Your method of adding [Spade-Length] - 3.5 seems reasonable, except I would halve that whenever partner has already made a bid of 4 or higher. Any bid in excess of 3 is very likely to include Spade length, and it is desirable to avoid double-counting that asset.
Even when partner's bid above 3 is solely based on high card strength, that reduces the value of extra Spades in your own hand as you will be attempting to not ruff those assets.
Also, I believe a refinement of the Spades' tricks estimate should consider the presence or absence of a void/singleton in one's hand. Balanced holdings around the table reduce the likelihood of ruffing tricks, while unbalanced holdings increase their likelihood. I'm not yet sure how I would do that.
Here is a table of all the hand pattern probabilities, with the top few (covering nearly 85% of possibilities) excerpted below.
Note that the 4333 pattern is only the fifth most common hand pattern, and the most common is 4432 at over 21%. If we take the 4432 pattern as standard, then we can rank the most common patterns as being either stronger or weaker than the standard (in ascending order of estimated strength:
- Distinctly Weaker: Estimates from Contract Bridge analysis suggest at east 0.25 trick weaker
- 4333 HPS = 2(4-5) + (3-3) = -2
- Standard:
- 4432 HPS = 2(4-5) + (4-2) = 0
- 5332 HPS = 2(5-5) + (3-2) = 1
- Stronger: Estimates from Bridge analysis suggests at least 0.25 tricks stronger than average
- 5422 HPS = 2(5-5) + (4-2) = 2
- 6322 HPS = 2(6-5) + (3-2) = 3
- 5431 HPS = 2(5-5) + (4-1) = 3
- Distinctly Stronger: Estimates from Bridge analysis suggest at least 0.5 tricks stronger than average.
- 6331 HPS = 2(6-5) + (3-1) = 4
- 6421 HPS = 2(6-5) + (4-1) = 5
In this context stronger should be interpreted as more capable of implementing the desired strategy. A 6421 hand with short Spades and all its high cards, even if Aces, in the two long suits might be very capable of successfully bidding Nil. Obviously the placement of a hand's high cards is of import as well, as an additional refinement.
Also, these estimates are a priori - before trumps have been established. Clearly a long trump holding (Spades playing Spades) is even more valuable than shown here for winning tricks - but is less able to lose tricks.
One numerical estimate of Hand Pattern Strength would be to take double the excess of the length of the longest suit over 5, plus the excess of the second longest suit over the shortest suit. I have marked this value as HPS for the hand patterns above.
My first attempt at a comprehensive hand evaluation for Spades would be the sum of:
That could be further refined, with experience, by adjusting the denominators for the second and third components for HPS and Spades length. When contemplating a Nil bid, consider subtracting the HPS term instead of adding it to the sum.
