2,491
20-Nov-44 3,246/2,401
30-Nov-44 2,998/2,256
10-Dec-44 2,874/2,147
20-Dec-44 2,853/2,166
31-Dec-44 2,260/1,521
10-Jan-45 2,265/1,610
Alfred Price reports as of 10 January 1945 operational unit single engine fighter strength was 1,937/1,427.
The growing numbers, the increased concentration in Germany and the performance upgrades as Bf109G-10, BF109K and Fw190D-9 appeared gave the allied commanders considerable concern, even without the Me262.
Germany had to defend a front of around 400 miles, it meant not all units could be used on a given day nor did all sorties result in encounters, see the Day to Day Diary of Day Fighters in Defence of the Reich by Caldwell. Similarly the escorts were also dispersed along and around the bomber formations, with the usual rule of more bombers than escorts. Talking about odds can either be done for an individual fight or aggregate, the latter is the Luftwaffe defences largely matched numerically the number of long range fighters able to make Germany during the first half of 1944, that shifted significantly by the final quarter of 1944 but most allied fighters present were not doing heavy bomber escort, while the 8th Air Force was flying straight courses to simplify missions and make interception easier given the usual results of air combat.
Mighty Eighth War Diary, escort sorties despatched, generally excluding targets outside Germany, April/May figures include 9th Air Force, smaller escort forces were generally for smaller bomber forces.
date Escort sorties
04-Jan-44 542
07-Jan-44 571
11-Jan-44 593
14-Jan-44 645
21-Jan-44 628
29-Jan-44 632
30-Jan-44 635
03-Feb-44 632
04-Feb-44 637
05-Feb-44 634
06-Feb-44 638
08-Feb-44 553
10-Feb-44 557
11-Feb-44 606
20-Feb-44 835
21-Feb-44 679
22-Feb-44 659
24-Feb-44 767
25-Feb-44 899
29-Feb-44 554
02-Mar-44 770
03-Mar-44 730
04-Mar-44 770
06-Mar-44 801
08-Mar-44 891
09-Mar-44 808
15-Mar-44 588
16-Mar-44 868
18-Mar-44 925
22-Mar-44 817
23-Mar-44 841
24-Mar-44 540
27-Mar-44 960
29-Mar-44 428
01-Apr-44 475
08-Apr-44 780
09-Apr-44 719
11-Apr-44 819
13-Apr-44 871
18-Apr-44 634
19-Apr-44 697
22-Apr-44 859
24-Apr-44 867
25-Apr-44 719
26-Apr-44 554
29-Apr-44 814
07-May-44 843
08-May-44 855
12-May-44 980
13-May-44 1,107
19-May-44 964
22-May-44 568
27-May-44 1,135
28-May-44 1,224
29-May-44 1,265
30-May-44 1,309
31-May-44 1,329
18-Jun-44 817
19-Jun-44 1,111
20-Jun-44 1,219
29-Jun-44 779
06-Jul-44 1,138
07-Jul-44 756
11-Jul-44 795
12-Jul-44 803
13-Jul-44 609
16-Jul-44 712
19-Jul-44 761
20-Jul-44 542
21-Jul-44 795
29-Jul-44 755
31-Jul-44 701
03-Aug-44 726
04-Aug-44 883
05-Aug-44 658
06-Aug-44 740
09-Aug-44 847
11-Aug-44 578
15-Aug-44 478
16-Aug-44 692
24-Aug-44 739
25-Aug-44 916
26-Aug-44 897
27-Aug-44 871
08-Sep-44 653
09-Sep-44 714
10-Sep-44 705
11-Sep-44 440
12-Sep-44 662
13-Sep-44 603
19-Sep-44 528
21-Sep-44 221
22-Sep-44 365
25-Sep-44 622
26-Sep-44 768
27-Sep-44 678
28-Sep-44 724
30-Sep-44 726
02-Oct-44 772
03-Oct-44 753
05-Oct-44 733
06-Oct-44 784
07-Oct-44 900
09-Oct-44 878
12-Oct-44 514
14-Oct-44 749
15-Oct-44 482
17-Oct-44 811
18-Oct-44 604
19-Oct-44 753
22-Oct-44 785
25-Oct-44 522
26-Oct-44 674
28-Oct-44 217
30-Oct-44 976
01-Nov-44 321
02-Nov-44 968
04-Nov-44 890
05-Nov-44 666
06-Nov-44 802
08-Nov-44 890
09-Nov-44 738
10-Nov-44 808
11-Nov-44 367
21-Nov-44 954
25-Nov-44 965
26-Nov-44 732
27-Nov-44 770
29-Nov-44 946
30-Nov-44 972
02-Dec-44 604
04-Dec-44 977
05-Dec-44 901
06-Dec-44 830
09-Dec-44 274
10-Dec-44 690
11-Dec-44 841
12-Dec-44 928
15-Dec-44 434
18-Dec-44 773
23-Dec-44 636
24-Dec-44 853
25-Dec-44 460
26-Dec-44 336
27-Dec-44 390
28-Dec-44 606
29-Dec-44 724
30-Dec-44 572
31-Dec-44 785