Horse racing
- Background
In three recent races at Rosetta Park, the results have been:
Race 1
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | A | 9.00 | 0.0 | Colt |
| 2 | B | 8.06 | 2.0 | Filly |
| 3 | C | 9.04 | 1.5 | Colt |
Time 1 minute 36.0 seconds
Race 2
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | D | 8.10 | 0.0 | Filly |
| 2 | E | 9.03 | 1.0 | Colt |
| 3 | F | 9.07 | 3.0 | Colt |
(F was slowly away and lost 2 lengths at the finish as a result)
Time 1 minute 36.4 seconds
Race 3
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | G | 8.04 | 0.0 | Colt |
| 2 | H | 8.10 | 1.5 | Colt |
| 3 | I | 9.05 | 0.5 | Filly |
Time 1 minute 35.8 seconds
It is assumed that:
1. Weights carried are expressed in stones and pounds (traditional in US and UK racing) where 1 stone equals 14 pounds.
2. The distances are the actual distances between horses at the finish of the race.
3. All races are run at 1 mile in similar going and weather conditions and the time shown is the time taken by the winner to run the race.
4. 2 pounds slows a horse down by 1 length at the finish.
5. 1 second is equivalent to 5 lengths at the finish.
- Task
All 9 of these horses, plus a further horse J, are due to compete against each other in Race 4 at Rosetta Park again over 1 mile and in similar conditions to the earlier races. Colts will carry 9.00 and fillies 8.11.
Suppose that:
1. Horse B has been moving well on the galops and her trainer thinks she has improved 4 pounds since her last outing.
2. Horse C has had a setback in training and his trainer expects him to perform 4 pounds below his best.
3. Horse H is being ridden by the champion jockey which is expected to improve his performance by 3 pounds compared to what it would otherwise have been.
4. Horse J, a filly, has never run before but her performance on the galops suggests she can run 1 mile in 1 minute 35.8 seconds when carrying 8.11.
Other things being equal (which they seldom are in actual horse racing!) what would you expect the full result of Race 4 to be including the time of the winner?
Wren
<lang ecmascript>import "/fmt" for Fmt
// ratings on past form, assuming a rating of 100 for horse A var a = 100 var b = a - 8 - 2 * 2 // carried 8 lbs less, finished 2 lengths behind var c = a + 4 - 2 * 3.5 var d = a - 4 - 10 * 0.4 // based on relative weight and time var e = d + 7 - 2 * 1 var f = d + 11 - 2 * (4 - 2) var g = a - 10 + 10 * 0.2 var h = g + 6 - 2 * 1.5 var i = g + 15 - 2 * 2
// adjustments to ratings for current race b = b + 4 c = c - 4 h = h + 3 var j = a - 3 + 10 * 0.2
// filly's allowance to give weight adjusted weighting b = b + 3 d = d + 3 i = i + 3 j = j + 3
// create map of horse to its weight adjusted rating and whether colt var m = {
"A": [a, true], "B": [b, false], "C": [c, true], "D": [d, false], "E": [e, true], "F": [f, true], "G": [g, true], "H": [h, true], "I": [i, false], "J": [j, false]
} // convert to list of {key, value} map entries var l = m.toList
// sort in descending order of rating l.sort{ |i, j| i.value[0] >= j.value[0] }
// show expected result of race System.print("Race 4\n") System.print("Pos Horse Weight Dist Sex") var p = 1 for (x in 0...l.count) {
var wt = l[x].value[1] ? "9.00" : "8.11"
var dist = 0
if (p > 1) dist = (l[x-1].value[0] - l[x].value[0]) * 0.5
var pos = (p == 1 || dist > 0) ? p.toString : (p - 1).toString + "="
var sx = l[x].value[1] ? "colt" : "filly"
Fmt.print("$-2s $s $s $3.1f $s", pos, l[x].key, wt, dist, sx)
p = p + 1
}
// weight adjusted rating of winner var wr = l[0].value[0]
// expected time of winner (relative to A's time in Race 1) var t = 96 - (wr - 100) / 10 var min = (t/60).floor var sec = t % 60 System.print("\nTime %(min) minute %(sec) seconds")</lang>
- Output:
Race 4 Pos Horse Weight Dist Sex 1 I 8.11 0.0 filly 2 J 8.11 2.0 filly 3 A 9.00 1.0 colt 4 F 9.00 0.5 colt 5 H 9.00 0.5 colt 6 E 9.00 0.5 colt 7 B 8.11 1.0 filly 7= D 8.11 0.0 filly 9 C 9.00 1.0 colt 10 G 9.00 0.5 colt Time 1 minute 35.4 seconds