NPDs

Non-Player Dominions or bots are randomly generated dominions that are spawned prior to OOP to facilitate attacking since inactive dominions are virtually non-existent after adding Click-Through Protection (CTP). Since Round 23, about half of them will automatically train and explore land.

Land Size

NPDs are located in Realm 0 'The Graveyard' along with inactive dominions that have not left protection. NPDs spawn at a human to bot ratio of ~1.74:1.

NPD Distribution
Land Size	Percentage of NPDs
525-600	30%
451-525	50%
400-450	20%

Defense

NPDs spawn with defense based on this formula 120 * exp(0.0058 * [Total Land]) multiplied by a random factor. The random factor for ~85% of NPDs is +/- 10%, but for the remaining ~15% it is +15-20%. Dominions on the lower end of the spectrum will spawn with a random amount of offensive specialists to mask the increased networth of those on the higher end. Every NPD will have an additional 20-35% defense incoming during the first 12 hours. The larger dominions are more likely to have Guard Towers, but none of them have walls until very late in the round (so no need to castle spy at OOP).

NPD Defense
Land Size	Base Defense	Low Range (85%)	High Range (15%)
400	1221	1099-1343	1404-1465
425	1412	1271-1553	1624-1694
450	1632	1469-1795	1877-1958
475	1887	1698-2076	2170-2264
500	2181	1963-2399	2508-2617
525	2521	2269-2773	2899-3025
550	2915	2624-3207	3352-3498
575	3369	3032-3706	3874-4043
600	3895	3506-4285	4479-4674

Behavior

On average, 50% of NPDs will begin to perform actions starting a few hours after OOP. Those that are inactive will remain inactive for the duration of the round. Each has a 1/3 chance of 'logging in' each hour. They will build barren acres, cast spells, train defense, train spies/wizards to a 0.05 ratio, invest, and explore. They will cast their spells any time they drop below 4 hours remaining, therefore it is rare that they drop off, but not impossible. If they recast, it is within the first minute or so of the hour. Each NPD is limited to exploring 18 acres in a single hour and between 72-89 over a twelve hour period. NPDs will train defense up to the following formula, which is then increased by 2% each time they are successfully invaded.

Post-OOP DPA Formula

(-0.0181 * [DaysAsFraction]^2)) + (2.5797 * [DaysAsFraction]) - 4.1725

Additional DPA to phase out over first 10 days

max(0, 5 - [DaysAsFraction]/2)

Expected Land Size Multiplier

[Land] / (40 * [DaysAsFraction] + 410) (capped between 0.8 and 1.2 and multiplied by the DPA above)

Post-OOP DPA
Day in Round	Defense per Acre	Expected Land Size
4	8.8567	570
5	10.7735	610
6	12.6541	650
7	14.4985	690
8	16.3067	730
9	18.0787	770
10	19.8145	810
11	22.0141	850
12	24.1775	890
13	26.3047	930
14	28.3957	970
15	30.4505	1010
16	32.4691	1050
17	34.4515	1090
18	36.3977	1130
19	38.3077	1170
20	40.1815	1210
21	42.0191	1250
22	43.8205	1290
23	45.5857	1330
24	47.3147	1370
25	49.0075	1410
26	50.6641	1450
27	52.2845	1490
28	53.8687	1530
29	55.4167	1570
30	56.9285	1610
31	58.4041	1650
32	59.8435	1690
33	61.2467	1730
34	62.6137	1770
35	63.9445	1810
36	65.2391	1850
37	66.4975	1890
38	67.7197	1930
39	68.9057	1970
40	70.0555	2010
41	71.1691	2050
42	72.2465	2090
43	73.2877	2130
44	74.2927	2170
45	75.2615	2210
46	76.1941	2250
47	77.0905	2290
48	77.9507	2330
49	78.7747	2370
50	79.5625	2410

Base Defense by Day/Land
Day/Land	450	530	610	690	770	850	930	1010	1090	1170	1250	1330	1410	1490	1570	1650	1730	1810	1890	1970	2050	2130	2210	2290	2370
4	3188	4365	5782	7333	8184	9034	9884	10734	11585	12435	13285	14135	14986	15836	16686	17536	18387	19237	20087	20937	21787	22638	23488	24338	25188
5	3878	4961	6572	8409	9955	10989	12023	13057	14092	15126	16160	17195	18229	19263	20297	21332	22366	23400	24434	25469	26503	27537	28571	29606	30640
6	4555	5469	7244	9269	11542	12907	14122	15337	16552	17766	18981	20196	21411	22626	23840	25055	26270	27485	28699	29914	31129	32344	33559	34773	35988
7	5219	6147	7819	10004	12458	14788	16180	17572	18964	20356	21748	23140	24531	25923	27315	28707	30099	31491	32883	34274	35666	37058	38450	39842	41234
8	5870	6914	8312	10635	13244	16139	18198	19764	21329	22895	24460	26025	27591	29156	30722	32287	33853	35418	36984	38549	40114	41680	43245	44811	46376
9	6508	7665	8822	11178	13921	16963	20176	21911	23647	25382	27118	28854	30589	32325	34060	35796	37531	39267	41002	42738	44474	46209	47945	49680	51416
10	7133	8401	9669	11647	14504	17674	21157	24015	25917	27820	29722	31624	33526	35428	37331	39233	41135	43037	44939	46841	48744	50646	52548	54450	56352
11	7925	9334	10743	12330	15355	18712	22400	26420	28794	30908	33021	35135	37248	39361	41475	43588	45701	47815	49928	52041	54155	56268	58381	60495	62608
12	8704	10251	11799	13346	16107	19627	23496	27712	31624	33945	36266	38587	40908	43229	45550	47871	50192	52514	54835	57156	59477	61798	64119	66440	68761
13	9470	11153	12837	14520	16770	20436	24463	28853	33605	36932	39457	41982	44508	47033	49558	52083	54609	57134	59659	62184	64710	67235	69760	72285	74811
14	10222	12040	13857	15674	17492	21150	25319	29862	34780	39868	42594	45320	48046	50772	53497	56223	58949	61675	64401	67127	69853	72579	75305	78031	80757
15	10962	12911	14860	16809	18758	21783	26076	30755	35820	41271	45676	48599	51522	54445	57369	60292	63215	66138	69062	71985	74908	77831	80755	83678	86601
16	11689	13767	15845	17923	20001	22342	26745	31545	36740	42330	48317	51821	54938	58055	61172	64289	67406	70523	73640	76757	79874	82991	86108	89225	92342
17	12403	14607	16812	19017	21222	23427	27337	32242	37552	43267	49386	54985	58292	61599	64907	68214	71521	74829	78136	81443	84751	88058	91365	94673	97980
18	13103	15433	17762	20092	22421	24750	27859	32858	38269	44093	50329	56977	61585	65079	68573	72067	75562	79056	82550	86044	89538	93033	96527	100021	103515
19	13791	16242	18694	21146	23598	26049	28501	33400	38900	44820	51159	57917	64817	68494	72172	75849	79527	83204	86882	90559	94237	97914	101592	105270	108947
20	14465	17037	19609	22180	24752	27323	29895	33875	39454	45458	51887	58741	66021	71845	75702	79559	83417	87274	91132	94989	98846	102704	106561	110419	114276
21	15127	17816	20505	23195	25884	28573	31262	34291	39938	46016	52524	59462	66831	74629	79164	83198	87232	91265	95299	99333	103367	107401	111435	115468	119502
22	15775	18580	21384	24189	26993	29798	32602	35407	40359	46501	53077	60088	67535	75415	82558	86765	90971	95178	99385	103592	107798	112005	116212	120419	124626
23	16411	19328	22246	25163	28081	30998	33916	36833	40722	46919	53555	60629	68142	76094	84484	90260	94636	99012	103388	107765	112141	116517	120893	125270	129646
24	17033	20061	23090	26118	29146	32174	35202	38230	41258	47277	53963	61091	68662	76674	85128	93683	98225	102768	107310	111852	116394	120936	125479	130021	134563
25	17643	20779	23916	27052	30189	33325	36462	39598	42735	47579	54308	61482	69101	77164	85673	94626	101740	106444	111149	115854	120558	125263	129968	134673	139377
26	18239	21482	24724	27967	31209	34452	37694	40937	44179	47830	54595	61807	69466	77572	86125	95126	104574	110042	114906	119770	124634	129497	134361	139225	144089
27	18822	22169	25515	28861	32207	35553	38900	42246	45592	48938	54829	62071	69763	77904	86494	95533	105022	113562	118581	123601	128620	133639	138658	143678	148697
28	19393	22840	26288	29736	33183	36631	40078	43526	46974	50421	55013	62280	69998	78166	86785	95855	105375	115346	122174	127346	132517	137688	142860	148031	153203
29	19950	23497	27043	30590	34137	37683	41230	44777	48323	51870	55417	62437	70174	78363	87004	96097	105641	115637	125685	131005	136325	141645	146965	152285	157605
30	20494	24138	27781	31425	35068	38711	42355	45998	49642	53285	56929	62547	70298	78501	87157	96266	105827	115841	126307	134579	140044	145509	150974	156440	161905
31	21025	24763	28501	32239	35977	39715	43453	47191	50928	54666	58404	62613	70372	78584	87249	96367	105938	115962	126440	137370	143674	149281	154888	160494	166101
32	21544	25374	29204	33034	36864	40694	44524	48354	52184	56014	59844	63673	70399	78615	87283	96405	105980	116008	126489	137424	147215	152960	158705	164450	170195
33	22049	25969	29888	33808	37728	41648	45568	49487	53407	57327	61247	65166	70384	78598	87264	96384	105957	115983	126462	137394	148780	156547	162426	168306	174186
34	22541	26548	30555	34563	38570	42577	46585	50592	54599	58606	62614	66621	70628	78536	87196	96308	105874	115892	126363	137287	148663	160041	166052	172062	178073
35	23020	27112	31205	35297	39390	43482	47575	51667	55760	59852	63945	68037	72129	78433	87081	96182	105735	115740	126197	137106	148468	160282	169581	175719	181858
36	23486	27661	31837	36012	40187	44363	48538	52713	56888	61064	65239	69414	73590	78290	86923	96007	105543	115530	125968	136858	148199	159991	172235	179277	185540
37	23939	28195	32451	36707	40962	45218	49474	53730	57986	62242	66498	70753	75009	79265	86725	95788	105302	115266	125680	136545	147860	159626	171842	182735	189119
38	24379	28713	33047	37381	41715	46049	50383	54718	59052	63386	67720	72054	76388	80722	86488	95527	105015	114952	125338	136173	147457	159190	171373	184005	192595
39	24806	29216	33626	38036	42446	46856	51266	55676	60086	64496	68906	73316	77726	82136	86546	95226	104684	114590	124943	135744	146993	158689	170834	183426	195968
40	25220	29704	34187	38671	43154	47638	52121	56605	61088	65572	70056	74539	79023	83506	87990	94889	104313	114183	124500	135263	146472	158127	170228	182775	195769
41	25621	30176	34731	39285	43840	48395	52950	57505	62059	66614	71169	75724	80279	84834	89388	94516	103903	113735	124011	134732	145897	157506	169560	182058	195000
42	26009	30633	35256	39880	44504	49128	53751	58375	62999	67623	72247	76870	81494	86118	90742	95365	103458	113247	123479	134154	145271	156830	168832	181276	194163
43	26384	31074	35764	40455	45145	49836	54526	59216	63907	68597	73288	77978	82669	87359	92049	96740	102978	112722	122907	133532	144597	156103	168049	180436	193263
44	26745	31500	36255	41010	45764	50519	55274	60029	64783	69538	74293	79047	83802	88557	93312	98066	102821	112161	122295	132868	143878	155327	167213	179538	192302
45	27094	31911	36728	41544	46361	51178	55995	60811	65628	70445	75262	80078	84895	89712	94528	99345	104162	111568	121648	132164	143116	154504	166328	178588	191283
46	27430	32306	37183	42059	46936	51812	56688	61565	66441	71318	76194	81071	85947	90823	95700	100576	105453	110942	120966	131423	142314	153638	165395	177586	190211
47	27753	32686	37620	42554	47488	52422	57355	62289	67223	72157	77091	82024	86958	91892	96826	101759	106693	111627	120251	130647	141473	152730	164418	176537	189087
48	28062	33051	38040	43029	48018	53006	57995	62984	67973	72962	77951	82940	87928	92917	97906	102895	107884	112873	119505	129836	140596	151783	163399	175443	187915
49	28359	33400	38442	43484	48525	53567	58608	63650	68692	73733	78775	83816	88858	93899	98941	103983	109024	114066	119107	128994	139684	150799	162339	174305	186696
50	28643	33735	38827	43919	49011	54103	59195	64287	69379	74471	79563	84655	89747	94839	99931	105023	110115	115207	120299	128122	138739	149779	161241	173126	185433

Highlighted cells are the land size at which the expected land multiplier is equal to 1 (same as base DPA formula)