Research:Major Shield

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Bonus vs. duration

This is a summary table of the results of performing Major Shield with different bonuses (usually de.se, but sometimes de.ta) and under different conditions. All durations are in seconds. The "base" column is the duration without any visible ritual modifiers whatsoever. A "-" indicates that isolating that particular modifier wasn't possible with that deity (e.g., all Sandelfon high altars are indoors, so it isn't possible to get only the high altar bonus with a Sandelfonian. Similarly, several deities only have one unique ritual modifier.).

Many thanks to Yukk, for all his help gathering the higher bonus data.  :)

Generally, these durations were the result of choosing the "best" duration from multiple performances (at least two). In cases where there was variation, the "best" numbers were the ones that were most consistent and seemed to be affected the least by lag. Since--when the MUD isn't lagging--duration seems to be consistent for a given bonus and conditions, I'm assuming that any variation was due to lag: either of the "protected by" message or the "expires" message. This seems more reasonable than supposing a random factor of a few seconds, and it's also encouraging that I was able to find a formula that fits all of these "best" base durations perfectly. However, there's still some possibility of error.

A scatterplot of the data in the table below: Major modifiers scatterplot.PNG

de.se god base high altar (ONLY) JUST outside high altar main unique bonus w/ 2nd unique prayed 1 minion 2 minions 3 minions 4 minions ritual assistance at 1% baton drunk poisoned witch/wizard opposing altar PENALTY out of align
231 Gapp 212 210
236 Gufnork 214 228 222 218
236 Gapp 218 218
240 Fish 236 228
241 Fish 220 234 238 228
243 Fish 222 232 218
244 Fish 240 232
251 Hat 232 246 244 240 228 - -
253 Hat 234 - -
262 Pishe 246 -
262 Hat 246 - -
263 Sek 246 260 -
264 Hat 248 - -
268 Pishe 252 266 260 - 260 248
268 Sek 252 -
277 Pishe 262 276 -
280 Sek 266 280 -
284 Pishe 270 284 - 278
291 Pishe 278 292 286 -
293 Sek 280 294 -
297 Pishe 286 298 -
302 Sandelfon 290 - 300 298 - 286 282 276 254 240 286
303 Pishe 292 - 294
304 Sek 292 304 -
309 Sek 298 -
310 Pishe 298 312 306 - 306 294 290 302 262 250
310 Sandelfon 298 - 308 306 - 286 294
313  ? 302 -
313 Sek 302 314 -
314 Pishe 302 -
315 Sandelfon 304 314 312 - 290 268 268 254 298
316 Sandelfon - - 292
317 Pishe -
318 Sek 308 -
321 Sek 310 322 - 306
323 Sandelfon 312 - 322 320 - 298 278 308
325 Sandelfon 314 - 322 - 322 310 306 300 254 280 280 266 310
326 Sek 316 326 -
333 Sandelfon 322 - 328 - 310 262 288 318
334 Sandelfon 322 - 332 330 - 330 320 316 310 276 318
334 Sek 322 334 -
340 Sandelfon 328 - 335 -
342 Sandelfon 330 - 338 - 318 298 326
343 Gufnork 340
348 Sandelfon 336 - 344 - 324 292 332
349 Sandelfon 338 - 346 344 - 344 334 330 324 304 292 332
349 Gufnork 338 348 280
350 Sandelfon 338 - 346 344 - 344 334 330 326 306 294 294 334
351 Sandelfon 340 - - 326
354 Gufnork 354
356 Sandelfon 344 - - 332 312 300
357 Sandelfon 344 - 352 - 332 290 314 314 300 340
358 Sandelfon 346 - - 334 302
359 Sandelfon 346 - - 334
362 Sandelfon - -
363 Sandelfon 350 - 356 - 338 346
365 Sandelfon 352 - 360 358 - 358 348 344 340 322 310 348
369 Gufnork 356 366
382 Gufnork 368
393 Gufnork 376
403 Gufnork 386
411 Gufnork 392 398 394 398 388 386 382 378 364 354 388
412 Gufnork 392 402
415 Gufnork 404
429 Gufnork 406 404 400
431 Gufnork 418
444 Gufnork 418 416 404
456 Gufnork 428
478 Gufnork 444 431
479 Gufnork 444
480 Gufnork 412
488 Gufnork 450 460 456 452 456 448 446 442 438
489 Gufnork 452
512 Gufnork

Base duration

A graph of the base durations:

Major shield base duration.png

For all of these points, this formua yielded the exact duration:

2 * ROUND((400 * (ln(bonus + 75)) - 2082.5) / 2)

While it still may be wrong, it seems very reliable.

Ritual modifiers

Ritual modifiers--both positive and negative--have a reduced effect as bonus increases, rather than providing a flat bonus or penalty to the duration. It therefore made sense that what they actually do is provide a bonus or penalty to effective bonus, since bonus vs. duration is a logarithmic function and the benefit of having, for example, a bonus ten points higher, decreases as your bonus increases. It turns out that this model fits the data.

To determine the exact effect of ritual modifiers, I took various bonuses and durations for the modifiers, and worked backwards to see what bonus should (according to the formula above) give that duration as a base duration. Since that typically resulted in a range, it usually takes at least two or three sets to narrow it down. For example, for a particular modifier--being out of alignment--performing with a 357 bonus results in a duration of 340. A bonus of 351 or 352 will give a base duration of 340 seconds. This means that being out of alignment reduces your effective bonus by either 5 or 6. Performing with a 363 bonus instead results in a duration of 346, and the bonuses that give that as a base duration are 358 or 359. According to that, being out of alingment reduces your effective bonus by either 4 or 5. Looking at both of those, being out of alignment appears to reduce your effective bonus by 5, because 5 is the overlap.

This was built under the assumption that the formula for determining the base duration (above) is correct, so if the formula is off, the conclusions here may be as well.

The following table is of those sets. It also has some sets of combined modifiers.

modifier actual bonus w/modifier duration range of predicted bonuses range of differences in bonuses:
1 minion 243 218 239 - 240 -4 to -3
1 minion 251 228 247 - 248 -4 to -3
1 minion 268 248 264 - 264 -4 to -4
1 minion 302 286 297 - 298 -5 to -4
1 minion 310 294 305 - 306 -5 to -4
1 minion 321 306 317 - 317 -4 to -4
1 minion 325 310 320 - 321 -5 to -4
1 minion 334 320 330 - 331 -4 to -3
1 minion 349 334 345 - 346 -4 to -3
1 minion 350 334 345 - 346 -5 to -4
1 minion 365 348 360 - 361 -5 to -4
1 minion 411 388 405 - 407 -6 to -4
1 minion 429 404 425 - 427 -4 to -2
1 minion 444 416 440 - 442 -4 to -2
1 minion 488 448 483 - 485 -5 to -3
2 minions 302 282 294 - 295 -8 to -7
2 minions 310 290 301 - 302 -9 to -8
2 minions 325 306 317 - 317 -8 to -8
2 minions 334 316 326 - 327 -8 to -7
2 minions 349 330 341 - 342 -8 to -7
2 minions 350 330 341 - 342 -9 to -8
2 minions 365 344 355 - 357 -10 to -8
2 minions 411 386 403 - 404 -8 to -7
2 minions 429 400 420 - 422 -9 to -7
2 minions 488 446 480 - 482 -8 to -6
3 minions 302 276 288 - 289 -14 to -13
3 minions 310 286 297 - 298 -13 to -12
3 minions 315 290 301 - 302 -14 to -13
3 minions 316 292 303 - 304 -13 to -12
3 minions 323 298 309 - 310 -14 to -13
3 minions 325 300 311 - 312 -14 to -13
3 minions 333 310 320 - 321 -13 to -12
3 minions 334 310 320 - 321 -14 to -13
3 minions 342 318 328 - 329 -14 to -13
3 minions 348 324 335 - 336 -13 to -12
3 minions 349 324 335 - 336 -14 to -13
3 minions 350 326 337 - 338 -13 to -12
3 minions 351 326 337 - 338 -14 to -13
3 minions 356 332 343 - 344 -13 to -12
3 minions 357 332 343 - 344 -14 to -13
3 minions 358 334 345 - 346 -13 to -12
3 minions 359 334 345 - 346 -14 to -13
3 minions 363 338 349 - 350 -14 to -13
3 minions 365 340 351 - 352 -14 to -13
3 minions 411 382 398 - 400 -13 to -11
3 minions 488 442 475 - 477 -13 to -11
4 minions 411 378 394 - 395 -17 to -16
4 minions 444 404 425 - 427 -19 to -17
4 minions 478 431 461 - 460 -17 to -18
4 minions 488 438 469 - 471 -19 to -17
altar, carrying fluff, fluffy surroundings, prayed 411 414 438 - 439 27 to 28
altar, indoors 302 310 320 - 321 18 to 19
altar, indoors 310 318 328 - 329 18 to 19
altar, indoors 349 354 366 - 368 17 to 19
altar, indoors 365 370 384 - 386 19 to 21
altar, indoors, prayed 349 360 373 - 374 24 to 25
altar, rain 310 318 328 - 329 18 to 19
carrying fluff 236 222 242 - 243 6 to 7
carrying fluff 411 398 418 - 419 7 to 8
carrying fluff 488 456 494 - 496 6 to 8
combat 318 312 322 - 323 4 to 5
combat 313 308 318 - 319 5 to 6
company, trespass 251 262 276 - 277 25 to 26
company, trespass 262 274 286 - 287 24 to 25
drunk 411 364 378 - 379 -33 to -32
drunk 365 322 332 - 334 -33 to -31
drunk 356 312 322 - 323 -34 to -33
drunk 357 314 324 - 325 -33 to -32
drunk 350 306 317 - 317 -33 to -33
drunk 349 304 315 - 316 -34 to -33
drunk 333 288 299 - 300 -34 to -33
drunk 325 280 292 - 293 -33 to -32
drunk 323 278 290 - 291 -33 to -32
drunk 315 268 281 - 282 -34 to -33
drunk 310 262 276 - 277 -34 to -33
drunk 302 254 269 - 270 -33 to -32
far from altar 348 334 345 - 346 -3 to -2
far from altar 340 326 337 - 338 -3 to -2
far from altar 340 324 335 - 336 -5 to -4
far from altar 348 333 345 - 343 -3 to -5
far from altar 348 332 343 - 344 -5 to -4
far from altar 348 330 341 - 342 -7 to -6
far from altar 340 321 333 - 331 -7 to -9
far from altar 348 329 341 - 339 -7 to -9
far from altar 348 328 339 - 340 -9 to -8
far from altar 340 322 332 - 334 -8 to -6
far from altar 340 323 335 - 333 -5 to -7
far from altar 357 338 349 - 350 -8 to -7
far from altar, Bad Ass 340 323 335 - 333 -5 to -7
far from altar, Creel Springs, plus indoors 340 326 337 - 338 -3 to -2
far from altar, Creel Springs, plus wizard guild, plus indoors 340 280 292 - 293 -48 to -47
far from altar, Genua 340 322 332 - 334 -8 to -6
far from altar, Genua 348 328 339 - 340 -9 to -8
far from altar, Genua 357 338 349 - 350 -8 to -7
far from altar, Genua, plus fluff 489 450 486 - 488 -3 to -1
far from altar, Genua, plus out of align 489 442 475 - 477 -14 to -12
far from altar, Holy Wood 340 324 335 - 336 -5 to -4
far from altar, Holy Wood 348 333 345 - 343 -3 to -5
far from altar, house, plus indoors 357 344 355 - 357 -2 to 0
far from altar, just outside no-message zone 357 344 355 - 357 -2 to 0
far from altar, just outside no-message zone 349 336 347 - 348 -2 to -1
far from altar, just outside no-message zone 325 312 322 - 323 -3 to -2
far from altar, Lancre 349 330 341 - 342 -8 to -7
far from altar, Lancre 357 338 349 - 350 -8 to -7
far from altar, Lancre 325 306 317 - 317 -8 to -8
far from altar, past Holy Wood 340 321 333 - 331 -7 to -9
far from altar, past Holy Wood 348 330 341 - 342 -7 to -6
far from altar, southeast corner of map 357 338 349 - 350 -8 to -7
far from altar, southeast corner of map 349 330 341 - 342 -8 to -7
far from altar, southeast corner of map 325 306 317 - 317 -8 to -8
floating in water 241 228 247 - 248 6 to 7
floating in water 244 232 250 - 251 6 to 7
floating in water 240 228 247 - 248 7 to 8
fluffy surroundings 488 452 489 - 491 1 to 3
fluffy surroundings 411 394 413 - 414 2 to 3
fluffy surroundings 236 218 239 - 240 3 to 4
from baton (276 bonus) 325 254 269 - 270 -56 to -55
from baton (282 bonus) 333 262 276 - 277 -57 to -56
from baton (285 bonus) 349 280 292 - 293 -57 to -56
from baton (292 bonus) 357 290 301 - 302 -56 to -55
high altar 488 460 500 - 502 12 to 14
high altar 431 418 443 - 444 12 to 13
high altar 415 404 425 - 427 10 to 12
high altar 412 402 423 - 424 11 to 12
high altar 369 366 380 - 381 11 to 12
high altar 354 354 366 - 368 12 to 14
high altar 349 348 360 - 361 11 to 12
high altar 343 340 351 - 352 8 to 9
high altar 334 334 345 - 346 11 to 12
high altar 326 326 337 - 338 11 to 12
high altar 321 322 332 - 334 11 to 13
high altar 313 314 324 - 325 11 to 12
high altar 310 312 322 - 323 12 to 13
high altar 304 304 315 - 316 11 to 12
high altar 297 298 309 - 310 12 to 13
high altar 293 294 305 - 306 12 to 13
high altar 291 292 303 - 304 12 to 13
high altar 284 284 296 - 296 12 to 12
high altar 280 280 292 - 293 12 to 13
high altar 277 276 288 - 289 11 to 12
high altar 268 266 279 - 280 11 to 12
high altar 263 260 274 - 275 11 to 12
high altar 251 246 262 - 263 11 to 12
high altar 241 234 252 - 253 11 to 12
high altar 236 228 247 - 248 11 to 12
in combat, no visible distance 321 315 327 - 325 6 to 4
in combat, no visible distance 326 320 330 - 331 4 to 5
in combat, no visible distance 313 308 318 - 319 5 to 6
in combat, no visible distance 321 316 326 - 327 5 to 6
indoors 333 328 339 - 340 6 to 7
indoors 350 344 355 - 357 5 to 7
indoors 363 356 369 - 370 6 to 7
indoors 365 358 371 - 372 6 to 7
indoors 349 344 355 - 357 6 to 8
indoors 302 298 309 - 310 7 to 8
indoors 310 306 317 - 317 7 to 7
indoors 334 330 341 - 342 7 to 8
indoors 349 344 355 - 357 6 to 8
indoors 315 312 322 - 323 7 to 8
indoors 323 320 330 - 331 7 to 8
indoors 325 322 332 - 334 7 to 9
indoors 342 338 349 - 350 7 to 8
indoors 348 344 355 - 357 7 to 9
indoors 357 352 364 - 365 7 to 8
near altar 348 342 353 - 354 5 to 6
near altar 340 332 343 - 344 3 to 4
near altar 340 337 350 - 348 10 to 8
near altar 340 338 349 - 350 9 to 10
near altar 303 298 309 - 310 6 to 7
near altar 357 342 353 - 354 -4 to -3
near altar 350 346 358 - 359 8 to 9
near altar 323 322 332 - 334 9 to 11
near altar 315 314 324 - 325 9 to 10
near altar 302 300 311 - 312 9 to 10
near altar 310 308 318 - 319 8 to 9
near altar 334 332 343 - 344 9 to 10
near altar 365 360 373 - 374 8 to 9
near altar 349 346 358 - 359 9 to 10
near altar (just outside CWC one) 357 354 366 - 368 9 to 11
near altar (just outside CWC one) 350 346 358 - 359 8 to 9
near altar (just outside CWC one) 315 314 324 - 325 9 to 10
near altar (Scoone's room) 253 244 260 - 261 7 to 8
near altar (Scoone's room) 262 254 269 - 270 7 to 8
near altar (Scoone's room) 264 256 271 - 271 7 to 7
near altar (Tuna Walk) 350 344 355 - 357 5 to 7
near altar (Tuna Walk) 357 350 362 - 363 5 to 6
near altar (Tuna Walk) 315 310 320 - 321 5 to 6
near altar, just outside AM (Rimwards) 349 340 351 - 352 2 to 3
near altar, just outside AM (Rimwards) 357 348 360 - 361 3 to 4
near altar, road outside AM—just before intersection into Coast Road from Rimwards 349 340 351 - 352 2 to 3
near altar, road outside AM—just before intersection into Coast Road from Rimwards 357 348 360 - 361 3 to 4
none, outer edge of no-message zone 349 338 349 - 350 0 to 1
none, outer edge of no-message zone 357 344 355 - 357 -2 to 0
none, outside AM, intersection leading to coast road, JUST inside no-message zone 357 344 355 - 357 -2 to 0
none, outside AM, intersection leading to coast road, JUST inside no-message zone 349 338 349 - 350 0 to 1
opposing altar 480 412 435 - 437 -45 to -43
opposing altar 411 354 366 - 368 -45 to -43
opposing altar 365 310 320 - 321 -45 to -44
opposing altar 358 302 313 - 314 -45 to -44
opposing altar 356 300 311 - 312 -45 to -44
opposing altar 350 294 305 - 306 -45 to -44
opposing altar 348 292 303 - 304 -45 to -44
opposing altar 349 292 303 - 304 -46 to -45
opposing altar 310 250 265 - 266 -45 to -44
out of alignment 302 286 297 - 298 -5 to -4
out of alignment 310 294 305 - 306 -5 to -4
out of alignment 315 298 309 - 310 -6 to -5
out of alignment 323 308 318 - 319 -5 to -4
out of alignment 325 310 320 - 321 -5 to -4
out of alignment 333 318 328 - 329 -5 to -4
out of alignment 334 318 328 - 329 -6 to -5
out of alignment 342 326 337 - 338 -5 to -4
out of alignment 348 332 343 - 344 -5 to -4
out of alignment 349 332 343 - 344 -6 to -5
out of alignment 350 334 345 - 346 -5 to -4
out of alignment 357 340 351 - 352 -6 to -5
out of alignment 363 346 358 - 359 -5 to -4
out of alignment 365 348 360 - 361 -5 to -4
out of alignment 411 388 405 - 407 -6 to -4
poisoned 315 268 281 - 282 -34 to -33
poisoned 325 280 292 - 293 -33 to -32
poisoned 342 298 309 - 310 -33 to -32
poisoned 357 314 324 - 325 -33 to -32
prayed 243 232 250 - 251 7 to 8
prayed 251 240 257 - 258 6 to 7
prayed 268 260 274 - 275 6 to 7
prayed 284 278 290 - 291 6 to 7
prayed 310 306 317 - 317 7 to 7
prayed 325 322 332 - 334 7 to 9
prayed 334 330 341 - 342 7 to 8
prayed 349 344 355 - 357 6 to 8
prayed 350 344 355 - 357 5 to 7
prayed 365 358 371 - 372 6 to 7
prayed 411 398 418 - 419 7 to 8
prayed 488 456 494 - 496 6 to 8
rain 268 260 274 - 275 6 to 7
rain 291 286 297 - 298 6 to 7
rain 310 306 317 - 317 7 to 7
stylish clothes 231 212 235 - 235 4 to 4
stylish clothes 236 218 239 - 240 3 to 4
stylish surroundings 231 210 233 - 234 2 to 3
stylish surroundings 236 218 239 - 240 3 to 4
trespass on holy ground 251 244 260 - 261 9 to 10
trespass on holy ground 253 246 262 - 263 9 to 10
trespass on holy ground 263 258 272 - 273 9 to 10
trespass on holy ground 256 250 265 - 266 9 to 10
trespass on holy ground 254 246 262 - 263 8 to 9
trespass on holy ground 262 256 271 - 271 9 to 9
underwater 241 238 255 - 256 14 to 15
underwater 240 238 255 - 256 15 to 16
witch/wizard (BP wizard guild) 302 240 257 - 258 -45 to -44
witch/wizard (BP wizard guild) 315 254 269 - 270 -46 to -45
witch/wizard (BP wizard guild) 325 266 279 - 280 -46 to -45
witch/wizard (BP wizard guild) 334 276 288 - 289 -46 to -45
witch/wizard (BP wizard guild) 350 294 305 - 306 -45 to -44
witch/wizard (BP wizard guild) 357 300 311 - 312 -46 to -45
with priests, near altar (Scoone's room) 253 262 276 - 277 23 to 24
with priests, near altar (Scoone's room) 264 274 286 - 287 22 to 23
underwater 244 240 257 - 258 13 to 14
underwater 240 236 254 - 254 14 to 14
floating in water 244 232 250 - 251 6 to 7
floating in water 240 228 247 - 248 7 to 8
floating in water 241 228 247 - 248 6 to 7
ritual assistance on, 1% 310 302 313 - 314 3 to 4
wrong altar, plus drunk, plus poisoned 357 224 244 - 245 -113 to -112
wrong altar, plus drunk, plus poisoned 349 214 236 - 237 -113 to -112
ritual assistance on, 1% 303 294 305 - 306 2 to 3
ritual assistance on, 10% 310 322 332 - 334 22 to 24
from baton, hands full (342 bonus) 310 250 265 - 266 -45 to -44
from baton (334 bonus) 303 268 281 - 282 -22 to -21
from baton (350 bonus) 312 274 286 - 287 -26 to -25
from baton, hands full (334 bonus) 303 240 257 - 258 -46 to -45
from baton (334 bonus) (hands not full) 303 268 281 - 282 -22 to -21
from baton (334 bonus) (hands full) 303 240 257 - 258 -46 to -45
from baton (342 bonus) (hands full) 310 250 265 - 266 -45 to -44
from baton (350 bonus) (hands not full) 312 274 286 - 287 -26 to -25
from baton (276 bonus) 325 254 269 - 270 -56 to -55
from baton (282 bonus) (hands full) 333 262 276 - 277 -57 to -56
from baton (285 bonus) 349 280 292 - 293 -57 to -56
from baton (285 bonus) (hands not full) 349 280 292 - 293 -57 to -56
from baton (285 bonus) (hands full) 349 280 292 - 293 -57 to -56
from baton (292 bonus) (hands full) 357 290 301 - 302 -56 to -55

The baton bonus seems to be special, varying widely. Sometimes having both hands full seems to roughly double it, but not always.

And the conclusions:

Modifier Increase or decrease to effective bonus
At own high altar +12
actively worshipping +7
rain/snow/sleet (Pishe) +7
carrying fluff (Gufnork) +7
fluffy surroundings (Gufnork) +3
wearing stylish clothes (Gapp) +4
stylish surroundings (Gapp) +3
indoors (Sandelfon) +7
underwater (Fish) +14
floating in the water (Fish) +7
in company of other priests (Hat) +16
trespassing on other deity's high altar (Hat) +9
in combat (Sek) +5
ritual assistance set to 1% ("the hand of <deity> guides you") +3
near high altar +3 to +9
far from high altar -2 to -8
1 priest minion -4
2 priest minions -8
3 priest minions -13
4 priest minions -17
out of alignment -5
performing from faith rod varies, but high penalty
drunk -33
poisoned -33
at wrong high altar -45
in witch/wizard-owned area -45