The maths of a form table: rolling windows, decay and the eviction problem
Every decaying performance measure has the same awkward property — playing can cost you. Here is the maths, why the alternatives are worse, and what to tell members.
Updated 8 July 2026 · 5 min read · Flagstick team
If you build a table that measures recent form, sooner or later a member will point out that playing a round made their score go down. They will be right, and the correct response is not to change the table.
The mechanism
A form score over a window of the last W rounds, counting the best M.
Window before: {38, 36, 34, 30, 28}. Best 3 = 38 + 36 + 34 = 108.
You play a 31. The window becomes {31, 38, 36, 34, 30} — the 28 is evicted. Best 3 = 38 + 36 + 34 = 108. No change.
You play a 31 again. Window: {31, 31, 38, 36, 34}, the 30 evicted. Best 3 = 38 + 36 + 34 = 108. Still no change.
Now play a third: {31, 31, 31, 38, 36}, the 34 evicted. Best 3 = 38 + 36 + 31 = 105. Your score dropped by 3 despite playing three rounds.
Nothing has gone wrong. Your recent form genuinely is worse than it was, and the table is reporting that. The complaint is not about the arithmetic; it is that the direction of travel feels punitive when the act of playing preceded the drop.
How often it actually happens
In our own data, a round lowers the player’s form score roughly 7% of the time, typically by one or two points. Put another way, more than nine rounds in ten either improve a member’s form score or leave it unchanged.
That number is worth measuring for your own club and your own parameters, because it depends heavily on W and M. Wider windows evict less often; a large M relative to W means more of the window counts and evictions bite harder.
Why the alternatives are worse
Alternative 1: keep your best W rounds ever
Removes eviction entirely. A round can only improve your score.
Why it fails: the board freezes. After a good month, a member’s score becomes permanent regardless of what they do afterwards, and the table stops reflecting form at all — it becomes a “personal best” table with a season attached. Positions stop changing, and a table that does not move is not watched.
Alternative 2: a calendar window
“Your rounds in the last eight weeks.” Intuitive, and it decays naturally.
Why it fails: it excludes the irregular member. Someone playing monthly can never hold M rounds inside an eight-week window, so they sit permanently at the baseline. A form board that structurally excludes a third of your membership is worse than no form board.
Alternative 3: exponential decay by date
Weight each round by age, so old rounds fade smoothly rather than dropping out. Mathematically elegant and genuinely used in other sports.
Why it usually fails here: nobody can compute their own score. The single most valuable property of a club table is that a member can look at it and reconstruct why they are where they are. “Best 3 of your last 5” passes that test. “Sum of e^(−λt) weighted scores” does not, and a table members cannot verify is a table members do not trust.
There is a real trade here — smooth decay is more accurate — and for a professional ranking it might be the right call. For a golf society it is not.
Alternative 4: an average
Average of your last W rounds. Simple, decays, and everyone understands it.
Why it is weaker: an average has no floor, so one blow-up round drags a member down hard and takes W rounds to work out of the system. Best-M-of-W with a baseline caps the damage of a single bad day, which matters a lot for turnout — the member who had a nightmare last week still has a reason to play this week.
Choosing W and M
| Small W (3–4) | Large W (8–10) | |
|---|---|---|
| Responsiveness | High — form moves fast | Low — slow to change |
| Eviction frequency | High | Low |
| Suits | Clubs playing weekly | Clubs playing monthly |
And M relative to W:
- M close to W (best 4 of 5): almost everything counts, so bad rounds hurt and the board is volatile.
- M small relative to W (best 3 of 8): forgiving, stable, and slow to reflect a genuine decline.
Defaults of W=5, M=3 sit in the middle and work for a club playing roughly fortnightly. Tune from there, and tune for your club rather than copying ours — the rest of the form board’s design explains why the baseline sits in the pool.
What to tell members
One sentence next to the table:
Your last five rounds count, best three of them. A new round replaces your oldest, so form moves in both directions.
That is the whole contract. Members are fine with a measure that can go down, as long as nobody pretended it couldn’t.
Frequently asked questions
- Why did my form score drop after playing a round?
- Because a rolling window keeps only your most recent W rounds. Your new round pushed out your oldest one, and if that old round was better than the ones now counting, your score falls. This is how any measure of recent form works — it is reporting that your recent scoring has changed, not penalising you for playing.
- Is it fair that playing can lower your position?
- It is inherent to measuring form rather than accumulating points. The alternatives are worse: keeping your best-ever rounds freezes the table, and a calendar window excludes anyone who plays irregularly. What matters is that the rule is stated plainly next to the table so nobody is surprised.
- What window size should a golf form table use?
- Five rounds counting the best three works well for a club playing roughly fortnightly. Clubs playing weekly can use a shorter window for a more responsive table; clubs playing monthly should use a longer one. The window should count rounds played rather than weeks elapsed, so irregular attendees are still measured on their own recent form.
- Should a form table use an average instead?
- An average is simpler but has no floor, so a single disaster round drags a member down for the whole window. Taking the best M of the last W, with a baseline in the pool, caps the damage of one bad day — which matters for turnout, because a member who had a nightmare last week still has a reason to come back this week.